The document presents an analytical approach to study the influence of dissipative heat energy on water-based nanofluid flow past a semi-infinite vertical plate embedded in a permeable medium. The nanofluid contains copper, aluminum oxide or titanium oxide nanoparticles suspended in water. Governing equations are derived that account for magnetic field effects, heat source/sink effects, and variable thermal properties. Both numerical and analytical solution techniques are employed to solve the equations, with results presented graphically and tabularly. The homotopy perturbation method is used as the analytical solution technique.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
Study on Thermal and Hydrodynamic Indexes of a Nanofluid Flow in a Micro Heat...A Behzadmehr
The paper numerically presents laminar forced convection of a nanofluid flowing in a duct at microscale.
Results were compared with both analytical and experimental data and observed good concordance with
previous studies available in the literature. Influences of Brinkman and Reynolds number on thermal and
hydrodynamic indexes have been investigated. For a given nanofluid, no change in efficiency (heat dissipation
to pumping power) was observed with an increasing in Reynolds number. It was shown that the pressure was
decrease with an increase in Brinkman number. Dependency of Nu increment changes with substrate material.
This document summarizes a research article that analyzes the stability of a horizontal porous layer saturated with a viscoelastic nanofluid when the boundaries are subjected to periodic temperature modulation. The analysis uses the Darcy-Brinkman-Oldroyd-B fluid model and considers infinitesimal disturbances. Three cases of oscillatory temperature fields are examined: symmetric modulation, asymmetric modulation, and modulation of only the bottom wall. A perturbation solution is obtained and the effect of modulation frequency on stability is shown. The stability is characterized by a correction Rayleigh number calculated as a function of various parameters representing viscoelasticity, concentration, porosity, heat capacity, and modulation frequency. Modulation is found to generally have a destabilizing
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Gravitational Instability in a Ferromagnetic Fluid Saturated Porous Medium wi...IOSR Journals
The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with
the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is
used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an
isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux
law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of
infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary
conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as
special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection
has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always
less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the
Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the
convection cells changes when the parameters involved in the study vary with the porous structure bringing out
considerable influence.
This article presents a numerical investigation of heat transfer performance and pressure drop of nanofluids flowing under laminar flow conditions. Various nanoparticles including Al2O3, CuO, carbon nanotube and titanate nanotube dispersed in water and ethylene glycol/water were simulated. A single-phase model was used to predict the effects of parameters such as particle concentration, diameter, Brownian motion, Reynolds number, nanoparticle type and base fluid on heat transfer coefficient and pressure drop. The results indicated that particle concentration, Brownian motion and aspect ratio increased heat transfer, while particle diameter decreased it. The study provides considerations for choosing appropriate nanofluids for applications.
Numerical Study of Heat Transfer in Ternary Nanofluid Over a Stretching Sheet...Atif75347
The new method of enhancing heat transfer through tri- hybrid nanofluid is discussed in the current study and represented in differential equation system.
The document presents an analytical approach to study the influence of dissipative heat energy on water-based nanofluid flow past a semi-infinite vertical plate embedded in a permeable medium. The nanofluid contains copper, aluminum oxide or titanium oxide nanoparticles suspended in water. Governing equations are derived that account for magnetic field effects, heat source/sink effects, and variable thermal properties. Both numerical and analytical solution techniques are employed to solve the equations, with results presented graphically and tabularly. The homotopy perturbation method is used as the analytical solution technique.
MHD Chemically Reacting and Radiating Nanofluid Flow over a Vertical Cone Emb...IJLT EMAS
In this study, we examine the combined effects of
thermal radiation, chemical reaction on MHD hydromagnetic
boundary layer flow over a vertical cone filled with nanofluid
saturated porous medium under variable properties. The
governing flow, heat and mass transfer equations are
transformed into ordinary differential equations using similarity
variables and are solved numerically by a Galerkin Finite
element method. Numerical results are obtained for
dimensionless velocity, temperature, nanoparticle volume
fraction, as well as the skin friction, local Nusselt and Sherwood
number for the different values of the pertinent parameters
entered into the problem. The effects of various controlling
parameters on these quantities are investigated. Pertinent
results are presented graphically and discussed quantitatively.
The present results are compared with existing results and found
to be good agreement. It is found that the temperature of the
fluid remarkably enhances with the rising values of Brownian
motion parameter (Nb).
Study on Thermal and Hydrodynamic Indexes of a Nanofluid Flow in a Micro Heat...A Behzadmehr
The paper numerically presents laminar forced convection of a nanofluid flowing in a duct at microscale.
Results were compared with both analytical and experimental data and observed good concordance with
previous studies available in the literature. Influences of Brinkman and Reynolds number on thermal and
hydrodynamic indexes have been investigated. For a given nanofluid, no change in efficiency (heat dissipation
to pumping power) was observed with an increasing in Reynolds number. It was shown that the pressure was
decrease with an increase in Brinkman number. Dependency of Nu increment changes with substrate material.
This document summarizes a research article that analyzes the stability of a horizontal porous layer saturated with a viscoelastic nanofluid when the boundaries are subjected to periodic temperature modulation. The analysis uses the Darcy-Brinkman-Oldroyd-B fluid model and considers infinitesimal disturbances. Three cases of oscillatory temperature fields are examined: symmetric modulation, asymmetric modulation, and modulation of only the bottom wall. A perturbation solution is obtained and the effect of modulation frequency on stability is shown. The stability is characterized by a correction Rayleigh number calculated as a function of various parameters representing viscoelasticity, concentration, porosity, heat capacity, and modulation frequency. Modulation is found to generally have a destabilizing
IOSR Journal of Mathematics(IOSR-JM) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mathemetics and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mathematics. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
Gravitational Instability in a Ferromagnetic Fluid Saturated Porous Medium wi...IOSR Journals
The problem of Rayleigh-Bénard convection in a ferromagnetic fluid saturated porous medium with
the Maxwell-Cattaneo law is studied by the method of small perturbation. Modified Darcy-Brinkman model is
used to describe the fluid motion. The horizontal porous layer is cooled from the upper boundary, while an
isothermal boundary condition is imposed at the lower boundary. The non-classical Maxwell-Cattaneo heat flux
law involves a wave type heat transport and does not suffer from the physically unacceptable drawback of
infinite heat propagation speed. The resulting eigenvalue problem is solved exactly for simplified boundary
conditions and the thresholds for the marginal stability are determined. Some of the known cases are derived as
special cases. The influence of porous, magnetic, and non-magnetic parameters on the onset of ferroconvection
has been analyzed. It is found that the Bénard problem for a Maxwell-Cattaneo ferromagnetic fluid is always
less stable than the classical ferroconvection problem. It is shown that the destabilizing influence of the
Cattaneo number is not attenuated by that of magnetic forces and vice versa, and that the aspect ratio of the
convection cells changes when the parameters involved in the study vary with the porous structure bringing out
considerable influence.
This article presents a numerical investigation of heat transfer performance and pressure drop of nanofluids flowing under laminar flow conditions. Various nanoparticles including Al2O3, CuO, carbon nanotube and titanate nanotube dispersed in water and ethylene glycol/water were simulated. A single-phase model was used to predict the effects of parameters such as particle concentration, diameter, Brownian motion, Reynolds number, nanoparticle type and base fluid on heat transfer coefficient and pressure drop. The results indicated that particle concentration, Brownian motion and aspect ratio increased heat transfer, while particle diameter decreased it. The study provides considerations for choosing appropriate nanofluids for applications.
Numerical Study of Heat Transfer in Ternary Nanofluid Over a Stretching Sheet...Atif75347
The new method of enhancing heat transfer through tri- hybrid nanofluid is discussed in the current study and represented in differential equation system.
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Moving Lids Direction Effects on MHD Mixed Convection in a Two-Sided Lid-Driv...A Behzadmehr
Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. The obtained results show that for a constant Grashof number (), the rate of heat transfer increases with a decrease in the Richardson and Hartmann numbers. Furthermore, an increase of the volume fraction of nanoparticles may result in enhancement or deterioration of the heat transfer performance depending on the value of the Hartmann and Richardson numbers and the configuration of the moving lids. Also, it is found that in the presence of magnetic field, the nanoparticles have their maximum positive effect when the top lid moves rightward and the bottom one moves leftward.
Increasing Thermal Conductivity of a Heat Exchanger Using Copper Oxide Nano F...IJERA Editor
A Nano fluid is the evolving concept which is very rarely used in the many core industries. Nano fluids have
found a great application in heat exchangers by increasing the thermal conductivity. We have aimed to
increasing the heat transfer co-efficient by using copper oxide Nano fluid. The Nano particles are formed by
using precipitation method and their fluids are formed by adding surfactants to the base fluid. The comparative
study on the Heat exchanger is made by using the CuO Nano Fluid and Hot water. The analysis and the results
shows that the overall heat transfer rate increases when subjected to Nano Fluids. The ethylene glycol fluid used
along with copper oxide Nano fluid will offer resistance to fouling.
1. article in mathematical problems in engineering 2020MohamedSANNAD2
This document summarizes a numerical study that simulated natural convection heat transfer in a cubical cavity filled with nanofluids. The cavity is heated by a partition maintained at a hot temperature, while the right and left walls are kept at a cold temperature and the rest are adiabatic. Results show that increasing the Rayleigh number, volume fraction of nanoparticles, and size of the heating partition all improve heat transfer. Copper-based nanofluids provided the best thermal transfer. The study analyzes temperature, velocity and heat transfer to understand how nanofluids affect natural convection in 3D enclosures.
Dive into the intricate world of mathematics through this thought-provoking and meticulously crafted presentation. We proudly present the groundbreaking research work of an MPhil student, a true testament to the dedication and intellectual prowess exhibited in unraveling new dimensions within the realm of mathematics.
🔍 Presentation Highlights:
Prepare to be captivated by a captivating journey into the depths of mathematical exploration. This presentation showcases a wealth of meticulously curated content, ranging from foundational concepts to cutting-edge theories. With a keen focus on innovation, this research endeavors to expand the boundaries of mathematical understanding.
📚 Topics Explored:
From abstract algebra to advanced calculus, and from number theory to geometric topology, this presentation encompasses a broad spectrum of mathematical domains. Whether you're a seasoned mathematician, a curious student, or simply intrigued by the beauty of numbers, this presentation promises to engage and enlighten.
🔬 Research Insights:
Delve into the mind of an MPhil student whose dedication to the subject has resulted in groundbreaking insights. The research work within this presentation unveils new perspectives, challenges conventional thinking, and paves the way for future mathematical exploration.
🧠 Intellectual Rigor:
Crafted with meticulous attention to detail, this presentation reflects not only the student's intellectual rigor but also their passion for mathematical inquiry. The dedication to unraveling complex theories and the commitment to fostering a deeper understanding of mathematics is evident in every slide.
🎓 Academic Excellence:
As a testament to academic excellence, this presentation is a showcase of the heights that can be achieved through relentless pursuit of knowledge. It encapsulates the essence of the student's journey as they progress towards their MPhil degree, solidifying their place within the academic community.
Join us in celebrating the pursuit of knowledge, innovation, and the boundless possibilities that mathematics offers. Whether you're a fellow researcher, a mathematics enthusiast, or someone simply curious about the beauty of numbers, this presentation promises to ignite your intellectual curiosity and leave you with a profound appreciation for the power of mathematical exploration.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction have a greater influence on fluid velocity and temperature profiles. Nan
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
This document summarizes a study on thermal radiation effects on magnetohydrodynamic (MHD) free convection flow of a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The governing equations for momentum, angular momentum, and energy are solved numerically. Key findings include:
1) The micropolar fluid model helps reduce drag forces and acts as a cooling agent compared to classical fluids.
2) Parameters like the Darcy number, radiation, magnetic field, and porous medium properties influence the velocity, microrotation, temperature, skin friction, and heat transfer.
3) Increased microrotation constant and coupling constant reduce skin friction but increase heat transfer.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
Advanced Energy: An International Journal (AEIJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Energy Engineering and allied fields. This multi disciplinary journal is devoted to the publication of high quality papers on theoretical and practical aspects of Energy Engineering.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
A drift-flux model is utilized to theoretically analyze the boundary layer flow and heat transfer of a
nanofluid over a flat plate. The concentration of nanoparticles at the plate is obtained using the solution of
the governing equations. Assuming a fixed magnitude of free stream velocity, the results show that the heat
transfer may enhance up to 22% or decrease about -7% by using nanofluids compared to the pure base
fluid.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
Study of Forced Convection Heat Transfer with Single phase and mixture phase ...IOSRJMCE
In this study, forced convection heat transfer of nanoliquids is done using both single-phase and mixture-phase models and the results are compared with experimental results. The governing equations of the study here are discretized using the finite volume method. Hybrid differencing scheme is used to calculate the face values of the control volumes. A code is written using SIMPLER algorithm and then solved using the MATLAB engine. The mixture-phase model studied here, considers two slip mechanisms between nanoparticle and base-fluid, namely Brownian diffusion and thermophoresis. Al2O3-water nanofluid is used for the study of nanofluid and the study shows significant increase in convective heat transfer coefficient while the mixturephase model demonstrates slightly lower values than the single-phase model. The study is done with various nanoparticle concentrations and Reynolds numbers. With increasing particle concentration and Reynolds number, the convective heat transfer coefficient increases and as well as the shear stress. For low concentrations of the nanoparticle, Nusselt number is slightly lower than the base fluid and as the concentration increases, the Nusselt number also rises higher than the base fluid
The document summarizes a presentation on convection heat transfer in nanofluids. It discusses nanofluid preparation techniques, heat transfer mechanisms like Brownian motion, clustering, and the effect of parameters like volume concentration on thermal conductivity and viscosity. It also reviews an experimental case study that investigated the density, viscosity, thermal conductivity and heat transfer capacity of aluminum oxide nanofluids and found linear relationships between these properties and nanoparticle concentration.
This document reviews research on the heat transfer of nanofluids when an electric or magnetic field is applied. It discusses how applied fields can affect the heat transfer performance and mechanisms of nanofluids. While studies show fields can significantly impact nanofluid heat transfer, there are differing opinions on their exact effects and mechanisms. The document aims to analyze the mechanism of thermal conductivity enhancement in nanofluids and how applied fields induce chaotic convection and heat transfer enhancement.
This document summarizes a study on the effects of magnetohydrodynamic mixed convection of a micropolar fluid near a stagnation point on a vertical stretching sheet, accounting for radiation and mass transfer. The governing equations are transformed into ordinary differential equations using similarity transformations and solved numerically. Parameters such as material property, radiation, magnetic field, and velocity ratio are varied to analyze their effects on velocity, temperature, concentration, skin friction, heat and mass transfer rates. It is observed that the micropolar fluid can reduce drag forces and act as a cooling agent, and that radiation effects are important for flows at high temperatures.
Entropy generation and heat transfer rate for MHD forced convection of nanoli...Barhm Mohamad
This document summarizes a numerical study that investigates magnetohydrodynamic forced convection of nanofluid in a rectangular channel with an extended surface and three cylindrical blocks. The study examines the effects of Reynolds number, Hartmann number, Eckert number, and nanoparticle volume fraction on temperature distribution, stream function, entropy generation, and mean Nusselt number. Governing equations for steady, incompressible, laminar, two-dimensional flow are presented. Thermophysical properties of water, copper nanoparticles, and the nanofluid are provided.
The International Journal of Engineering and Science (IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
International journal of engineering and mathematical modelling vol2 no3_2015_1IJEMM
A weak nonlinear stability analysis has been performed for an oscillatory mode of convection, heat and mass transports in terms of
Nusselt, Sherwood numbers are derived and evaluated by a non$-$autonomous complex Ginzburg-Landau equation. The porous layer boundaries are heated sinusoidally with time. The basic state temperature is defined in terms of study and oscillatory parts, where study part show nonlinear throughflow effect on the system and time dependant part show modulation effect. The generalized Darcy model is employed for the momentum equation. The disturbances of the flow are expanded in power series of amplitude of modulation, which is assumed to be small and employed using normal mode technics. The effect of vertical throughflow is found to stabilize or destabilize the system depending on its direction. The time relaxation parameter $\lambda_1$ has destabilizing effect, while time retardation parameter $\lambda_2$ has stabilizing effect on the system. Three types of modulations have been analyzed, and found that, OPM, LBMO cases are effective on heat and mass transfer than IPM case. The effects of amplitude and frequency of modulation on heat and mass transports have been analyzed and depicted graphically. The study establishes that the heat and mass transports can be controlled effectively by a mechanism that is external to the system.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
Effect of Radiation on Mixed Convection Flow of a Non-Newtonian Nan fluid ove...IJMER
International Journal of Modern Engineering Research (IJMER) is Peer reviewed, online Journal. It serves as an international archival forum of scholarly research related to engineering and science education.
Moving Lids Direction Effects on MHD Mixed Convection in a Two-Sided Lid-Driv...A Behzadmehr
Magnetohydrodynamic (MHD) mixed convection flow of Cu–water nanofluid inside a two-sided lid-driven square enclosure with adiabatic horizontal walls and differentially heated sidewalls has been investigated numerically. The effects of moving lids direction, variations of Richardson number, Hartmann number, and volume fraction of nanoparticles on flow and temperature fields have been studied. The obtained results show that for a constant Grashof number (), the rate of heat transfer increases with a decrease in the Richardson and Hartmann numbers. Furthermore, an increase of the volume fraction of nanoparticles may result in enhancement or deterioration of the heat transfer performance depending on the value of the Hartmann and Richardson numbers and the configuration of the moving lids. Also, it is found that in the presence of magnetic field, the nanoparticles have their maximum positive effect when the top lid moves rightward and the bottom one moves leftward.
Increasing Thermal Conductivity of a Heat Exchanger Using Copper Oxide Nano F...IJERA Editor
A Nano fluid is the evolving concept which is very rarely used in the many core industries. Nano fluids have
found a great application in heat exchangers by increasing the thermal conductivity. We have aimed to
increasing the heat transfer co-efficient by using copper oxide Nano fluid. The Nano particles are formed by
using precipitation method and their fluids are formed by adding surfactants to the base fluid. The comparative
study on the Heat exchanger is made by using the CuO Nano Fluid and Hot water. The analysis and the results
shows that the overall heat transfer rate increases when subjected to Nano Fluids. The ethylene glycol fluid used
along with copper oxide Nano fluid will offer resistance to fouling.
1. article in mathematical problems in engineering 2020MohamedSANNAD2
This document summarizes a numerical study that simulated natural convection heat transfer in a cubical cavity filled with nanofluids. The cavity is heated by a partition maintained at a hot temperature, while the right and left walls are kept at a cold temperature and the rest are adiabatic. Results show that increasing the Rayleigh number, volume fraction of nanoparticles, and size of the heating partition all improve heat transfer. Copper-based nanofluids provided the best thermal transfer. The study analyzes temperature, velocity and heat transfer to understand how nanofluids affect natural convection in 3D enclosures.
Dive into the intricate world of mathematics through this thought-provoking and meticulously crafted presentation. We proudly present the groundbreaking research work of an MPhil student, a true testament to the dedication and intellectual prowess exhibited in unraveling new dimensions within the realm of mathematics.
🔍 Presentation Highlights:
Prepare to be captivated by a captivating journey into the depths of mathematical exploration. This presentation showcases a wealth of meticulously curated content, ranging from foundational concepts to cutting-edge theories. With a keen focus on innovation, this research endeavors to expand the boundaries of mathematical understanding.
📚 Topics Explored:
From abstract algebra to advanced calculus, and from number theory to geometric topology, this presentation encompasses a broad spectrum of mathematical domains. Whether you're a seasoned mathematician, a curious student, or simply intrigued by the beauty of numbers, this presentation promises to engage and enlighten.
🔬 Research Insights:
Delve into the mind of an MPhil student whose dedication to the subject has resulted in groundbreaking insights. The research work within this presentation unveils new perspectives, challenges conventional thinking, and paves the way for future mathematical exploration.
🧠 Intellectual Rigor:
Crafted with meticulous attention to detail, this presentation reflects not only the student's intellectual rigor but also their passion for mathematical inquiry. The dedication to unraveling complex theories and the commitment to fostering a deeper understanding of mathematics is evident in every slide.
🎓 Academic Excellence:
As a testament to academic excellence, this presentation is a showcase of the heights that can be achieved through relentless pursuit of knowledge. It encapsulates the essence of the student's journey as they progress towards their MPhil degree, solidifying their place within the academic community.
Join us in celebrating the pursuit of knowledge, innovation, and the boundless possibilities that mathematics offers. Whether you're a fellow researcher, a mathematics enthusiast, or someone simply curious about the beauty of numbers, this presentation promises to ignite your intellectual curiosity and leave you with a profound appreciation for the power of mathematical exploration.
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction more strongly influence velocity and temperature profiles. Nanoparticle shape
Radiation and magneticfield effects on unsteady naturalAlexander Decker
This document discusses research on the effects of thermal radiation and magnetic fields on unsteady natural convective flow of nanofluids past an infinite vertical plate with a heat source. The following key points are discussed:
- Governing equations for the unsteady, two-dimensional flow are derived taking into account radiation, magnetic fields, and thermophysical properties of nanofluids.
- The equations are solved numerically using Laplace transform techniques. Parameters like radiation, magnetic field, heat source, and nanoparticle volume fraction are examined.
- It is found that increasing the magnetic field decreases fluid velocity, while radiation, heat source, and nanoparticle volume fraction have a greater influence on fluid velocity and temperature profiles. Nan
Thermal radiation effects on mhd free convection flow of a micropolar fluid p...Alexander Decker
This document summarizes a study on thermal radiation effects on magnetohydrodynamic (MHD) free convection flow of a micropolar fluid past a stretching surface embedded in a non-Darcian porous medium. The governing equations for momentum, angular momentum, and energy are solved numerically. Key findings include:
1) The micropolar fluid model helps reduce drag forces and acts as a cooling agent compared to classical fluids.
2) Parameters like the Darcy number, radiation, magnetic field, and porous medium properties influence the velocity, microrotation, temperature, skin friction, and heat transfer.
3) Increased microrotation constant and coupling constant reduce skin friction but increase heat transfer.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
Advanced Energy: An International Journal (AEIJ) is a quarterly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Energy Engineering and allied fields. This multi disciplinary journal is devoted to the publication of high quality papers on theoretical and practical aspects of Energy Engineering.
The Force Convection Heat Transfer of A Nanofluid Over A Flat Plate: Using Th...AEIJjournal2
A drift-flux model is utilized to theoretically analyze the boundary layer flow and heat transfer of a
nanofluid over a flat plate. The concentration of nanoparticles at the plate is obtained using the solution of
the governing equations. Assuming a fixed magnitude of free stream velocity, the results show that the heat
transfer may enhance up to 22% or decrease about -7% by using nanofluids compared to the pure base
fluid.
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
This document summarizes a study that investigates the effect of thermophoresis on unsteady free convective heat and mass transfer in a viscoelastic fluid past a semi-infinite vertical plate. The study uses the Walters-B fluid model to simulate rheological fluids. The dimensionless governing equations are solved using an implicit finite difference scheme. Results show that increasing the thermophoretic parameter decreases velocity and concentration but increases temperature within the boundary layer. Thermophoresis is found to significantly increase the surface mass flux.
Study of Forced Convection Heat Transfer with Single phase and mixture phase ...IOSRJMCE
In this study, forced convection heat transfer of nanoliquids is done using both single-phase and mixture-phase models and the results are compared with experimental results. The governing equations of the study here are discretized using the finite volume method. Hybrid differencing scheme is used to calculate the face values of the control volumes. A code is written using SIMPLER algorithm and then solved using the MATLAB engine. The mixture-phase model studied here, considers two slip mechanisms between nanoparticle and base-fluid, namely Brownian diffusion and thermophoresis. Al2O3-water nanofluid is used for the study of nanofluid and the study shows significant increase in convective heat transfer coefficient while the mixturephase model demonstrates slightly lower values than the single-phase model. The study is done with various nanoparticle concentrations and Reynolds numbers. With increasing particle concentration and Reynolds number, the convective heat transfer coefficient increases and as well as the shear stress. For low concentrations of the nanoparticle, Nusselt number is slightly lower than the base fluid and as the concentration increases, the Nusselt number also rises higher than the base fluid
The document summarizes a presentation on convection heat transfer in nanofluids. It discusses nanofluid preparation techniques, heat transfer mechanisms like Brownian motion, clustering, and the effect of parameters like volume concentration on thermal conductivity and viscosity. It also reviews an experimental case study that investigated the density, viscosity, thermal conductivity and heat transfer capacity of aluminum oxide nanofluids and found linear relationships between these properties and nanoparticle concentration.
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This document summarizes a study on the effects of magnetohydrodynamic mixed convection of a micropolar fluid near a stagnation point on a vertical stretching sheet, accounting for radiation and mass transfer. The governing equations are transformed into ordinary differential equations using similarity transformations and solved numerically. Parameters such as material property, radiation, magnetic field, and velocity ratio are varied to analyze their effects on velocity, temperature, concentration, skin friction, heat and mass transfer rates. It is observed that the micropolar fluid can reduce drag forces and act as a cooling agent, and that radiation effects are important for flows at high temperatures.
Entropy generation and heat transfer rate for MHD forced convection of nanoli...Barhm Mohamad
This document summarizes a numerical study that investigates magnetohydrodynamic forced convection of nanofluid in a rectangular channel with an extended surface and three cylindrical blocks. The study examines the effects of Reynolds number, Hartmann number, Eckert number, and nanoparticle volume fraction on temperature distribution, stream function, entropy generation, and mean Nusselt number. Governing equations for steady, incompressible, laminar, two-dimensional flow are presented. Thermophysical properties of water, copper nanoparticles, and the nanofluid are provided.
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2. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
two most general approaches for preparing nanofluids.13
These may be done using either a chemical or mechan-
ical process. Shadlaghani et al.14
investigated the impact
of natural convection on the transport phenomenon within
the annulus that is equivalent to either circular or square
or may be of triangular cross sections. They have pro-
posed control volume method, a numerical technique for
the solution. Goodarzi et al.15
done experimental study
the effect of concentration and temperature of nanoparti-
cle in engine oil. However, the experimentation is con-
ducted with the contribution of volume fractions by
considering 0.05%, 0.1%, 0.2%, 0.4%, 0.6%, and 0.8%,
whereas the range of the temperature 5–55
C, and the
rate of shear stress within the range 666.5 to 13,330
s-1. Further, “Brookfield digital viscometer (CAP2000)”
is used to measure the viscosity of hybrid nanolubri-
cant. The inclusion of augmented particle concentration
enhances the conductivity of the nanoliquid and that leads
to increase the side effects of viscosity. Looking into
the matter, researchers16–18
have presented their report on
the rheological behaviour of nanofluids. Mishra et al.19
and his team recently proposed their investigation by
considering ethylene–glycol-based liquid for the thermal
enhancement in the nanofluid flow past a semi-infinite
vertical plate imposed with porous matrix. For the bet-
ter enhanced properties of the thermophysical properties
they have used Cu, and oxide, Al2O3, as the nanoparti-
cles. ADM was used to solve the non-linear differential
equations and presented graphical analysis. Authors con-
cluded that, the velocity profiles retards with the enhanced
particle concentration since the density of the Cu nanopar-
ticle is likely to be greater, but the impact is opposite
for Al2O3 nanoparticles. Nazari et al.2021
also devoted
their recent work to understand thermophysical properties
of nanofluids. Williamson nanofluid flow through porous
medium was studied under heat transfer boundary condi-
tions, and in other paper they discussed about micropo-
lar nanofluids. Naimi et al.23
in the year 2002 proposed
their investigation by imposing both analytically as well
as numerically. Sheikholeslami and Chamka24
investigated
the influence of Lorentz forces on nanofluid forced con-
vection with Marangoni convection effects for two-phase
nanofluid.
Further, in recent studies several experimental inves-
tigations have been proposed for the thermal enhance-
ment treatment considering both nano and hybrid nanofluid
in various environments. An exhaustive review on the
free convection of nanofluid in various enclosures have
been presented by Sadeghi et al.25
In different geome-
try i.e., within a gamma-shaped cavity, Chamkha et al.26
presented their investigation on the mixed convection
of an electrically conducting nanofluid. They have also
analyzed the entropy generation within the system due
to the heat transport phenomenon. Dogonchi et al.2728
illustrate the natural convection of nanofluid within a
square cavity as well as wavy channel for the impact of
magnetic field. Their focus goes to the shape factor of
the nanoparticles impacts on the flow behaviour. Several
authors including Chamkha and their co-workers29–35
have
analyzed the influence of various characterizing parame-
ters on the flow of nanofluids in different physical sit-
uation. Biswas et al.36
proposed the hybrid nanoliquid
composed of Cu and Al2O3 nanoparticles considering
water as a base liquid for the impact of half-sinusoidal
non-uniform heating. They have imposed the thermal con-
vection boundary approach in their investigation. Further,
Biswas et al.37
convey magnetohydrodynamic thermal con-
vection in the same hybrid nanofluid past a saturated
porous medium. Recently, Manna et al.38
illustrates the
multi-banding application of the proposed magnetic field
within the porous medium. However, Biswas et al.3940
analyzed the heat transport phenomenon of several
nanofluids within a porous cavity embedding with porous
matrix.
Following aforementioned reference, the present inves-
tigation performs the heat transfer features of a conduct-
ing Casson hybrid nanofluid through a rotating permeable
channel. Further, the thermal properties of nanofluid
enriches with the consideration of radiating heat and
dissipative heat. Numerical treatment is employed for
the solution of the nonlinear problem and the analysis
is carried out through graphs for the numerous param-
eters affecting the flow profiles. Further, the numeri-
cal results for the rate coefficients are deployed and
discussed.
2. MATHEMATICAL FORMULATION
A non-Newtonian Casson hybrid nanofluid is presented for
the addition of both Copper and Aluminium is used in the
base liquid Ethylene glycol (Cu/Al2O3∼C2H6O2) through
infinite permeable parallel plates. Consider MHD flow of
an electrically conducting through parallel plates placed at
a distance ‘h’ apart. The flow is along x-axis and y-axis
is normal to it. A uniform magnetic field is applied and
thermal radiation with dissipative heat in a rotation system
also incorporated for the development in the flow phenom-
ena. The plate temperature at the lower part of the channel
is considered to be T0 (“injection takes place”) whereas at
the upper plate it is Th (“suction occurs”) such that T0
Th. A uniform angular velocity through which the body is
rotating about the y-axis is displayed in Figure 1. Because
of the small value of assumed magnetic Reynolds number,
it is wise to omit the impact of induced magnetic field.
The upper wall is moving in a constant velocity u0 towards
y-direction whereas lower one is at rest. The flow charac-
teristic suggests that except pressure, all the physical quan-
tities depend on ‘y’ only since the channel is long enough.
Though the channel wall is permeable it is assumed that
2 J. Nanofluids, 11, 1–12, 2022
3. Mishra et al. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium
ARTICLE
Fig. 1. Schematic diagram.
the suction velocity is v = −v0. Following,41
the rheolog-
ical equation for the assumed flow phenomena is
ij =
⎧
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎩
2
b +
py
√
2
eij c
2
b +
p
2c
eij c
(1)
where b, dynamic viscosity, py, the yield stress, , defor-
mation rate in the product form namely, = eij eij , eij , the
deformation rate for the i jth
component, and basing
on the model the critical value of is considered as c.
Therefore, Eq. (1) gives rise to c,
ij = b
1+
1
2eij (2)
where = b 2c/py, the Casson fluid parameter.
For the large value of the non-Newtonian parameter i.e.,
→ the problem became Newtonian. Following the
Ohm’s law a resistive force i.e., “Lorentz force”
J ×
B
is formed because of the conjunction of applied magnetic
field where the electric current density
J expressed as
J = hnf
E +
q ×
B (3)
Where the vector quantities present their usual meanings
i.e., hnf the conductivity of the electrical current,
q the
momentum,
E, the electric field, and
B stands for the
magnetic field. The appearance of constant magnetic is
obtained from
B = 0 where
B = 0B00. With respect
to the mentioned quantities and conditions the momentum
and the energy along x- and z-directions take the following
form,2627
− 0hnf
du
dy
+2w
=
p
x
+hnf
1+
1
d2
u
dy2
−B0Jz
−
hnf
k∗
p
u (4)
− 0hnf
dw
dy
−2u
=
p
z
+hnf
1+
1
d2
w
dy2
+B0Jx
+
hnf
k∗
p
w (5)
− 0cphnf
dT
dy
= khnf
d2
T
dy2
−
qr
y
+hnf
1+
1
×
u
y
2
+
w
y
2
+ hnf J2
x +J2
y (6)
The associated boundary conditions are
u = w = 0 T = T0 at y = 0
u = u0 w = 0 T = Th at y = h
(7)
where the velocity components u and w are presented
along the flow directions respectively, T, the fluid tempera-
ture, the current density J with components JxJyJz, p,
the pressure, qr , radiative heat flux, hnf , the density, hnf ,
the dynamic viscosity, cphnf , specific heat, and khnf , ther-
mal conductivity of hybrid nanofluid. The Tables I and II
presents the details on the physical properties of the hybrid
as well as the nanoparticles.
Here, 1 ≈ Cu and 2 ≈ Al2O3
are the volume fractions
of Cu and Al2O3 nanoparticles, respectively. Table II dis-
plays the physical properties of Cu and Al2O3 along with
the base liquid EG. The subscripts s1, s2, denotes the alu-
mina and copper particle correspondingly, f and hnf, used
for standard liquid and hybrid nanoliquid, respectively.
In case of steady state,
×
E = 0 that leads to Ex/y = 0 and
Ez/y = 0 and therefore, Ex and Ez are both
constants.
Hence Eq. (3) becomes
Jx = hnf Ex −B0w Jz = hnf Ez +B0w (8)
For non-conducting channel plate, Jx = 0, Jz = 0 at y = h.
Using the boundary condition at y = h, one can easily find
that Ex = 0 and Ez = −B0u0.
Which in turn yields from Eq. (8),
Jx = − hnf B0w Jz = hnf B0u−u0 (9)
Introducing (9), (4)–(6) gives rise to,
− 0hnf
du
dy
+2w
=hnf
1+
1
d2
u
dy2
−
B2
0 hnf +
hnf
k∗
p
u−u0 (10)
− 0hnf
dw
dy
−2u−u0
=hnf
1+
1
d2
w
dy2
+
B2
0 hnf +
hnf
k∗
p
w (11)
J. Nanofluids, 11, 1–12, 2022 3
4. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
Table I. Physicothermal properties of nano and hybrid nanofluids.50
Attributes Nano fluid Hybrid nano fluid
Density nf = 1−1f +1s1 hnf = 1−2nf +2s2
Dynamic viscosity nf = f 1−1−2 5
hnf = nf 1−2−2 5
Thermal capacity cpnf = 1−1cpf +1cps1 cphnf = 1−2cpnf +2cps2
Thermal conductivity
knf
kf
=
ks +2kf −21kf −ks
ks +2kf +1kf −ks
khnf
knf
=
ks +2knf −22knf −ks
ks +2knf +2knf −ks
Electrical conductivity nf
f
=
s1 +2 f −21 f − s1
s1 +2 f +1 f − s1
hnf
nf
= s2 +2 nf −22 nf − s2
s2 +2 nf +2 nf − s2
− 0cphnf
dT
dy
= khnf
d2
T
dy2
−
qr
y
+hnf
1+
1
×
u
y
2
+
w
y
2
+ hnf B2
0
×w2
+u−u02
(12)
Imposing the Cogley radiation following,42
the radiative
heat flux can be expressed as
qr
y
= 4T −T0
0
K0
e0
T
0
d (13)
where K0
, absorption coefficient, 0, length of the
wave and e0
, Planck’s function, and T0, the reference
temperature.
So Eq. (12) can be written as,
− 0cphnf
dT
dy
= khnf
d2
T
dy2
−4T −T0I +hnf
1+
1
×
u
y
2
+
w
y
2
+ hnf B2
0
×w2
+u−u02
(14)
Where,
I =
0
K
e
T
d (15)
Following variables are considered to get non-dimensional
form:
=
y
h
u1 =
u
u0
w1 =
w
u0
=
T −T0
Th −T0
(16)
Table II. Thermophysical properties of regular fluid, nanoparticle and
hybrid nanoparticle.50
Physical properties Cu Al2O3 C2H6O2
Cp (J/Kg K) 385 765 1115
(Kg/m3
) 8933 3970 2430
(W/mK) 400 40 0.253
5.96×107
35×106
1.07×10−4
Involvement of (16) in (10), (11) and (14) lead to,
−A1Re
du1
d
= A2
1+
1
d2
u1
d2
−A3M +Dau1 −1
−2A1Kw1 (17)
−A1Re
dw1
d
= A2
1+
1
d2
w1
d2
−A3M +Daw1
−2A1Ku1 −1 (18)
−A4Pe
d
d
= A5
d2
d2
−Ra +A2 Pr Ec
1+
1
×
du1
d
2
+
dw1
d
2
+A3M
×u1 −12
+w1
2
(19)
where all the physicothermal parameters
A1A2A3A4A5 and physical parameters such as, Re,
Reynolds number (when Re 0 the upper plate affected
by suction whereas Re 0 injection occurs at the lower
plate), M magnetic parameter, Da, Darcy number, K,
rotation parameter, Pe, Peclet number, Ra, radiation
parameter, Pr, Prandtl number, and Ec, Eckert number are
defined as,
A1 =
hnf
f
A2 =
hnf
f
A3 = hnf
f
A4 =
cphnf
cpf
A5 =
khnf
kf
Re = 0h
f
M =
f B2
0h
2
f f
Da =
h2
k∗
p
K =
h2
f
Pe =
0hcpf
kf
Ra =
4lh2
kf
Pr =
f cpf
kf
Ec =
u2
0
cpf
Th −T0
The non-dimensional boundary conditions are,
u1 = w1 = 0 = 0 at = 0
u1 = 1 w1 = 0 = 1 at = 1
(20)
4 J. Nanofluids, 11, 1–12, 2022
5. Mishra et al. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium
ARTICLE
Taking, F = u1 −1+iw1i =
√
−1, (17) and (18) can
be combined as:
A2
1+
1
d2
F
d2
+A1Re
dF
d
−A3M +Da−2iA1KF = 0
(21)
A5
d2
d2
+A4Pe
d
d
−Ra +A2 Pr Ec
1+
1
dF
d
2
+A3M F 2
= 0 (22)
where : stands for absolute value.
The boundary conditions (20) become,
F = −1 = 0 at = 0
F = 0 = 1 at = 1
(23)
2.1. Shear Stresses
The interference of both the velocities suggests the shear
stresses at both the plates i.e., = 0 and = 1 respec-
tively can be expressed as,
R0 =
du1
d
2
+
dw1
d
2 1/2
=0
=
dF
d
=0
R1 =
du1
d
2
+
dw1
d
2 1/2
=1
=
dF
d
=1
(24)
The simulations for the shear stresses coefficients i.e.,
R0, R1 are tabulated in Table III for several contributing
parameters governing the flow of Casson nanofluid as well
as hybrid nanofluid.
2.2. Rate of Heat Transfer
In thermo-physical system the rate of heat transfer is a
major component to be carried out for several parameters.
The non-dimensional form at the plates = 0 and = 1
can be obtain and presented as
0 =
=0
1 =
=1
(25)
The simulated results for the coefficients − 0 and
− 1 are also tabulated in Table III for the various
parameters affecting the flow phenomena of Casson hybrid
nanofluid.
Table III. Validation of shear rate for Da = 0.
R0 (2 = 0) R1 (2 = 0 05)
M K Re Das et al.50
Present Das et al.50
Present
5 4 −1 0.5 1.71944 1.70327 1.78261 1.76932
0 1.89867 1.86493 1.98017 1.96275
2.3. Entropy Generation
The contribution of entropy generation is an important
aspect in the current investigation within a flow system. It
is wise to note that to preserve the quality of energy, the
entropy generation is to minimize in a thermal system. Fol-
lowing Das et al.43
and Cogley et al.,44–46
the entropy gen-
eration, the local volumetric rate in the flow of a viscous
electrically conducting hybrid nanofluid through a parallel
plate channel under the action of radiation is proposed as,
EG =
khnf
T 2
0
dT
dy
2
Thermal irreversibility
+
hnf
T0
1+
1
u
y
2
+
w
y
2
Fluid friction irreversibility
+ hnf B2
0
T0
u−u02
+w2
Joule dissipation irreversibility
(26)
The beginning two terms are organized for the irreversibil-
ity due to the heat transfer and the frictional force of the
fluid, however, the remaining suggests the irreversibility
occurs because of the interaction of applied magnetic field.
The entropy generation is presented as,4748
Ns =
T 2
0 h2
EG
kf Th −T02
(27)
where Br = PrEc = f v2
0/kf Th −T0, the Brinkmann
number corresponds to the relation between the heat con-
duction obtained at the surface to the heat caused by
the shear stress within the bounding surface and p =
Th −T0/T0, the difference in temperature.
On the use of (16) and (27), Eq. (26) reduces to,
Ns = Nh+Nf (28)
Nh = A5
d
dy
2
, entropy caused by heat transfer
Nf =
Br
p
A2
1+
1
u1
y
2
+
w1
y
2
+A3u1 −12
+w2
1
=
Br
p
A2
1+
1
dF
d
2
+A3 F 2
entropy caused by the frictional force for the conjunction
of magnetic field.
2.4. Analysis of Irreversibility
The process of the irreversibility ratio between the contri-
bution of entropy due to hea and the frictional force of the
fluid is termed as
=
Nh
Nf
=
heat transfer irreversibility
fluid friction irreversibility
(29)
J. Nanofluids, 11, 1–12, 2022 5
6. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
For 0 1 the dominance of the heat transfer irre-
versibility is rendered and the fluid friction with magnetic
field dominates for 1. When = 1, the contribu-
tion of the frictional force conducted by the magnetic field
and permeability of the medium is equivalent to the heat
transfer in the fluid flow therefore, Paoletti et al.51
pre-
sented a different irreversibility, known as Bejan number
and expressed as:
Be =
Nh
Ns
=
Nh
Nh +Nf
=
1
1+
(30)
The range of the Bejan number is described as 0 Be 1.
Here, Be = 1 indicates the case of no irreversibility for
the heat transfer therefore only dissipation is accountable
for the process of irreversibility. However, Be 0 5 means
the fluid friction irreversibility dominants over the heat
transfer irreversibility and Be = 0 5 indicates that the heat
transfer and fluid friction for the consideration of magnetic
field the production of entropy rates are identical.
3. RESULTS AND DISCUSSION
The conducting Casson hybrid nanofluid flow through a
rotating channel subjected to porous medium is presented
in this analysis. For enriching the heat transfer criterion,
ethylene glycol (EG) is taken care of as a base fluid
and as a best conductor Cu is considered as the metal
nanoparticle and for oxide Al2O3 is used. Radiative heat
along with dissipative heat augments the temperature pro-
files. The physical properties relating to the nanofluid as
well as the hybrid nanofluid such as density, conductiv-
ities associated to both thermal and electrical are elabo-
rated in Table I. Further, Table II deliberates the physical
parameters of the base liquid EG and nanoparticles. The
transformed governing equations are handled numerically
employing Runge-Kutta technique. The profiles of both
the primary and secondary velocity and the temperature
profile are obtained for the several values of the param-
eters involved in the flow phenomena and illustrated via
Figures 2–21. The corroboration of the existing outcomes
for the shear rate with the nonappearance of the porous
matrix is presented in Table III. It displays the results are
good correlation with the work of Das et al.50
Further,
the shear stress and the Nusselt number at both the walls
are presented after getting the simulated results that are
displayed in Table IV. The main attraction is the entropy
analysis because of the irreversibility of the process. The
comparative study reveals that the earlier analytical and
the current numerical treatment correlates each other with
a good agreement and suggests achieving our goal.
Figure 2 deliberates the primary velocity profiles for
the non-Newtonian hybrid nanofluid with an inclusion of
magnetic parameter. The result is obtained for both the
nanofluids comprised of Cu/Al2O3∼EG hybrid nanofluid.
Here, M = 0 validates for the earlier result without mag-
netic field. Further, the enhanced values of the magnetic
parameter showing the increasing behaviour that’s resulted
in the thickness of the bounding surface decelerates. The
involvement of the “Lorentz force” due to the inclusion
of magnetic field offers a resistive force that causes a
strong retardation throughout the domain and further meets
the boundary condition smoothly. The comparative results
reveals that Cu∼EG nanofluid has stronger retarding effect
as that of the hybrid nanoliquid. Since, Cu has higher
density than Al2O3 so that the profiles of primary veloc-
ity decrease in case of Cu∼EG nanofluid. The impact
of magnetic parameter on the secondary velocity is pre-
sented in Figure 3. From the observation it is found that
the profile gets enhanced near the lower wall and further
the profile retards with the increasing values of magnetic
parameter to meet the upper wall. Comparison shows that
Cu∼EG nanofluid has greater retarding effect than that of
Cu/Al2O3∼EG hybrid nanofluid. The behaviour of thermo-
physical properties associated to nanofluid is vital for the
enrichment of energy profile. Figure 4 reveals the magne-
tization properties on the temperature profile for both the
Fig. 2. Variation of M on primary velocity profile.
Fig. 3. Variation of M on secondary velocity profile.
6 J. Nanofluids, 11, 1–12, 2022
7. Mishra et al. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium
ARTICLE
Fig. 4. Variation of M on temperature profile.
Fig. 5. Variation of Da on primary velocity profile.
Fig. 6. Variation of Da on secondary velocity profile.
Fig. 7. Variation of Da on temperature profile.
Fig. 8. Variation of K on primary velocity profile.
Fig. 9. Variation of K on secondary velocity profile.
J. Nanofluids, 11, 1–12, 2022 7
8. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
Fig. 10. Variation of K on temperature profile.
Fig. 11. Variation of Re on primary velocity profile.
Fig. 12. Variation of Re on secondary velocity profile.
Fig. 13. Variation of Re on temperature profile.
Fig. 14. Variation of on primary velocity profile.
Fig. 15. Variation of on secondary velocity profile.
8 J. Nanofluids, 11, 1–12, 2022
9. Mishra et al. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium
ARTICLE
Fig. 16. Variation of on temperature profile.
Fig. 17. Variation of Ra on temperature profile.
Fig. 18. Variation of Pe on temperature profile.
Fig. 19. Variation of M and Pe on Bejan number and entropy variation.
Fig. 20. Variation of Ra and on Bejan number and entropy variation.
Fig. 21. Variation of Brp−1
on Bejan number and entropy variation.
J. Nanofluids, 11, 1–12, 2022 9
10. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
Cu∼EG nanofluid and Cu/Al2O3∼EG hybrid nanofluid.
The thermal bounding surface near the lower wall decel-
erates causes the fluid temperature increases significantly.
The fact is that heat conductivity of Cu is good for which
the profile enhances within the domain 0 2 and fur-
ther the profile retards. However, in the second region the
impact is also opposite to the behaviour shown in the first
region. As described earlier, similar to the earlier discus-
sion, porosity is also a resistive force and the impact is
deliberated due to the flow through the permeable medium.
Here, Da = 0 suggests the flow through a clear fluid region
and Da = 0 indicates the behaviour through the permeable
region. Figure 5 illustrates the characteristic of Darcy num-
ber on the primary velocity profile. Increasing Darcy num-
ber produces a force that has a tendency to resists the fluid
motion so that the lower wall thickness retards and further
it became smooth up to the upper wall of the channel. The
behaviour of the Darcy number on the secondary velocity
is rendered in Figure 6. The impact is similar to that of
the magnetic parameter as described earlier in Figure 3.
Further, the nano as well as hybrid nanofluid temperature
profile for the behaviour of the Darcy number in deployed
in Figure 7. It is seen that the profile augmented with
augment in the Darcy number for the Cu∼EG nanofluid
and the amount of enhancement is more in contrast to the
Cu/Al2O3∼EG hybrid nanofluid. It is quite interesting to
observe that in the second region i.e., for 0 2 the pro-
files for both the nano as well as hybrid nanofluid have
reverse impact due to increasing Darcy number. Both the
primary and the secondary velocity combine to each other
due to the appearance of the rotational parameter that is
presented in Eqs. (17) and (18). Figure 8 portrays the
influence of the rotational parameter on the primary veloc-
ity distribution for the presence of other fixed parameters
involved in the governing flow phenomena. Here, K = 0
suggests the without rotation the primary velocity for the
nanofluid and the hybrid nanofluid coincides each other
whereas the increasing rotation decelerates the thickness
of the bounding surface near the lower wall of the chan-
nel. Figure 9 portrays the secondary velocity distribution
for the variation of the rotation parameter. The pick in the
profiles is rendered near the lower wall of the channel and
thus it again boosts up the profile with the decelerating
nature throughout the domain. The hike in the values of
the rotational parameter on the fluid temperature is pre-
sented in Figure 10. In all the profiles for the variation of
rotation parameter it is observed that the Cu∼EG nanofluid
has a greater impact on the primary velocity than that
of Cu/Al2O3∼EG hybrid nanofluid. Further, the impact is
reversed in case of secondary velocity. Inertial force in
combination with the viscous force leads to the effect of
Reynolds number and the impact of Re is vital for the flow
phenomena. The influence of Re on the primary velocity
is rendered in Figure 11. Decelerating effect of viscous
force enriches the Reynolds number and the result shows
that the primary velocity enhances. This is because of the
dominating effect of the inertial force. Due to this reason
the thickness of the bounding surface decreases. It quan-
tifies the relative importance of these two forces. Further,
the behaviour of the Reynolds number on the secondary
velocity profiles. The dominating nature of inertial force
over the viscous force retards the secondary velocity that is
displayed in Figure 12. In both of these figures it is seen
that the Cu∼EG nanofluid has a tendency to decelerate
the velocity profiles in assessment to the Cu/Al2O3∼EG
hybrid nanofluid. The fact is straight forwards because
of the density of the Cu particle and thus the agglom-
eration of the particle is found near the lower wall sur-
face. Further, it is found that as the domain increases
the profile became sooth to meet the boundary condi-
tion. Figure 13 describes the impact of Reynolds number
on the temperature profile considering both the nano and
hybrid nanofluid. The enhanced value of Re augments the
fluid temperature nearby the lower wall and afterwards the
impact decelerates gradually. Casson parameter signifies
the non-Newtonian features of the magnetized fluid. Large
value of Casson parameter leads to perform the Newtonian
characteristics. Figure 14 illustrates the behaviour of the
Casson parameter on the flow phenomenon of the primary
velocity of hybrid nanofluid. The elasticity of the param-
eter is due to the relationship between the relaxations
with retardation time. An increase in Casson parameter
the flow profile increases showing the lower bounding sur-
face thickness ceases to zero. The fact is, higher Casson
value suggests the Newtonian case for which the primary
velocity rises up. Further, reverse impact is rendered for
the secondary velocity distribution that is presented in
Figure 15. Initially the hike is faster nearby the lower
surface and then the behaviour is opposite. However, the
comparative result exposes that the denser Cu nanoparticle
agglomerated near the lower surface resulted in the decel-
eration is ore in the case of Cu∼EG nanofluid than that of
Cu/Al2O3∼EG hybrid nanofluid. Figure 16 portrays a sig-
nificant deceleration in the fluid temperature due to an aug-
mentation in the Casson parameter. Thus, it is concluded
that the non-Newtonian characteristic of the magnetized
fluid favors to enhance the nanofluid as well as the hybrid
nanofluid temperature profiles at points within the domain.
The release of electromagnetic radiation from the fluid sur-
face encoded as radiation. Figure 17 exhibits the behaviour
of the thermal radiation on the fluid temperature. The
radiative heat energy is the reciprocal of the thermal con-
ductivity of the base fluids. Thermal radiation enhances
with decreasing conductivity. Therefore, increasing radia-
tion the amount of heat radiate from the lower wall surface
radiated greatly and thus the fluid temperature increases
significantly. Figure 18 shows the significance of the Peclet
number on the fluid temperature profiles considering both
the nanofluid and the hybrid nanofluid. Pe is defined as
10 J. Nanofluids, 11, 1–12, 2022
11. Mishra et al. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium
ARTICLE
Table IV. The rate coefficients for several values of the parameters.
R0 ×102
R1 ×102
− 0×102
− 1×102
M K Re 2 = 0 2 = 0 05 2 = 0 2 = 0 05 2 = 0 2 = 0 05 2 = 0 2 = 0 05
1 10 10 0.5 0.0164 0.0157 0.0077 0.0079 −2.3742 −2.2169 0.4023 0.4569
3 0.0219 0.0215 0.0052 0.0053 −2.862 −2.7362 0.2446 0.2834
5 0.0314 0.0314 0.0027 0.0027 −3.9213 −3.821 0.1334 0.1637
1 5 0.0343 0.0338 0.0025 0.0026 −4.3764 −4.1895 0.1319 0.1636
10 0.048 0.0461 0.0016 0.0019 −6.812 −6.3169 0.1247 0.1626
15 0.06 0.0573 0.06 0.0011 −8.9819 −8.3188 0.1194 0.1608
5 5 0.0391 0.0383 0.0013 0.0014 −4.7961 −4.5944 0.0965 0.1274
10 0.0505 0.0484 0.0004 0.0005 −6.1276 −5.7551 0.0747 0.1038
15 0.0663 0.0623 0.0001 0.0002 −7.996 −7.3777 0.0631 0.0901
5 1 0.0389 0.0388 0.0016 0.0016 −3.2366 −3.1548 0.0663 0.0853
5 0.0512 0.051 0.0006 0.0006 −2.5735 −2.5073 0.0299 0.0405
10 0.0537 0.0534 0.0005 0.0005 −2.4767 −2.4126 0.0263 0.0359
the product of Re and Pr. The use of base fluid EG corre-
sponds to the higher values of the Prandtl number there-
fore, increasing Pr retards the fluid temperature for both of
the cases. Entropy generation is the major aspects of the
energy system that is due to various irreversibilities i.e.,
the combination of the thermal, fluid friction and Joule
dissipation irreversibility. Figures 19–21 show the entropy
analysis along with the Bejan number for the impact of
various contributing parameters. The effects of Pe num-
ber on the entropy and the variation of magnetic param-
eter on the Bejan value is deliberated in Figure 19. It is
clear to see that increasing Pe number enriches the entropy
throughout the domain. The profile of Bejan shows its dual
characteristics for the variation of magnetic parameter. It
is observed that the increasing magnetic parameter decel-
erates the Bejan value near the lower wall whereas reverse
impact is rendered far away from it. Figure 20 describes
the behaviour of the non-Newtonian Casson parameter on
the entropy generation and the behaviour of the Ra on
Bejan number. An augmentation in the Casson parame-
ter retards the entropy and the similar behaviour of Ra on
Bejan value is rendered as described in the earlier figure.
The impact of Brinkman number on the entropy analy-
sis and the Bejan number is presented in Figure 21. Br
is the product of Pr and Ec. An augmentation in the Br
enriches the entropy and the reverse impact is detected for
the Bejan value. Table IV shows the shear stress coeffi-
cients and Nusselt number at both of the lower and upper
walls of the channel in two different situations i.e., in case
of nanofluid 2 = 0 and in case of hybrid nanofluid 2 =
0 05. The behaviour of magnetization, rotational as well
as Reynolds number and the Casson parameter is obtained
keeping others as fixed. An inclusion of magnetic, rota-
tion parameter and the Reynolds number enhance the skin
friction rate at the lower surface whereas the influence is
counterproductive in the upper surface for both the case
of nanofluid and hybrid nanofluid. Similar observation is
encountered for the rate of heat transfer. The compara-
tive result reveals that the magnitude is more for Cu∼EG
nanofluid. Further, it is clarified that the non-Newtonian
parameter exhibits greater impact to enhance the skin fric-
tion rate about lower part and decelerates about the upper
wall whereas the impact is reversed in case of rate of heat
transfer for both the nano and hybrid nanofluid.
4. CONCLUSION
Flow of conducting Casson hybrid nanoliquid via a rotat-
ing permeable channel is considered in this study. The
novelty is to minimize the energy flow rate due to the irre-
versibility of the process for the analysis of the entropy.
The thermal enhancement is carried out due to the inclu-
sion of the radiative and dissipative eat energy. However,
the characteristic of the thermophysical properties of sev-
eral nanoparticles i.e., Cu and Al2O3 with the base fluid
EG augments the significance of the flow properties. The
numerical treatment is obtained for the solution of com-
plex nonlinear problem and further, the behaviour of the
physical parameters is presented graphically and then dis-
cussed. However, the following conclusions are presented
as;
• The inclusion of metal and oxide nanoparticle with the
base fluid EG enriches the flow phenomena of the nanoflu-
ids as well as the hybrid nanofluid, Thermophysical prop-
erties therefore the flow profiles boost up.
• The magnetized fluid energizes the primary as well as
secondary velocity that resulted in to decelerates the thick-
ness of the lower bounding surface further, the energy
transport boost up the profiles significantly.
• The augmentation in the inertial force dominating over
viscous force augments the Reynolds number for which
the primary and secondary velocity decelerates the thick-
ness of both the velocity profiles and enhances the thermal
bounding surface.
• Similar tendency is rendered for the variation of the
nono-Newton Casson parameter for the velocity profiles
however the temperature profile also retards.
• Rate of shear stress and heat transfer rate rises up for
the increasing magnetic parameter, rotation parameter, and
J. Nanofluids, 11, 1–12, 2022 11
12. Hybrid Nanofluid Flow of Non-Newtonian Casson Fluid for the Analysis of Entropy Through a Permeable Medium Mishra et al.
ARTICLE
Reynolds number near the lower wall surface whereas
impact is reversed near the upper wall.
References and Notes
1. J. R. A. Pearson, J. Fluid Mech. 4, 489 (1958).
2. A. M. Cazabat, F. Heslot, S. M. Troian, and P. Carles, Nature 346,
824 (1990).
3. K. Arafune and A. Hirata, J. Cryst. Growth 197, 811 (1999).
4. D. M. Christopher and B. X. Wang, Int. J. Heat Mass Transfer 44,
799 (2001).
5. P. K. Pattnaik, S. R. Mishra, and M. M. Bhatti, Inventions 5, 1
(2020).
6. A. K. Barik, S. K. Mishra, P. K. Pattnaik, and S. R. Mishra, Heat
Transfer Asian Research 49, 477 (2020).
7. S. R. Mishra, P. K. Pattnaik, and G. C. Dash, Alexandria Engineering
Journal 54, 681 (2015).
8. P. K. Pattnaik, S. R. Mishra, A. K. Barik, and A. K. Mishra, Inter-
national Journal of Fluid Mechanics Research 47, 1 (2020).
9. P. K. Pattnaik, S. Jena, A. Dei, and G. Sahu, JP Journal of Heat and
Mass Transfer 18, 207 (2019).
10. P. K. Pattnaik, S. R. Mishra, B. Mahanthesh, B. J. Gireesha, and
M. R. Gorji, Multidiscipline Modeling in Materials and Structures
16, 1295 (2020).
11. F. M. Abbasi, T. Hayat, and B. Ahmad, Physica E 67, 47 (2015).
12. N. V. Ganesh, P. K. Kameswaran, Q. M. Al-Mdallal, A. K. A.
Hakeem, and B. Ganga, J. Nanofluids 7, 944 (2018).
13. A. Bhattad, J. Sarkar, and P. Ghosh, Renewable and Sustainable
Energy Reviews 82, 3656 (2018).
14. A. Shadlaghani, M. Farzaneh, M. Shahabadi, M. R. Tavakoli,
M. R. Safaei, and I. Mazinani, J. Therm. Anal. Calorim. 135, 1429
(2019).
15. M. Goodarzi, D. Toghraie, M. Reiszadeh, and M. Afrand, J. Therm.
Anal. Calorim. 136, 513 (2019).
16. A. H. Pordanjani, S. Aghakhani, A. Karimipour, M. Afrand, and
M. Goodarzi, J. Therm. Anal. Calorim. 137, 997 (2019).
17. H. Arasteh, R. Mashayekhi, M. Goodarzi, S. H. Motaharpour,
M. Dahari, and D. Toghraie, J. Therm. Anal. Calorim. 138, 1461
(2019).
18. A. M. Arabbeiki, H. M. Ali, M. Goodarzi, and M. R. Safaei, Nano-
materials 10, 901 (2020).
19. A. K. Mishra, P. K. Pattnaik, S. R. Mishra, and N. Senapati, J.
Therm. Anal. Calorim. (2020).
20. S. Nazari, R. Ellahi, M. M. Sarafraz, M. R. Safaei, A. Asgari, and
O. A. Akbari, J. Therm. Anal. Calorim. 140, 1121 (2020).
21. S. R. Mishra and P. Mathur, Multidiscip. Model. Mater. Struct
(2020).
22. S. R. Mishra, P. Mathur, and H. M. Ali, J. Therm. Anal. Calorim. 1
(2021).
23. M. Naïmi, M. Hasnaoui, and J. K. Platten, Eng. Comput. (Swansea,
Wales) 19, 49 (2002).
24. M. Sheikholeslami and A. J. Chamkha, J. Mol. Liq. 225, 750 (2017).
25. M. S. Sadeghi, N. Anadalibkhah, R. Ghasemiasl, T. Armaghani,
A. S. Dogonchi, A. J. Chamkha, H. Ali, and A. Asadi, J. Therm.
Anal. Calorim. (2020).
26. A. J. Chamkha, M. A. Mansour, A. M. Rashad, H. Kargar-
sharifabad, and T. Armaghani, J. Thermophys. Heat Transfer
(2020).
27. A. S. Dogonchi, T. Armaghani, A. J. Chamkha, and D. D. Ganji,
Arabian Journal for Science and Engineering (2019).
28. M. Ghalambaz, A. Doostani, E. Izadpanahi, and A. J. Chamkha, J.
Therm. Anal. Calorim. (2019).
29. A. S. Dogonchi, T. Tayebi, A. J. Chamkha, and D. D. Ganji, J.
Therm. Anal. Calorim. (2019).
30. M. V. Krishna and A. J. Chamkha, Results in Physics (2019), DOI:
10.1016/j.rinp.2019.102652.
31. B. Kumar, G. S. Seth, R. Nandkeolyar, and A. J. Chamkha, Int. J.
of Thermal Sciences 146, 106101 (2019).
32. M. A. Ismaela, T. Armaghanib, and A. J. Chamkha, Journal of the
Taiwan Institute of Chemical Engineers (2015).
33. A. J. Chamkha and A. R. A. Khaled, Int. J. of Numerical Methods
for Heat and Fluid flow 10, 94 (2000).
34. M. Modather, A. M. Rashad, and A. J. Chamkha, Turkish J. Eng.
Env. Sci. 33, 245 (2009).
35. S. Parvin and A. J. Chamkha, International Communications in Heat
and Mass Transfer 54, 8 (2014).
36. N. Biswas, N. K. Manna, and A. J. Chamkha, J. Therm. Anal.
Calorim. 143 (2020).
37. N. Biswas, U. K. Sarkar, A. J. Chamkha, and N. K. Manna, J. Therm.
Anal. Calorim. 143, 1727 (2021).
38. N. K. Manna, M. K. Mondal, and N. Biswas, Phys. Scr. 96 (2021).
39. N. Biswas, N. K. Manna, P. Datta, and P. S. Mahapatra, Powder
Technol. 326, 356 (2018).
40. N. Biswas and N. K. Manna, Mathematical Methods in the Applied
Sciences (2021), DOI: 10.1002/mma.7280.
41. A. S. Eegunjobi and O. D. Makinde, Defect and Diffusion Forum
374, 47 (2017).
42. O. D. Makinde and E. Osalusi, Entropy 7, 148 (2005).
43. S. Das, R. N. Jana, and O. D. Makinde, Defect and Diffusion Forum
377, 42 (2017).
44. A. C. Cogley, W. C. Vincentine, and S. E. Gilles, Ameri-
can Institute of Aeronautics and Astronautics Journal 6, 551
(1968).
45. L. C. Wood, Thermodynamics of fluid systems, Oxford University
Press, Oxford (1975).
46. A. Bejan, Energy 5, 721 (1980).
47. A. Bejan, Entropy generation minimization, CRC Press, New York
(1996).
48. A. Bejan, I. Dincer, S. Lorente, A. F. Miguel, and A. H. Reis, Porous
and complex flow structures in modern technologies, Springer, New
York (2004).
49. S. Das, S. Sarkar, and R. N. Jana, Journal Nanofluids 7, 1217 (2018).
50. S. Das, S. Sarkar, and R. N. Jana, BioNanoScience 10, 1 (2020).
51. S. Paoletti, F. Rispoli, and E. Sciubba, ASME Advanced Energy Sys-
tems 10, 21 (1989).
12 J. Nanofluids, 11, 1–12, 2022