Ludwig Prandtl contributed significantly to transport phenomena and boundary layer concepts. He introduced the boundary layer concept to study turbulent flow, modified the Navier-Stokes equations to fit boundary layers, defined the Prandtl number as the ratio of thermal to momentum diffusivity which determines relative boundary layer thicknesses, proposed the mixing length theory which uses a mixing length to model Reynolds stress similar to the mean free path of molecules, and collaborated with von Karman on the universal logarithmic velocity distribution for flow in the inertial sublayer.
Dimensionless number in chemical engineering Hardi Trivedi
Dimensionless number are the key parameter used in major designing parameter and understanding of the behavior of the fluid, heat and mass transfer. Heat transfer, Mass transfer and Fluid mechanics are major subject for the designing purpose also the understanding of chemical engineering and this dimensionless number are helps to determine the behavior, basic understanding of the system. In advanced software of chemical engineering, Dimensionless number play major role for the simulation , optimization of the chemical plant and their design.
Dimensionless number in chemical engineering Hardi Trivedi
Dimensionless number are the key parameter used in major designing parameter and understanding of the behavior of the fluid, heat and mass transfer. Heat transfer, Mass transfer and Fluid mechanics are major subject for the designing purpose also the understanding of chemical engineering and this dimensionless number are helps to determine the behavior, basic understanding of the system. In advanced software of chemical engineering, Dimensionless number play major role for the simulation , optimization of the chemical plant and their design.
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.
Radiation and Mass Transfer Effects on MHD Natural Convection Flow over an In...IJMER
A numerical solution for the unsteady, natural convective flow of heat and mass transfer along an inclined plate is presented. The dimensionless unsteady, coupled, and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields have been studied for the effect of Magnetic parameter, buoyancy ratio parameter, Prandtl number, radiation parameter and Schmidt number. The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically.
A Computational Study Of Heat Transfer Due To The Inlet Oscillating Condition...theijes
Heat transferis numerically investigated in aconfined oscillating laminar slot jet. The inlet velocity profile is uniform, and oscillating with an angle φ (in radians) as follows:휑 = 휑푚푎푥 ∗ 푠푖푛(2휋푓푡).φmax is the maximum jet angle, and f is the frequency of oscillation. The height-to-jet-width ratio was set to 5, the fluid’s Prandtl number is 0.74 and Reynolds number was fixed at 250.Strouhal’s numberSt, which is the other dimensionless group characterizing this problem, was varied in the range 0.05<st><0.75.The jet hydraulic diameter (2w), was used in the definition of both Strouhal and Reynolds numbers. φmax was defined, based on a solid finding presented later in this paper. At St=0.4, and 0.5, a modest enhancement of heat transfer was noticed in the stagnation region, when compared to a steady jet
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.
Radiation and Mass Transfer Effects on MHD Natural Convection Flow over an In...IJMER
A numerical solution for the unsteady, natural convective flow of heat and mass transfer along an inclined plate is presented. The dimensionless unsteady, coupled, and non-linear partial differential conservation equations for the boundary layer regime are solved by an efficient, accurate and unconditionally stable finite difference scheme of the Crank-Nicolson type. The velocity, temperature, and concentration fields have been studied for the effect of Magnetic parameter, buoyancy ratio parameter, Prandtl number, radiation parameter and Schmidt number. The local skin-friction, Nusselt number and Sherwood number are also presented and analyzed graphically.
A Computational Study Of Heat Transfer Due To The Inlet Oscillating Condition...theijes
Heat transferis numerically investigated in aconfined oscillating laminar slot jet. The inlet velocity profile is uniform, and oscillating with an angle φ (in radians) as follows:휑 = 휑푚푎푥 ∗ 푠푖푛(2휋푓푡).φmax is the maximum jet angle, and f is the frequency of oscillation. The height-to-jet-width ratio was set to 5, the fluid’s Prandtl number is 0.74 and Reynolds number was fixed at 250.Strouhal’s numberSt, which is the other dimensionless group characterizing this problem, was varied in the range 0.05<st><0.75.The jet hydraulic diameter (2w), was used in the definition of both Strouhal and Reynolds numbers. φmax was defined, based on a solid finding presented later in this paper. At St=0.4, and 0.5, a modest enhancement of heat transfer was noticed in the stagnation region, when compared to a steady jet
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Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
2. Boundary Layers
• Introduced the concept of boundary layer to study turbulent
flow
• Modified Navier-Stokes equations to fit boundary layer
conditions
3. Prandtl number
• Ratio of thermal diffusivity to momentum
diffusivity
• Relative thickness of heat and momentum
boundary layers
4.
5. Mixing Length
• An expression for Reynold’s stress
• Compared an elemental fluid mass to gas
molecule defined by kinetic theory of gases
• Mixing length is the average length travelled
by a fluid element for which it retains its
properties
