scholarly journals Effect of Variable Thermal Conductivity on Buoyant Convection in a Cavity with Internal Heat Generation

2007 ◽  
Vol 12 (1) ◽  
pp. 113-122 ◽  
Author(s):  
S. Sivasankaran
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Study ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Governing Equations ◽  
Heat Transfer Characteristics ◽  
Square Cavity ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

A numerical study has been made to analyze the effects of variable thermal conductivity on the natural convection of heat generating fluids contained in a square cavity with isothermal walls and the top and bottom perfectly insulated surfaces. The flow is assumed to be two-dimensional. Calculations are carried out by solving governing equations for different parameters. The flow pattern and the heat transfer characteristics inside the cavity are presented in the form of steady-state streamlines, isotherms and velocity profiles. The heat transfer rate is increased by an increase in the thermal conductivity parameter.

Flow and Heat Transfer of Powell–Eyring Fluid due to an Exponential Stretching Sheet with Heat Flux and Variable Thermal Conductivity

2015 ◽  
Vol 70 (3) ◽  
pp. 163-169 ◽  
Author(s):  
Ahmed M. Megahed
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Flux ◽  
Differential Equations ◽  
Variable Thermal Conductivity ◽  
Physical Parameters ◽  
Flow And Heat Transfer ◽  
Non Linear ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

AbstractAn analysis was carried out to describe the problem of flow and heat transfer of Powell–Eyring fluid in boundary layers on an exponentially stretching continuous permeable surface with an exponential temperature distribution in the presence of heat flux and variable thermal conductivity. The governing partial differential equations describing the problem were transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the shooting method over the entire range of physical parameters. The effects of various parameters like the thermal conductivity parameter, suction parameter, dimensionless Powell–Eyring parameters and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. In this work, special attention was given to investigate the effect of the thermal conductivity parameter on the velocity and temperature fields above the sheet in the presence of heat flux. The numerical results were also validated with results from a previously published work on various special cases of the problem, and good agreements were seen.

scholarly journals Electrically Conducting Flow through Exponential Power Law Fluid with Variable Thermal Conductivity

2019 ◽  
Vol 24 (3) ◽  
pp. 539-548
Author(s):  
M. Ferdows ◽  
M.Z.I. Bangalee ◽  
D. Liu
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Thermal Conductivity ◽  
Variable Thermal Conductivity ◽  
Skin Friction Coefficient ◽  
Momentum Equation ◽  
Electrically Conducting ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Exponential Power

Abstract The problem of exponential law of steady, incompressible fluid flow in boundary layer and heat transfer are studied in an electrically conducting fluid over a semi-infinite vertical plate assuming the variable thermal conductivity in the presence of a uniform magnetic field. The governing system of equations including the continuity equation, momentum equation and energy equation have been transformed into nonlinear coupled ordinary differential equations using appropriate similarity variables. All the numerical and graphical solutions are obtained through the use of Maple software. The solutions are found to be dependent on three dimensionless parameters including the magnetic field parameter M, thermal conductivity parameter β and Prandtl number Pr. Representative velocity and temperature profiles are presented at various values of the governing parameters. The skin-friction coefficient and the rate of heat transfer are also calculated for different values of the parameters.

Analysis of Nonlinear Heat Transfer in Solids of Various Geometries with Variable Thermal Conductivity and Heat Source

2017 ◽  
Vol 377 ◽  
pp. 1-16
Author(s):  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solutions ◽  
Heat Generation ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Power Law Function

In this paper we consider heat transfer in a hot body with different geometries. Here, the thermal conductivity and internal heat generation are both temperature-dependent. This assumption rendered the model considered to be nonlinear. We assume that thermal conductivity is given by a power law function. We employ the preliminary group classification to determine the cases of internal heat generation for which the principal Lie algebra extends by one. Exact solutions are constructed for the case when thermal conductivity is a differential consequence of internal heat generation term. We derive the approximate numerical solutions for the cases where exact solutions are difficult to construct or are nonexistent. The effects of parameters appearing in the model on temperature profile are studied.

A Numerical Study of Unsteady Mixed Convection in a Square Cavity: Transition From Laminar to Turbulent Flow

2013 ◽  
Author(s):  
K. M. Akyuzlu
Keyword(s):  
Heat Transfer ◽  
Mixed Convection ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Numerical Study ◽  
Working Fluid ◽  
Heat Transfer Characteristics ◽  
Square Cavity ◽  
Transfer Characteristics ◽  
Unsteady Mixed Convection

A study was conducted to simulate the circulation patterns and heat transfer characteristics of flows in a square cavity during transition from laminar to turbulent mixed convection conditions using numerical techniques. The cavity under study is assumed to be filled with a compressible fluid. The bottom of the cavity is insulated and stationary where as the top of the cavity (the lid) is assumed to be stationary initially and then pulled at constant speed for times greater than zero. The vertical walls of the cavity are kept at constant but unequal temperatures. A two-dimensional, physics based mathematical model is adopted to predict the momentum and heat transfer inside this rectangular cavity. A standard two equation turbulence model is used to model the turbulent flow inside the enclosure and the compressibility of the working fluid is represented by an ideal gas relation. The numerical solution techniques adopted in this study is a hybrid one (implicit-explicit) where the conservation equations for the velocity, temperature, and pressure are solved using an implicit technique (Coupled Modified Strongly Implicit Procedure -CMSIP) whereas the equations for the standard K-ε turbulence model are solved using an explicit (MacCormack) technique. In both techniques, a second order accurate finite difference technique is used to discretize the governing equations. Then numerical experiments were carried out to simulate the unsteady flow and heat transfer characteristics of mixed convection flow inside a square cavity filled with air (Pr = 0.72) for different Richardson numbers in the range of 0.00868–0.03470; corresponding to Reynolds numbers ranging from 2000 to 4000, respectively, when the Rayleigh number was kept constant at 105. Vertical and horizontal temperature and velocity profiles were generated while the flow goes through transition from laminar to turbulent. Changes in wall heat flux were calculated and average Nusselt numbers were determined for each parametric study.

scholarly journals Two dominant analytical methods for thermal analysis of convective step fin with variable thermal conductivity

2014 ◽  
Vol 18 (2) ◽  
pp. 431-442 ◽  
Author(s):  
Mohsen Torabi ◽  
Hessameddin Yaghoobi
Keyword(s):  
Thermal Conductivity ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Transformation Method ◽  
Variable Thermal Conductivity ◽  
Step Change ◽  
Homotopy Perturbation ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter ◽  
Accurate Numerical Solution

Heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by convection to its surroundings is developed via differential transformation method (DTM) and variational iteration method (VIM). In this study, we compare DTM and VIM results, with those of homotopy perturbation method (HPM) and an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM and HPM. After these verifications the effects of parameters such as thickness ratio, ?, dimensionless fin semi thickness,?, length ratio, ?, thermal conductivity parameter, ?, Biot number, Bi, on the temperature distribution are illustrated and explained.

scholarly journals Numerical Study of the Turbulent Natural Convection in a Trapezoidal Cavity: Influence of the Inclination of the Lateral Walls

2020 ◽  
Vol 14 ◽  
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Numerical Study ◽  
Boussinesq Approximation ◽  
Governing Equations ◽  
Square Cavity ◽  
Turbulent Natural Convection ◽  
Side Walls ◽  
Volume Method ◽  
Calculation Code

In this paper, we study the heat transfer in turbulent natural convection in a two- dimensional cavity with a trapezoidal section and isoscales filled out of air with as height H =2.5 m. In these conditions, the side walls are differentially heated while the horizontal walls are adiabatic. The k-ε turbulence model with a small Reynolds number was integrated in our calculation code. The governing equations of the problem were solved numerically by the commercial CFD code Fluent; which is based on the finite volume method and the Boussinesq approximation. The elaborated model is validated from the experimental results in the case of the turbulent flow in a square cavity. Then, the study was related primarily to the influence of the slope of the side walls of the cavity on the dynamic behavior and the heat transfer within the cavity.

Analysis of a Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity

2020 ◽  
Vol 21 (3-4) ◽  
pp. 379-388
Author(s):  
Partner L. Ndlovu ◽  
Raseelo J. Moitsheki
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Dissipation ◽  
Surrounding Medium ◽  
Physical Parameters ◽  
Nonlinear Boundary Value Problems ◽  
Temperature Dependent ◽  
Transform Method ◽  
Thermal Conductivity Parameter ◽  
Conductivity Parameter

AbstractIn this article, the differential transform method (DTM) is used to solve the nonlinear boundary value problems describing heat transfer in continuously moving fins undergoing convective-radiative heat dissipation. The thermal conductivity is variable and temperature dependent. The surface of the moving fin is assumed to be gray with a constant emissivity ɛ. The flow in the surrounding medium provides a constant heat transfer coefficient h over the entire surface of the moving fins. The effects of some physical parameters such as the Peclet number, Pe, thermal conductivity parameter, β, convection-conduction parameter, Nc, radiation-conduction parameter, Nr, and dimensionless convection-radiation sink temperature, θa, on the temperature distribution are illustrated and explained.

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