Combined effects of internal heat generation and mass effects on MHD Casson fluid with convective boundary conditions

2017 ◽  
Vol 54 (2) ◽  
pp. 211-221 ◽  
Author(s):  
B. Ahmed ◽  
Z. Iqbal ◽  
E. Azhar
Keyword(s):  
Boundary Conditions ◽  
Heat Generation ◽  
Internal Heat ◽  
Casson Fluid ◽  
Internal Heat Generation ◽  
Combined Effects ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Mass Effects

Heat Transfer in a Couple Stress Fluid over a Continuous Moving Surface with Internal Heat Generation and Convective Boundary Conditions

2012 ◽  
Vol 67 (5) ◽  
pp. 217-224 ◽  
Author(s):  
Tasawar Hayat ◽  
Zahid Iqbal ◽  
Muhammad Qasim ◽  
Omar M. Aldossary
Keyword(s):  
Heat Transfer ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Couple Stress ◽  
Couple Stress Fluid ◽  
Physical Parameters ◽  
Series Solutions ◽  
Convective Boundary Conditions ◽  
Convective Boundary ◽  
Moving Surface

This investigation reports the boundary layer flow and heat transfer characteristics in a couple stress fluid flow over a continuos moving surface with a parallel free stream. The effects of heat generation in the presence of convective boundary conditions are also investigated. Series solutions for the velocity and temperature distributions are obtained by the homotopy analysis method (HAM). Convergence of obtained series solutions are analyzed. The results are obtained and discussed through graphs for physical parameters of interest.

Simulation of Nanoscale Multidimensional Transient Heat Conduction Problems Using Ballistic-Diffusive Equations and Phonon Boltzmann Equation

2005 ◽  
Vol 127 (3) ◽  
pp. 298-306 ◽  
Author(s):  
Ronggui Yang ◽  
Gang Chen ◽  
Marine Laroche ◽  
Yuan Taur
Keyword(s):  
Heat Conduction ◽  
Boltzmann Equation ◽  
Boundary Conditions ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Computational Time ◽  
Discrete Ordinates ◽  
Fourier Law ◽  
Phonon Boltzmann Equation

Heat conduction in micro- and nanoscale and in ultrafast processes may deviate from the predictions of the Fourier law, due to boundary and interface scattering, the ballistic nature of the transport, and the finite relaxation time of heat carriers. The transient ballistic-diffusive heat conduction equations (BDE) were developed as an approximation to the phonon Boltzmann equation (BTE) for nanoscale heat conduction problems. In this paper, we further develop BDE for multidimensional heat conduction, including nanoscale heat source term and different boundary conditions, and compare the simulation results with those obtained from the phonon BTE and the Fourier law. The numerical solution strategies for multidimensional nanoscale heat conduction using BDE are presented. Several two-dimensional cases are simulated and compared to the results of the transient phonon BTE and the Fourier heat conduction theory. The transient BTE is solved using the discrete ordinates method with a two Gauss-Legendre quadratures. Special attention has been paid to the boundary conditions. Compared to the cases without internal heat generation, the difference between the BTE and BDE is larger for the case studied with internal heat generation due to the nature of the ballistic-diffusive approximation, but the results from BDE are still significantly better than those from the Fourier law. Thus we conclude that BDE captures the characteristics of the phonon BTE with much shorter computational time.

Conduction in Rings With Internal Heat Generation

2021 ◽  
Vol 143 (5) ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Cross Section ◽  
Heat Generation ◽  
Cross Sections ◽  
Rectangular Cross Section ◽  
Ritz Method ◽  
Circular Cross Section ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Convective Boundary ◽  
Steady State Heat

Abstract The basic problem of steady-state heat conduction in a ring with internal heat generation and convective boundary conditions is considered. An exact solution is found for the ring with a rectangular cross section and an efficient Ritz method is presented for general cross sections. The latter is applied to the torus or the ring with a circular cross section. Hot spots and cold spots are determined.

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