The document summarizes previous research on mixed convection heat transfer in inclined tubes and describes an experimental study. The study investigated the effects of heat flux, tube inclination angles, and tube diameters on heat transfer for laminar to turbulent air flows in inclined circular tubes under constant wall heat flux. Local and average Nusselt numbers were measured for tube inclinations of 30°, 45°, and 60° and diameters of 0.75, 1.5, and 2 inches. The results showed that Nusselt numbers increased with higher heat flux and as the tube moved from 60° to 30° inclination, and decreased with larger diameter to length ratios.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
Thermal analysis of various duct cross sections using altair hyperworks softwaresushil Choudhary
In this work thermal analysis and comparison of various duct cross sections is done computationally using Altair
Hyperworks Software. Simple Analytical results were obtained for conduction and convection through the ducts
which can be used to build up thermal circuit. The inner surface of all ducts is maintained at constant
temperature and ambient air is at certain temperature that is less than inner surface temperature of pipe. Due to
temperature difference heat will flow from higher temperature to lower temperature. Due to temperature
difference heat will flow from higher temperature to lower temperature. The material of pipe provides
conductive resistance and air provides convective resistance. Hence this is a mix mode of heat transfer. The heat
transfer takes place in one dimension only and properties are considered to be isotropic. The ducts are assumed
to be made of aluminium having known thermal conductivity and density. The surroundings of ducts have
known convective heat transfer coefficient and temperature. The results are obtained on hyperview which are for
heat flux, temperature gradient and grid temperature. The different characteristics can be obtained by varying the
material of the ducts.
The results show that, with proper selection of physical parameters, significant heat transfer
enhancements and pressure drop reductions can be achieved simultaneously with porous pin fins and
the overall heat transfer performances in porous pin fin channels are much better than those in
traditional solid pin fin channels. The effects of pore density are significant. As PPI increases, the
pressure drops and heat fluxes in porous pin fin channels increase while the overall heat transfer
efficiencies decrease and the maximal overall heat transfer efficiencies are obtained at PPI 20.
Furthermore, the effects of pin fin form are also remarkable. With the same physical parameters, the
overall heat transfer efficiencies in the long elliptic porous pin fin channels are the highest while they
are the lowest in the short elliptic porous pin fin channels
Thermal analysis of various duct cross sections using altair hyperworks softwaresushil Choudhary
In this work thermal analysis and comparison of various duct cross sections is done computationally using Altair
Hyperworks Software. Simple Analytical results were obtained for conduction and convection through the ducts
which can be used to build up thermal circuit. The inner surface of all ducts is maintained at constant
temperature and ambient air is at certain temperature that is less than inner surface temperature of pipe. Due to
temperature difference heat will flow from higher temperature to lower temperature. Due to temperature
difference heat will flow from higher temperature to lower temperature. The material of pipe provides
conductive resistance and air provides convective resistance. Hence this is a mix mode of heat transfer. The heat
transfer takes place in one dimension only and properties are considered to be isotropic. The ducts are assumed
to be made of aluminium having known thermal conductivity and density. The surroundings of ducts have
known convective heat transfer coefficient and temperature. The results are obtained on hyperview which are for
heat flux, temperature gradient and grid temperature. The different characteristics can be obtained by varying the
material of the ducts.
Transient Three-dimensional Numerical Analysis of Forced Convection Flow and ...IOSR Journals
A three-dimensional transient numerical study of a constant property Newtonian fluid in curved pipe under laminar flow conditions is presented for a uniform wall temperature boundary condition. Numerical solutions were obtained using the control volume method described by Patankar for the range of. The working fluid was water. The transient flow pattern and the temperature distribution on the tube section were derived for different values of the Reynolds number. Graphical results for velocity and temperature are presented and analyzed. Results have shown that the maximum velocity in center of velocity profile increase with increasing of Reynolds number. In curved pipes, time averaged results exhibited Dean circulation and a strong velocity and temperature stratification in the radial direction. Flow and heat transfer were strongly asymmetric, with higher values near the outer pipe bend.
In compact heat exchangers, thermal resistance is generally dominant on the air-side and may
account for 80% or more of the total thermal resistance. The air-side heat transfer surface area is 8 to
10 times larger than the water-side. Any improvement in the heat transfer on air-side therefore
improves the overall performance of the heat exchanger. Due to the high thermal resistance on the
air-side, the optimization of such fins is essential to increase the performance of the heat exchangers
which results in thermal systems enhancement. This helps to reduce CO2 emissions through a
reduction of mass and fuel consumption.
Optimization of louvered fin geometry in such heat exchangers is essential to increase the
heat transfer performance and reduce weight, packaging, and cost requirements. In this study deals
with Computational Fluid Dynamics (CFD) studies of the interactions between the air flow and
louvered fins which equipped the automotive heat exchangers is carried out. 3D numerical
simulation results is obtained by using the ANSYS Fluent 14.0 code and compared with
experimental data. Finally the effect of louver angle and louver pitch geometrical parameters, on
overall thermal hydraulic performances of louvered fins is studied.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
An Experimental Research on Heat Transfer Enhancement of a Circular Tube with...IRJESJOURNAL
ABSTRACT:- In the literature, internal tube baffles are widely studied. There is a lack of data for baffles mounted on outside of the tubes. This study aims to fill this gap. Therefore, the effect of baffle inclination angles on heat transfer improvement has been studied experimentally. The experiments were carried out for forced convection of air on a circular tube with inclined baffles. Air has been used as the cold fluid. Experimental results for eight different velocities of air flow (2 – 20 m/s) are presented. Pitch between baffles is 12 mm.The baffle inclination angles with respect to the tube axis were 45º, 60º and 80º. Water temperature is fixed as 65 °C. According to the experimental results, the baffles with an inclination angle of 45º enhance the heat transfer over 60º and 80º around 13.7 % and 10.5 %, respectively. However, pressure drop values for 45º and 60º are 18 % higher than pressure drop values for 80º. The empirical correlations of the Nusselt number have also been obtained for each angle.
FLUID FLOW ANALYSIS IN AIR DUCT FLOW WITH AND WITHOUT INTERNAL THREADS USING ...IAEME Publication
Computational heat transfer flow modeling is one of the great challenges in the classical sciences. As with most problems in engineering, the interest in the heat transfer augmentation is increasing due to its extreme importance in various industrial applications. This paper deals with the analysis of heat transfer for fluid flowing through the pipe with and without internal threads using CFD. Using CFD codes for modeling the heat and fluid flow is an efficient tool for predicting equipment performance. CFD offers a convenient means to study the detailed flows and heat exchange processes, which take place inside the tube. Simulations were carried out using commercial CFD software ANSYS Fluent version 14.5. Friction factor and Nusselt number for air flowing through the specified tube (internal diameter = 0.005 m, length = 0.1 m) were obtained first for the plain tube and then for the tube with internal threads with pitch 5mm in the Reynolds number range of 2000 to 5000. Finally results will be compared to available experimental and analytical calculations. The data obtained by simulation are matching with the literature value for a plain tube with the discrepancy of less than plus or minus 5% for Nusselt number and for the friction factor.
Enhanced heat transfer for the tube with internal threads has been observed. Heat flux is more uniform all along the tube and decreases uniformly towards the center.
THERMO HYDRAULICS PERFORMANCE OF TURBULENT FLOW HEAT TRANSFER THROUGH SQUARE ...IAEME Publication
This paper describes the experimental study of square ducts with inserts. Experiments are conducted for air with uniform heat flux condition. The top wall surface is made rough with metal ribs of square section. The roughened wall is uniformly heated and other walls are insulated. The heat transfer coefficient enhances square channel at injection of different inserts. The performance of the geometry under investigation has been evaluated .The heat transfer coefficient of air is increase by 46% than plane square ducts with inserts. The heat transfer and pressure drop measurements have been taken in separate sections .
NATURAL CONVECTION HEAT TRANSFER INSIDE INCLINED OPEN CYLINDERIAEME Publication
Natural convection is investigated experimentally in an inclined open cylindrical passege heated under constant heat flux condition to study the effect of angle of inclination and heat flux on heat transfer. Heat transfer results are given for inclination angles of 0o (horizontal), 30o , 60o and 90o (vertical).Using cylinder diameter of 4.8 cm, cylinder length 50 cm and heat flux from 70 W/m2 to 600 W/m2 . Empirical correlations are given for the average Nusselt number as a function of the
Rayleigh number. The results show that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o (horizontal) to 90o
(vertical). An empirical correlations of average Nusselt number as a function of Rayleigh number were obtained.
NATURAL CONVECTION HEAT TRANSFER IN INCLINED OPEN ANNULUS PASSEGE HEATED FROM...IAEME Publication
Natural convection is investigated experimentally in an open cylindrical annulus heated with both annulus inner and outer sides under same constant heat flux condition to study the effect of angle of inclination and heat flux on heat transfer. Heat transfer results are given for inclination angles of 0o
(horizontal), 30o , 60o and 90o (vertical) using annulus diameter ratio of 1.8, inner and outer tube length 50 cm and heat flux from 70 W/m2 to 600W/m2 . The results show that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o
(horizontal) to 90o (vertical).An empirical correlations of average Nusselt number as a function of Rayleigh number were deduced.
A Detailed Review on Artificial Roughness Geometries for Optimizing Thermo-Hy...IJMER
It is well known fact that the heat transfer coefficient between the absorber surface of solar air collector & flowing fluid i.e. air can be improved by providing artificial roughness geometry on heat transfer surface (absorber surface).In this way the Thermal efficiency is increased. But at the same time due to roughness geometry pumping power of solar air collector in increased due to fictional losses in duct. So it necessary to examine the shape, size & flow pattern of various roughness elements to get maximum efficiency with minimum frictional losses. Therefore the selection of roughness geometry has to be based on the parameter that takes into account both Thermal & Hydraulic (friction) performance i.e. Thermo-hydraulic Performance of Solar air collector. Number of roughness elements has been investigated on heat transfer & friction characteristics of solar air collectors. In this paper, reviews of various artificial roughness elements used as passive heat transfer techniques, in order to improve Thermo-hydraulic performance of solar air collectors is reviewed & presented. Correlations developed by various researchers with the help of experimental results for heat transfer & friction factor for solar air collector by taking different roughness geometries are given & these correlations are useful to predict the Thermo-hydraulic performance of solar air collector having roughened ducts. The objective of this paper is also the awareness of effect of various types’ roughness geometries on heat
Convective heat transfer and pressure drop in v corrugatedMohamed Fadl
New energy system development and energy
conservation require high performance heat exchanger, so
the researchers are seeking to find new methods to enhance
heat transfer mechanism in heat exchangers. The objectives
of this study are investigating heat transfer performance
and flow development in V-corrugated channels, numerical
simulations were carried out for uniform wall heat flux
equal 290 W/m
2
using air as a working fluid, Reynolds
number varies from 500 to 2,000, phase shifts,
0 \ Ø \ 180, and channel heights (S = 12.5, 15.0, 17.5
and 20 mm). Governing equations of flow and energy were
solved numerically by using finite volume method. The
numerical results indicated that, wavy (V-corrugated)
channels have a significant impact on heat transfer
enhancement with increase in pressure drop though chan-
nel due to breaking and destabilizing in the thermal
boundary layer are occurred as fluid flowing through the
corrugated surfaces and the effect of corrugated phase shift
on the heat transfer and fluid flow is more significant in
narrow channel, the goodness factor (j/f) was increased
with increasing channel phase shift, the best performance
was noticed on phase shift, Ø = 180 and channel height,
S = 12.5 mm.
Assessment of thermo-hydraulic performance of inward dimpled tubes with varia...CFD LAB
This paper presents a numerical investigation and assessment of thermal and hydraulic performance of dimpled
tubes of varying topologies at constant heat flux of 10 kW m2 and Reynolds numbers ranging from 2300 to
15,000. The performance of the tubes consisting of conical, spherical and ellipsoidal dimples with equivalent
flow volumes were compared using steady state Reynolds Averaged Navier Stokes simulations. The ellipsoidal
dimples, in comparison to other dimple shapes, demonstrated large increment in heat transfer rate. The variation
in the orientation of the ellipsoidal dimples was examined to further improve thermal and hydraulic performances of the tube. A 45° inclination angle of ellipsoidal dimple, from its major axis, increased the thermohydraulic performance by 58.1% and 20.2% in comparison to smooth tube and 0° ellipsoidal dimpled tube,
respectively. Furthermore, Large Eddy Simulations (LES) were carried out to investigate the role geometrical
assistance to fluid flow and heat transfer enhancement for the 45° and 90° ellipsoidal dimpled tubes. LES results
revealed a flow channel of connected zones of wakes which maximized fluid-surface contact and therefore
enhanced the thermal performance of the tube. In addition, correlations for Nusselt number and friction factor
for all angular topologies of ellipsoidal dimpled tube have been proposed.
Transient Three-dimensional Numerical Analysis of Forced Convection Flow and ...IOSR Journals
A three-dimensional transient numerical study of a constant property Newtonian fluid in curved pipe under laminar flow conditions is presented for a uniform wall temperature boundary condition. Numerical solutions were obtained using the control volume method described by Patankar for the range of. The working fluid was water. The transient flow pattern and the temperature distribution on the tube section were derived for different values of the Reynolds number. Graphical results for velocity and temperature are presented and analyzed. Results have shown that the maximum velocity in center of velocity profile increase with increasing of Reynolds number. In curved pipes, time averaged results exhibited Dean circulation and a strong velocity and temperature stratification in the radial direction. Flow and heat transfer were strongly asymmetric, with higher values near the outer pipe bend.
In compact heat exchangers, thermal resistance is generally dominant on the air-side and may
account for 80% or more of the total thermal resistance. The air-side heat transfer surface area is 8 to
10 times larger than the water-side. Any improvement in the heat transfer on air-side therefore
improves the overall performance of the heat exchanger. Due to the high thermal resistance on the
air-side, the optimization of such fins is essential to increase the performance of the heat exchangers
which results in thermal systems enhancement. This helps to reduce CO2 emissions through a
reduction of mass and fuel consumption.
Optimization of louvered fin geometry in such heat exchangers is essential to increase the
heat transfer performance and reduce weight, packaging, and cost requirements. In this study deals
with Computational Fluid Dynamics (CFD) studies of the interactions between the air flow and
louvered fins which equipped the automotive heat exchangers is carried out. 3D numerical
simulation results is obtained by using the ANSYS Fluent 14.0 code and compared with
experimental data. Finally the effect of louver angle and louver pitch geometrical parameters, on
overall thermal hydraulic performances of louvered fins is studied.
International Journal of Engineering and Science Invention (IJESI)inventionjournals
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
An Experimental Research on Heat Transfer Enhancement of a Circular Tube with...IRJESJOURNAL
ABSTRACT:- In the literature, internal tube baffles are widely studied. There is a lack of data for baffles mounted on outside of the tubes. This study aims to fill this gap. Therefore, the effect of baffle inclination angles on heat transfer improvement has been studied experimentally. The experiments were carried out for forced convection of air on a circular tube with inclined baffles. Air has been used as the cold fluid. Experimental results for eight different velocities of air flow (2 – 20 m/s) are presented. Pitch between baffles is 12 mm.The baffle inclination angles with respect to the tube axis were 45º, 60º and 80º. Water temperature is fixed as 65 °C. According to the experimental results, the baffles with an inclination angle of 45º enhance the heat transfer over 60º and 80º around 13.7 % and 10.5 %, respectively. However, pressure drop values for 45º and 60º are 18 % higher than pressure drop values for 80º. The empirical correlations of the Nusselt number have also been obtained for each angle.
FLUID FLOW ANALYSIS IN AIR DUCT FLOW WITH AND WITHOUT INTERNAL THREADS USING ...IAEME Publication
Computational heat transfer flow modeling is one of the great challenges in the classical sciences. As with most problems in engineering, the interest in the heat transfer augmentation is increasing due to its extreme importance in various industrial applications. This paper deals with the analysis of heat transfer for fluid flowing through the pipe with and without internal threads using CFD. Using CFD codes for modeling the heat and fluid flow is an efficient tool for predicting equipment performance. CFD offers a convenient means to study the detailed flows and heat exchange processes, which take place inside the tube. Simulations were carried out using commercial CFD software ANSYS Fluent version 14.5. Friction factor and Nusselt number for air flowing through the specified tube (internal diameter = 0.005 m, length = 0.1 m) were obtained first for the plain tube and then for the tube with internal threads with pitch 5mm in the Reynolds number range of 2000 to 5000. Finally results will be compared to available experimental and analytical calculations. The data obtained by simulation are matching with the literature value for a plain tube with the discrepancy of less than plus or minus 5% for Nusselt number and for the friction factor.
Enhanced heat transfer for the tube with internal threads has been observed. Heat flux is more uniform all along the tube and decreases uniformly towards the center.
THERMO HYDRAULICS PERFORMANCE OF TURBULENT FLOW HEAT TRANSFER THROUGH SQUARE ...IAEME Publication
This paper describes the experimental study of square ducts with inserts. Experiments are conducted for air with uniform heat flux condition. The top wall surface is made rough with metal ribs of square section. The roughened wall is uniformly heated and other walls are insulated. The heat transfer coefficient enhances square channel at injection of different inserts. The performance of the geometry under investigation has been evaluated .The heat transfer coefficient of air is increase by 46% than plane square ducts with inserts. The heat transfer and pressure drop measurements have been taken in separate sections .
NATURAL CONVECTION HEAT TRANSFER INSIDE INCLINED OPEN CYLINDERIAEME Publication
Natural convection is investigated experimentally in an inclined open cylindrical passege heated under constant heat flux condition to study the effect of angle of inclination and heat flux on heat transfer. Heat transfer results are given for inclination angles of 0o (horizontal), 30o , 60o and 90o (vertical).Using cylinder diameter of 4.8 cm, cylinder length 50 cm and heat flux from 70 W/m2 to 600 W/m2 . Empirical correlations are given for the average Nusselt number as a function of the
Rayleigh number. The results show that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o (horizontal) to 90o
(vertical). An empirical correlations of average Nusselt number as a function of Rayleigh number were obtained.
NATURAL CONVECTION HEAT TRANSFER IN INCLINED OPEN ANNULUS PASSEGE HEATED FROM...IAEME Publication
Natural convection is investigated experimentally in an open cylindrical annulus heated with both annulus inner and outer sides under same constant heat flux condition to study the effect of angle of inclination and heat flux on heat transfer. Heat transfer results are given for inclination angles of 0o
(horizontal), 30o , 60o and 90o (vertical) using annulus diameter ratio of 1.8, inner and outer tube length 50 cm and heat flux from 70 W/m2 to 600W/m2 . The results show that the local and average Nusselt number increase as the heat flux increase and when angle of inclination changed from 0o
(horizontal) to 90o (vertical).An empirical correlations of average Nusselt number as a function of Rayleigh number were deduced.
A Detailed Review on Artificial Roughness Geometries for Optimizing Thermo-Hy...IJMER
It is well known fact that the heat transfer coefficient between the absorber surface of solar air collector & flowing fluid i.e. air can be improved by providing artificial roughness geometry on heat transfer surface (absorber surface).In this way the Thermal efficiency is increased. But at the same time due to roughness geometry pumping power of solar air collector in increased due to fictional losses in duct. So it necessary to examine the shape, size & flow pattern of various roughness elements to get maximum efficiency with minimum frictional losses. Therefore the selection of roughness geometry has to be based on the parameter that takes into account both Thermal & Hydraulic (friction) performance i.e. Thermo-hydraulic Performance of Solar air collector. Number of roughness elements has been investigated on heat transfer & friction characteristics of solar air collectors. In this paper, reviews of various artificial roughness elements used as passive heat transfer techniques, in order to improve Thermo-hydraulic performance of solar air collectors is reviewed & presented. Correlations developed by various researchers with the help of experimental results for heat transfer & friction factor for solar air collector by taking different roughness geometries are given & these correlations are useful to predict the Thermo-hydraulic performance of solar air collector having roughened ducts. The objective of this paper is also the awareness of effect of various types’ roughness geometries on heat
Convective heat transfer and pressure drop in v corrugatedMohamed Fadl
New energy system development and energy
conservation require high performance heat exchanger, so
the researchers are seeking to find new methods to enhance
heat transfer mechanism in heat exchangers. The objectives
of this study are investigating heat transfer performance
and flow development in V-corrugated channels, numerical
simulations were carried out for uniform wall heat flux
equal 290 W/m
2
using air as a working fluid, Reynolds
number varies from 500 to 2,000, phase shifts,
0 \ Ø \ 180, and channel heights (S = 12.5, 15.0, 17.5
and 20 mm). Governing equations of flow and energy were
solved numerically by using finite volume method. The
numerical results indicated that, wavy (V-corrugated)
channels have a significant impact on heat transfer
enhancement with increase in pressure drop though chan-
nel due to breaking and destabilizing in the thermal
boundary layer are occurred as fluid flowing through the
corrugated surfaces and the effect of corrugated phase shift
on the heat transfer and fluid flow is more significant in
narrow channel, the goodness factor (j/f) was increased
with increasing channel phase shift, the best performance
was noticed on phase shift, Ø = 180 and channel height,
S = 12.5 mm.
Assessment of thermo-hydraulic performance of inward dimpled tubes with varia...CFD LAB
This paper presents a numerical investigation and assessment of thermal and hydraulic performance of dimpled
tubes of varying topologies at constant heat flux of 10 kW m2 and Reynolds numbers ranging from 2300 to
15,000. The performance of the tubes consisting of conical, spherical and ellipsoidal dimples with equivalent
flow volumes were compared using steady state Reynolds Averaged Navier Stokes simulations. The ellipsoidal
dimples, in comparison to other dimple shapes, demonstrated large increment in heat transfer rate. The variation
in the orientation of the ellipsoidal dimples was examined to further improve thermal and hydraulic performances of the tube. A 45° inclination angle of ellipsoidal dimple, from its major axis, increased the thermohydraulic performance by 58.1% and 20.2% in comparison to smooth tube and 0° ellipsoidal dimpled tube,
respectively. Furthermore, Large Eddy Simulations (LES) were carried out to investigate the role geometrical
assistance to fluid flow and heat transfer enhancement for the 45° and 90° ellipsoidal dimpled tubes. LES results
revealed a flow channel of connected zones of wakes which maximized fluid-surface contact and therefore
enhanced the thermal performance of the tube. In addition, correlations for Nusselt number and friction factor
for all angular topologies of ellipsoidal dimpled tube have been proposed.
Experimental Investigation on Heat Transfer Analysis in a Cross flow Heat Ex...IJMER
Heat exchanger is devices used to exchange the heat between two liquids that are at different
temperature .These are used as a reheated in many industries and auto mobile sector and power
plants. The main aim of our project is thermal analysis of heat exchanger with waved baffles for
different types of materials at different mass flow rates and different tube diameters using FLOEFD
software and comparing the results that are obtained. The work is a simplified model for the study of
thermal analysis of shell-and-tubes heat exchangers having water as cold and hot fluid. Shell and
Tube heat exchangers are having special importance in boilers, oil coolers, condensers, pre-heaters.
They are also widely used in process applications as well as the refrigeration and air conditioning
industry. The robustness and medium weighted shape of Shell and Tube heat exchangers make them
well suited for high pressure operations. The project shows the best material, best boundary conditions
and parameters of materials we have to use for better heat conduction. For this we are chosen a
practical problem of counter flow shell and tube heat exchanger having water, by using the data that
come from cfd analysis. A design of sample model of shell and tube heat exchanger with waved baffles
is using Pro-e and done the thermal analysis by using FLOEFD software by assigning different
materials to tubes with different diameters having different mass flow rates and comparing the result
that obtained from FLOEFD software.
Heat transfer studies were carried out in a laboratory scale gas-solid fluidized bed with 0.1m
ID x 1 m length column, using three sizes of local sand particles of 301, 454, and 560 µm. the bed
region was heated bya horizontal heat transfer probe. It was made of copper rod (15 mm ODx50 mm
long) and insulated at the ends by Teflon. A hole was drilled at the center of the rod to accommodate
a cartridge heater 200 W (6.5 mm OD x 42 mm long). Three bed inventories of sand 1.5 kg, 2.0 kg,
and 2.5 kg, four superficial air velocities of 1.0 m/s, 1.25 m/s, 1.5 m/s, 1.75 m/s were used. Three
heat fluxes of 1698.9, 2928.4, 4675.7 W m-2 were employed. The data obtained showed how the heat
transfer coefficient effected by the above operating parameters. The heat transfer coefficient is
directly proportional with air superficial velocity as well as the bed inventory and heat fluxes but
inversely proportional with sand particles size.
NUMERICAL SIMULATION OF FORCED CONVECTION HEAT TRANSFER ENHANCEMENT BY POROUS...IAEME Publication
Pin fins have a variety of applications in industry due to their excellent heat transfer performance, e.g., in cooling of electronic components, in cooling of gas turbine blades, and
recently, in hot water boilers of central heating systems. The forced convective heat transfer in three dimensional porous pin fin channels is numerically studied using ANSYS Fluent. Geometric modelling is done using Design Modeller and CFD Meshing is carried out using ANSYS Meshing Preprocessor. The effects of Reynolds number (Re), pore density (PPI) and pin fin form are studied in detail.
Mixed Convection of Variable Properties Al2O3-EG-Water Nanofluid in a Two-Dim...A Behzadmehr
In this paper, mixed convection of Al2O3-EG-Water nanofluid in a square lid-driven enclosure is investigated numerically. The focus of this study is on the effects of variable thermophysical properties of the nanofluid on the heat transfer characteristics. The top moving and the bottom stationary horizontal walls are insulated, while the vertical walls are kept at different constant temperatures. The study is carried out for Richardson numbers of 0.01–1000, the solid volume fractions of 0–0.05 and the Grashof number of 104. The transport equations are solved numerically with a finite volume approach using the SIMPLER algorithm. The results show that the Nusselt number is mainly affected by the viscosity, density and conductivity variations. For low Richardson numbers, although viscosity increases by increasing the nanoparticles volume fraction, due to high intensity convection of enhanced conductivity nanofluid, the average Nusselt number increases for both constant and variable cases. However, for high Richardson numbers, as the volume fraction of nanoparticles increases heat transfer enhancement occurs for the constant properties cases but deterioration in heat transfer occurs for the variable properties cases. The distinction is due to underestimation of viscosity of the nanofluid by the constant viscosity model in the constant properties cases and states important effects of temperature dependency of thermophysical properties, in particular the viscosity distribution in the domain.
Effect of Thermo-Diffusion and Chemical Reaction on Mixed Convective Heat And...IJERA Editor
A finite element study of combined heat and mass transfer flow through a porous medium in a circular cylindrical annulus with Soret and Dufour effects in the presence of heat sources has been analyzed. The coupled velocity, energy, and diffusion equations are solved numerically by using Galerkin- finite element technique. Shear stress, Nusslet number and Sherwood number are evaluated numerically for different values of the governing parameters under consideration and are shown in tabular form.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
Visualization of Natural Convection in a Vertical Annular Cylinder with a Par...IJERA Editor
In this work, we visualize the effect of varying wall temperature on the heat transfer by supplying the heat at
three different positions to the vertical annular cylinder embedded with porous medium. Finite element method
has been used to solve the governing equations. Influence of Aspect ratio 𝐴𝑟 , Radius ratio 𝑅𝑟 on Nusselt
number 𝑁 𝑢 is presented. The effect of power law exponent effect for different values of Rayleigh number is
discussed. The fluid flow and heat transfer is presented in terms of streamlines and isotherms.
technoloTwo dimensional numerical simulation of the combined heat transfer in...ijmech
A numerical investigation was conducted to analyze the flow field and heat transfer characteristics in a vertical channel withradiation and blowing from the wall. Hydrodynamic behaviour and heat transfer results are obtained by the solution of the complete Navier–Stokesand energy equations using a control volume finite element method. Turbulent flow with "Low Reynolds Spalart-Allmaras Turbulence Model" and radiation with "Discrete Transfer Radiation Method" had been modeled. In order to have a complete survey, this article has a wide range of study in different domains including velocity profiles at different locations, turbulent viscosity, shear stress, suctioned mass flow rate in different magnitude of the input
Rayleigh number, blowing Reynoldsnumber, radiation parameter, Prandtl number, the ratio of length to width and also ratio of opening thickness to width of the channel. In addition, effects of variation in any of the above non-dimensional numbers on parameters of the flow are clearly illustrated. At the end resultants had been compared with experimental data which demonstrated that in the present study, results have a great accuracy, relative errors are very small and the curve portraits are in a great
agreement with real experiments.
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of mechanical and civil engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in mechanical and civil engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
THE STUDY OF THE EFFECTS OF RADIATION AND BLOWING FROM THE WALL OF A VERTICAL...ijmech
This article investigates the effects of radiation and blowing from a wall on a turbulent heat transfer in vertical channels with asymmetrical heating. The equations involved were numerically solved with three turbulent models including SpalartAllmaras, R-N-G k-
with"Standard Wall Function" wall nearby model, R-N-G k- with "Enhanced Wall Treatment" wall nearby model and "Ray Tracing" radiation techniques. The results were compares with experimental data and appropriate methods were selected for turbulent modeling. The problem
of Rayleigh number, Reynolds, radiation parameters and Prandtl were solved and the effects of these parameters on the flow lines, lines of constant temperature, radiation, convection, heat transfer caused by blowing and the total heat transfer were determined.
Similar to Mixed convection heat transferin inclined tubes with constant heat flux (20)
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Mixed convection heat transferin inclined tubes with constant heat flux
1. European Journal of Scientific Research
ISSN 1450-216X / 1450-202X Vol. 97 No 1 February, 2013, pp.144-158
http://www.europeanjournalofscientificresearch.com
Mixed Convection Heat Transfer in Inclined
Tubes with Constant Heat Flux
Ahmed Tawfeeq Ahmed Al-Sammarraie
Mechanical Engineering Department, College of Engineering
University of Tikrit, Tikrit, Iraq
E-mail: ahtawfeeq@gmail.com
Tel: +964 770 3769881
Raaid Rashad Jassem
Mechanical Engineering Department, College of Engineering
University of Tikrit, Tikrit, Iraq
E-mail: rrj5388@gmail.com
Tel: +964 781 0040167
Thamir K. Ibrahim
Mechanical Engineering Department, College of Engineering
University of Tikrit, Tikrit, Iraq
E-mail: thamirmathcad@yahoo.com
Tel: +964 771 1775455
Abstract
Mixed convection heat transfer in inclined tubes of circular cross section has been
experimentally studied for assisting, thermally developing and thermally fully developed
laminar-to-turbulent air flows, under constant wall heat flux boundary condition, at
Reynolds numbers (Re<2300) for the laminar and (2300<Re<4000) for transition-to-
turbulent air flows, and the heat flux is varied from 492 to 1442 W/m2
. The mixed
convection regime has been bounded by the convenient selection of Reynolds number
range and the heat flux range so that the obtained Richardson number (Ri) is varied
approximately from 0.146 to 1.058. The experimental rig consists of three copper tubes as
test section with 600 mm heated length and length to diameter ratio (L/D= 11.8, 15.75 and
31.5). This study has investigated the effect of the heat flux, diameters and inclination
angle of the tube on the mixed convection heat transfer process. In this search, the local
Nusselt numbers (Nu) with the dimensionless axial distance (Z) are presented. The results
have clearly shown that an increase in the Nusselt number values as the heat flux increases
and as the tube inclination angle moves from (θ = 60°) to (θ = 30°), vice versa the Nusselt
number decrease with effect of increase the length to diameter ratio (L/D). For the range of
Reynolds numbers used in experiments, the maximum Nusselt number has occurred at
about 30° inclination relative to the horizon. Present experimental results have a good
agreement with previous results obtained for similarly tubes inclination angles. Based on
the experimental results, the average Nusselt number ( Nu ) has been correlated in an
empirical equation with the effect of the Rayleigh number, Reynolds number, length to
diameter ratio and inclination angle. Good agreement can be seen between the experimental
results and this equation.
2. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 145
Keywords: Mixed Convection Heat Transfer, Constant Heat Flux, Inclined Tube,
Diameter.
1. Introduction
Convection heat transfer for thermally developing air flow in circular ducts is encountered in a wide
variety of thermal engineering applications such as compact heat exchangers, cooling of electronic
equipment, solar collectors, and thermal-energy conversion devices. The performance of these devices
depends on the nature of heat dissipation and the operation modes of the system. In convective heat
transfer problems, the flow that caused by external forces, such as pumps or fans is classified usually
as forced convection, while the convection flows with effect fluid density variations due to the wall to
fluid temperature difference under the influence of body forces are called free convection flows. The
superposition of free convection on the forced convection heat transfer process gives rise to a new field
of study called mixed convection. Therefore, the mixed convection situation extends from the extremes
of the free convection regime on one hand, when the motion results from buoyancy alone, to the forced
convection regime on the other hand, when external forces alone create the motion and buoyancy
forces are insignificant (Mohammed and Salman, 2007).
The interaction of the free and forced convection currents can be extremely complex and
difficult because it depends not-only on all the parameters determining both free and forced convection
relative to one another. An understanding of the various fluid flow and heat exchange processes
enables proficient design of these devices. Therefore, investigate on fluid flow and heat transfer
through circular ducts requires significant attention. The nature of the flow, thermal boundary
conditions and the diameter of the circular duct has a significant impact on the amount of heat energy
transported by the working fluid in a circular duct. Air is a most common working fluid and is
extensively preferred as a medium for cooling of electronic equipments, due to the behavior advantages
of the air and its low cost. The application potential of the inclined of circular ducts underscores the
importance of the study of mixed convection with surface radiation effects (Mohammed and Salman,
2007; Jackson et al, 1989; Yan and Li, 2001).
Comprehensive review of experimental studies has been presented on convection heat transfer
in internal flows (Mohammed and Salman, 2007; Jackson et al, 1989). Experimental study was carried
out to show the behavior of convection flow in a channel heated from one side wall (Gau et al, 2000;
Yang et al, 2009). Convection laminar flow between parallel plates heated uniformly from below was
investigated (Maughan and Incropera, 1987; Maughan and Incropera, 1990), and correlations were
predicted for the fully developed Nusselt numbers and the locations of the inception of secondary flow.
Many researchers (Mohammed and Salman, 2007; Chang and Lin, 1997; Dogan et al, 2005) performed
extensive experimental studies on bottom heated horizontal ducts, horizontal circular cylinders, aspect
ratio effects in a horizontal duct, hydrodynamically and thermally developed flow in a horizontal
circular cylinder and a rectangular channel with separate heat sources.
Iqbal and Stachiewicz (1966) performed a theoretical analysis for fully developed upward
laminar flow inside circular tube with constant wall heat flux and constant pressure gradient. The
temperature, velocity, and Nusselt number were calculated by perturbation analysis. It was concluded
that as the tube inclination varies from horizontal to vertical, Nusselt number increases up to a
maximum value, which may occur before the vertical position is reached. Cheng and Hong (1973)
applied a numerical solution using a combination of boundary vorticity method and line iterative
relaxation method for upward fully developed laminar flow in tube subjected to thermal boundary
conditions of axially uniform wall heat flux and peripherally uniform wall temperature at any axial
position. The results showed that, in high Rayleigh number regime, the tube orientation effect had a
significant effect on the results in the neighborhood of horizontal position. Sabbagh et al (1976)
introduced experimental study for developing air flow in an inclined circular tube with uniform
peripheral temperature and axial wall heat flux. The variation of the Nusselt number with tube
inclination angles had been compared with a theoretical study done by (Iqbal and Stachiewicz, 1972),
at low Rayleigh numbers and low Reynolds numbers.
3. 146 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
Mare et al (2005) numerically solved, the elliptical coupled steady state three-dimensional
governing partial differential equations for heated ascending laminar mixed convection in an inclined
isothermal tube using a finite volume staggered grid approach, to determine the axial evolution of the
hydrodynamic, thermal fields and investigate the presence of flow reversal. The effect of Grashof
number on the axial evolution of the wall shear stress and Nusselt number was shown to be very
important in the region of developing flow. The results had been calculated for one Reynolds number
(Re = 100), a single fluid (air), and one tube inclination 45o
. Mohammed and Salman (2007) conducted
an experimental study for the local and average heat transfer by mixed convection for
hydrodynamically fully developed, thermally developing and thermally fully developed laminar air
flow in an inclined circular cylinder. The results of surface temperature, the local and average Nusselt
number distributions with the dimensionless axial distance were presented. For all entrance sections,
the results showed an increase in the Nusselt number values as the heat flux increases and as the angle
of cylinder inclination moves from θ = 60o
inclined cylinder to θ = 0o
horizontal cylinder. Mohammed
and Salman (2009) investigated experimentally the effect of different inlet geometries on laminar air
flow combined convection heat transfer inside a horizontal circular pipe. A wall boundary heating
condition of a constant heat flux was imposed. It was observed that, the Nusselt number values for
bell-mouth inlet geometry were higher than other inlet geometries due to the differences in the average
temperatures and densities of the air. The average heat transfer results were correlated with an
empirical correlation in terms of dependent parameters.
2. Object of Study
The purpose of the present study is to determine experimentally the effects of heat flux, tube
inclination angles with the horizon and tubes diameters on the laminar-to-turbulent air flows heat
transfer process, under mixed heat convection for assisting, thermally developing and thermally fully
developed air flows situation in uniformly heated an inclined circular tube angle (30o
, 45o
and 60o
) and
for different values of diameters (0.75, 1.5 and 2 inch).
3. Experimental Work
Published works on mixed convection heat transfer in inclined circular cross-section tubes dating to
1966, when Iqbal and Stachiewicz (1966) used perturbation analysis to calculate velocity and
temperature fields for laminar, fully-developed, upward flow and uniform heat flux. Since then, the
problem has been investigated experimentally by several research groups, but the published results
cover a rather limited range of the independent parameters. The literature contains a comparable
number of numerical studies, but once again, they are far from being exhaustive. The heat transfer by
mixed convection is represented an important form of the convection heat transfer. An experimental
test model accomplishes to measure the mixed convection in circular inclined ducts with different
angles (30o
, 45o
and 60o
) heated with a constant heat flux.
The experimental rig is shown photographically in Figure (1) and schematically in Figure (2). It
consists mainly of three copper tubes which were used in this study, they have internal diameters of
(19.05, 38.1 and 50.8 mm) with wall thickness (2 mm). The length was (1000 mm) for each tube, but
the active heated length (test section) only is (600 mm). The tubes were provided with air by a blower
operates at (2500 rpm and AC 220 V).
For each tube, surface temperatures were measured by (12) thermocouples (T type), which were
positioned along the test section in the rate of one thermocouple for each location. Also, one
thermocouple was used to measure the inlet air temperature which was located in the entrance of each
tube, another one was located at the end of each tube to measure the outlet air temperature so that it
was positioned in the same pervious way. Another thermocouple measures the laboratory ambient
temperature.
4. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 147
In each tube, the test section was heated electrically using nickel-chrome wire with appropriate
resistance for each tube diameter, it was electrically isolated by ceramic beads, and the wire was
wounded uniformly along it as a coil in order to give uniform wall heat flux. The test section was
thermally insulated with fiber glass of (100 mm) in thickness. The two ends of each tube were
insulated electrically and thermally using two pieces made of Teflon, also they were used to reduce the
thermal losses in the axial direction. The entrance sector was packed to be insuring to get
hydrodynamically fully developed before the test section.
The heater was supplied with an alternative electrical power using voltage regulator (0 - 220 V)
that supplied with a steady voltage through a stabilizer. The current pass through the heater and the
voltage across both its ends were measured by a digital ammeter and an accurate voltmeter,
respectively. Digital Anemometer was used to measure the velocity of entering air to the test section.
Figure 1: Photo of the experimental rig. Figure 2: Schematic drawing for the test rig including
the test sections.the test sections.
1. Blower
2. Air control valve
3. Fiber glass
4. Thermal resistance
5. Copper tube
6. Thermal insulator
7. Adjusting angular position
8. Base
9. Steel stand
The primary purpose of the test is to demonstrate the impact of heat flux, tube inclination
angles and tubes diameters on mixed convection heat transfer through the test section. The procedure
for that can be listed as follow:
1. In the beginning of any test, is determined the tube and its inclination angle with the
horizon.
2. The air blower is turned on in order to supply the test section by the required amount of the
air, which can be controlled using the control valve that shown in Figure (2). Waiting for
few minutes to ensure that the hydrodynamic homogeneity state within test section is
achieved.
3. Supply an elected electrical power to the electric heater by the voltage regulator and
consequently obtained the amount of heat to be supplied to the test section.
4. The test rig is left for enough time (40- 45) minutes until accessing the steady state.
5. Then, the readings are taken for: the internal surface temperatures along the test section
( szT ), the inlet and outlet and ambient air temperature ( aoi TTT ,, ), the amount of voltage
(V ) and the current ( I ), and outlet air velocity (U ) which it fixed at a constant value in
the present work.
6. After that, the electrical power supplied to the heaters is altered with another amount
through the voltage regulator and the process is repeated again.
5. 148 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
4. Calculation Procedures
The results obtained were reduced from the present experimental work -for each tube diameter- in
terms of local Nusselt number (Nu) with the dimensionless axial distance (Z=z/L), as a function of the
tube inclination angle (θ ) at constant wall heat flux boundary condition. Then, the total input power
supplied to the test section can be calculated using the following equation:
tQ V I= × (1)
The convection heat transferred from the test section surface:
.. condtconv QQQ −= (2)
where .condQ are the total conduction heat losses (lagging and ends losses).
The convection heat flux can be represented by:
.
.
conv
conv
s
Q
q
A
= (3)
where sA is the surface area ( LDAs ××= π ), D is the test section diameter, and L it is length.
The local heat transfer coefficient (hz) was calculated by the following equation:
bzsz
conv
z
TT
q
h
−
= .
(4)
where szT is the local surface temperature, and bzT is the local bulk air temperature which can be
evaluated as reported by (Peyghambarzadeh, 2011):
.conv
bz i
P
q D
T T z
mC
π
= + (5)
where m is the air mass flow rate ( )4/( 2
DUm πρ= ).
The local Nusselt number (Nu) can be determined as:
z
fz
h D
Nu
k
= (6)
where fzk is the local film air thermal conductivity, which can be evaluated at the local film air
temperature. Then, the local film air temperature ( fzT ) is presented by:
2
sz bz
fz
T T
T
+
= (7)
The average values of Nusselt number ( Nu ) can be calculated based on the calculated average
surface temperature, average bulk air temperature and average film air temperature ( fT ) as follows:
∫
=
=
=
Lz
z
szs dzT
L
T
0
1
,
0
1
2
z L
i o
b bz
z
T T
T T dz
L
=
=
+
= =∫ , and
2
s b
f
T T
T
+
= (8)
then:
.
( )
conv
s b
hD q D
Nu
k k T T
×
= =
−
(9)
The average values of the other parameters can be calculated as follows:
Reynolds number: Re
UDρ
µ
= (10)
Grashof number:
3
2
( )s bg T T D
Gr
β
υ
−
= (11)
where g is the acceleration of gravity (9.81 m/s2
) and
1
( 273)fT
β =
+
Rayleigh number: PrRa Gr= × (12)
6. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 149
Richardson number: 2
Re
Gr
Ri = (13)
All the air physical properties ( ,,,,, υµρ kCP and Pr) were evaluated at the film air temperature
as reported by (Incropera and DeWitt, 2003).
Kline and McClintock method (Holman, 2012) was used for the experimental error analysis of
heat transfer coefficient (Nusselt number), Reynolds number, Grashof number, Rayleigh number and
Richardson number. The error was limited between (2%) to (11%) for all experimental data.
5. Results and Discussion
Mixed convection heat transfer from inclined tubes of circular cross section under constant heat flux
condition has been studied. The effects of three different parameters: heat flux, inclination angles of the
tube and tube diameter on the mixed convection heat transfer from the internal surface of the tube were
investigated. To investigate steady state mixed convection heat transfer represented by Richardson
number ( Ri ) bounded by the range of ( 101.0 << Ri ) through inclined tubes at Reynolds number
(Re<2300) for the laminar and (2300<Re<4000) for transition-to-turbulent air flows under thermally
developing and thermally fully developed air flows, an experimental rig was constructed.
The obtained Richardson numbers (Ri) from this study is varied approximately from 0.146 to
1.058. This range means that the mixed convection regime has been bounded by the suitable selection
of the Reynolds number range (the air flow rate) and the Grashof number range (the input power) in
the current study.
In the present work, Figures from (3) to (11) were represented the results in terms of local
Nusselt number (Nu) with the dimensionless axial distance (Z):
a. Figures (3, 4, 5) highlights the influence of the heat flux on heat transfer from certain tube
diameter - 0.75 in (L/D = 31.5), 1.5 in (L/D = 15.75), or 2 in (L/D = 11.8) - at various
inclination angles ( ooo
60,45,30=θ ).
b. Figures (6, 7, 8) highlights the influence of the inclination angle on heat transfer from
certain tube diameter - 0.75 in (L/D = 31.5), 1.5 in (L/D = 15.75), or 2 in (L/D = 11.8) - at
various heat fluxes (492, 752, 1016, 1448 W/m2
).
c. Figures (9, 10, 11) highlights the influence of the tube diameter on heat transfer from
certain inclination angles ( ooo
or60,45,30=θ ) at various heat fluxes (492, 752, 1016,
1448 W/m2
).
For all these Figures, it is obvious that the local Nusselt number values decreased with increase
of the dimensionless axial distance of the tube. This reveals that the local Nusselt number near the inlet
of the tube heated region (test section) are very high values because the thickness of the thermal
boundary layer is zero, and it decreases continuously due to the thermal boundary layer develops and
then near the exit of the tube heated region the local Nusselt number values slightly increases due to
the laminarization effect in the near wall region (buoyancy effect) and tube end losses.
Regarding Figures (3, 4 and 5), it is noticed that the local Nusselt number values increased with
increase of the heat flux for all length to diameter ratios (tested tubes diameters) at various inclination
angles. This is due to the fact that, the increase in the heat flux leads to increase the energy added to the
fluid flowing through the test section, and it may be attributed to the secondary flow superimposed on
the forced flow which its effect increase as the heat flux increases leading to a higher heat transfer
coefficient, also due to the free convection currents domination on the heat transfer process. This result
was consistent with the results that reported by (Mohammed and Salman, 2007; Mohammed and
Salman, 2009).
7. 150 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
Figure 3: The relation between local Nusselt number and the dimensionless axial distance for heat fluxes of
the ratio (L/D = 31.5) at various inclination angles (a, b, c).
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
Inclined 45
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(3b)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
Inclined 60
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(3c)
2
2
2
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
Inclined 30
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
(3a)
Figure 4: The relation between local Nusselt number
and the dimensionless axial distance for
heat fluxes of the ratio (L/D = 15.75) at
various inclination angles (a, b, c).
Figure 5: The relation between local Nusselt number
and the dimensionless axial distance for
heat fluxes of the ratio (L/D = 11.8) at
various inclination angles (a, b, c).
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
Inclined 30
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(4a)
2
2
2
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
Inclined 30
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
(5a)
8. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 151
Figure 4: The relation between local Nusselt number
and the dimensionless axial distance for
heat fluxes of the ratio (L/D = 15.75) at
various inclination angles (a, b, c). -
continued
Figure 5: The relation between local Nusselt number
and the dimensionless axial distance for
heat fluxes of the ratio (L/D = 11.8) at
various inclination angles (a, b, c). -
continued
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
15
25
35
45
10
20
30
40
Nu
Inclined 45
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(4b)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
25
35
45
55
20
30
40
50
60
Nu
Inclined 45
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(5b)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
Inclined 60
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(4c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
Inclined 60
q=1448 W/m
q=1016 W/m
q=752 W/m
q=492 W/m
2
2
2
2
(5c)
As for Figures (6, 7 and 8), it is clear that the local Nusselt number values increased with
decrease of the inclination angle values for all length to diameter ratios (tested tubes diameters) at
various heat fluxes. In more detail, it is noticed from the Figures the higher local Nusselt number has
occurred with tube inclination angle (30o
) and its lower value has appeared with tube inclination angle
(60o
). It was because that the increase of inclination angle led to increase the impact of buoyancy force
on the fluid flow through the mixed convection heat transfer condition ( 101.0 << Ri ). This
remarkable buoyancy effect causes an obstruction fluid flow in the tube and reducing the fluid
discharge slightly. In addition, growth the backward flow cause increased the time that necessary to
absorb the heat from the tube by the fluid flowing inside it. In other words, the local Nusselt number
values increased as the inclination angle moves toward to the horizon due to the increase of the
secondary flow, which enhances the heat transfer process.
9. 152 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
Figure 6: The relation between local Nusselt number and the dimensionless axial distance for inclination
angles of the ratio (L/D = 31.5) at various heat fluxes (a, b, c, d).
(6a) 2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
q=492 W/m
Inclined 30
Inclined 45
Inclined 60
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
q=752 W/m
Inclined 30
Inclined 45
Inclined 60
2
(6b)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
q=1016 W/m
Inclined 30
Inclined 45
Inclined 60
2
(6c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
10
20
30
Nu
q=1448 W/m
Inclined 30
Inclined 45
Inclined 60
2
(6d)
Figure 7: The relation between local Nusselt number and the dimensionless axial distance for inclination
angles of the ratio (L/D = 15.75) at various heat fluxes (a, b, c, d).
(7a)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
q=492 W/m
Inclined 30
Inclined 45
Inclined 60
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
q=752 W/m
Inclined 30
Inclined 45
Inclined 60
2
(7b)
10. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 153
Figure 7: The relation between local Nusselt number and the dimensionless axial distance for inclination
angles of the ratio (L/D = 15.75) at various heat fluxes (a, b, c, d). - continued
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
q=1016 W/m
Inclined 30
Inclined 45
Inclined 60
(7c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
10
20
30
40
Nu
q=1448 W/m
Inclined 30
Inclined 45
Inclined 60
2
(7d)
Figure 8: The relation between local Nusselt number and the dimensionless axial distance for inclination
angles of the ratio (L/D = 11.8) at various heat fluxes (a, b, c, d).
angles of the ratio (L/D = 11.8) at various heat fluxes (a, b, c, d).
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
q=492 W/m
Inclined 30
Inclined 45
Inclined 60
2
(8a)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
q=752 W/m
Inclined 30
Inclined 45
Inclined 60
2
(8b)
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
q=1016 W/m
Inclined 30
Inclined 45
Inclined 60
(8c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
25
35
45
55
20
30
40
50
60
Nu
q=1448 W/m
Inclined 30
Inclined 45
Inclined 60
2
(8d)
11. 154 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
From Figures (9, 10 and 11), it is evident that the local Nusselt number values increased with
increase of the tube diameter (with decrease the length to diameter ratio) for all inclination angles at
various heat fluxes, i.e., the higher local Nusselt number value is observed at tube diameter (2 in
(L/D=11.8)) while the lower value is noticed at tube diameter (0.75 in (L/D=31.5)). It is because that
the increased of the tube diameter -with fixed values of tube length, heat flux and inclination angle of
the tube- cause increased the heat transfer surface area between the tube inner surface and the fluid
flowing through it. So this increase of the heat exchange surface gave the flowing fluid a good
opportunity to contact with tube inner surface, and then increased the heat transfer process. On the
other hand, this increase for the tube diameter -with fixed all other values- leads to increase of
Reynolds numbers which leading to the transformation in the flow from the laminar at (L/D=31.5),
transition-to-turbulent at (L/D = 15.75) and turbulent at (L/D=11.8), respectively. The transformation
in the shape of flow from laminar to turbulent is a significant effect in increasing the rate of heat
transfer from the heat exchange surface. So this influence was clear on the results of the current study.
Figure 9: The relation between local Nusselt number and the dimensionless axial distance for all tubes
diameters at inclination angle ( o
30=θ ) at various heat fluxes (a, b, c, d).
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
55
10
20
30
40
50
60
Nu
q=752 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(9b)(9a)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
55
10
20
30
40
50
60
Nu
q=492 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(9c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
55
10
20
30
40
50
60
Nu
q=1016 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(9d)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
15
25
35
45
55
10
20
30
40
50
60
Nu
q=1448 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
12. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 155
Figure 10: The relation between local Nusselt number and the dimensionless axial distance for all tubes
diameters at inclination angle ( o
45=θ ) at various heat fluxes (a, b, c, d).
(10a)
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
55
10
20
30
40
50
Nu q=492 W/m
L/D=11.8
L/D=15.75
L/D=31.5
(10b)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
55
10
20
30
40
50
Nu
q=752 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(10d)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
55
10
20
30
40
50
Nu
q=1448 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(10c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
55
10
20
30
40
50
Nu
q=1016 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
Figure 11: The relation between local Nusselt number and the dimensionless axial distance for all tubes
diameters at inclination angle ( o
60=θ ) at various heat fluxes (a, b, c, d).
diameters at inclination angle ( 60=θ ) at various heat fluxes (a, b, c, d).
(11a)
2
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
10
20
30
40
Nu
q=492 W/m
L/D=11.8
L/D=15.75
L/D=31.5
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
10
20
30
40
Nu
q=752 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(11b)
13. 156 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
Figure 11: The relation between local Nusselt number and the dimensionless axial distance for all tubes
diameters at inclination angle ( o
60=θ ) at various heat fluxes (a, b, c, d). - continued
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
10
20
30
40
Nu
q=1016 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(11c)
7 8 9 2 3 4 5 6 7 8 9
0.1 1.0
Z
5
15
25
35
45
10
20
30
40
Nu
q=1448 W/m
L/D=11.8
L/D=15.75
L/D=31.5
2
(11d)
An empirical formula was extracted for the experimental data of mixed convection heat transfer
with the effective parameters on this process. The least squares fitting method was used for this
purpose. The average heat transfer from any tested tube was represented by average Nusselt number
( Nu ) as a function of the Rayleigh number to Reynolds number ratio (Ra/Re), length to diameter ratio
(L/D) and the tube inclination angle with the horizon (θ ). The correlating equation can be expressed
as:
( ) ( )/ Re / (1 cos )
b c d
Nu a Ra L D θ= + (14)
Where a, b, c, and d represented the experimental constants, it can be calculated by applied the
least squares fitting method on the experimental results. The experimental constants were calculated
from this method, and it was as follows:
a = 19.59, b = 0.174, c = -0.567, d = 1.286
Therefore, the general formula of the equation that used to calculate the mixed convection heat
transfer for all tested tubes is expressed as:
( ) ( )
0.174 0.567 1.286
19.59 / Re / (1 cos )Nu Ra L D θ
−
= + , at
30 60
11.8 / 31.5
o o
L D
θ ≤ ≤
≤ ≤
(15)
Figure (12) shows the relationship between heat transfer results and their own correlating
equation for all the tubes diameters at all inclination angles. It is obvious that, there is a good
agreement between the experimental data and correlating equation.
The graphical presentation of predicted results versus experimental data of the average values
of Nusselt number is presents in Figure (13). It is clear that, for thirty six reading points that (89%) of
these points are located within the deviation range of ( %15± ) from the correlating equation and this
shows how the compatibility was good between this formula and the experimental results.
14. Mixed Convection Heat Transfer in Inclined Tubes with Constant Heat Flux 157
Figure 12: The relation between heat transfer results
and their own correlating equation for all
the tubes diameters at all inclination
angles.
Figure 13: The comparison between measured
Nusselt number and calculated Nusselt
number from correlating equation.
4.5 5.5 6.5 7.5 8.5
4 5 6 7 8 9
ln (Ra/Re)
4.5
5.5
6.5
7.5
8.5
4
5
6
7
8
9
ln(Nu)
-15%
+15%
5 15 25 35 45
10 20 30 40
Nu (Measured)
5
15
25
35
45
10
20
30
40
Nu(Correlated)
6. Summary and Concluding Remarks
Mixed convection heat transfer in uniformly heated inclined circular tubes for assisting air flow with
different diameters and same sections length, under constant wall heat flux, has been experimentally
studied. The conclusions of results were summarized as follows:
1. The mixed convection regime has been bounded by the suitable selection of Reynolds
number range and the heat flux range. The obtained Richardson numbers is varied
approximately from 0.146 to 1.058.
2. The local Nusselt number values decreased along the tube test section as a result of thermally
developing process along it.
3. For the same inclination angle and length to diameter ratio, the local Nusselt number values
increased as the heat flux increases.
4. For the same heat flux and length to diameter ratio, the local Nusselt number values
increased as the tube inclination angle moves from =60° toward =30°. The maximum and
minimum amount of heat transfer occurs at about =30° and =60° from the horizontal axis,
respectively.
5. For the same heat flux and tube inclination angle, the local Nusselt number values decreased
as the length to diameter ratio increases.
6. A correlating equation for assisting flow, Eq. (15), has been derived to evaluate the average
Nusselt number in terms of Rayleigh number, Reynolds number, length to diameter ratio and
the tube inclination angle, with overall accuracy in order of (±15%).
7. Mixed convection heat transfer results have been compared with available literature and
showed satisfactory agreement.
Acknowledgements
The authors would like to thank University of Tikrit for providing laboratory facilities and financial
support.
15. 158 Ahmed Tawfeeq Ahmed Al-Sammarraie, Raaid Rashad Jassem and Thamir K. Ibrahim
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