Influence of Internal Heat Generation on the Natural Convection of Non-Newtonian Fluids over a Vertical Plate in Porous Media with Thermal Radiation and Soret/Dufour Effects: Variable Wall Temperature/Concentration

2018 ◽  
Vol 89 (4) ◽  
pp. 737-745 ◽  
Author(s):  
Chuo-Jeng Huang
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Variable Wall Temperature ◽  
Variable Wall

scholarly journals Similarity Solution of Heat and Mass Transfer for Natural Convection over a Moving Vertical Plate with Internal Heat Generation and a Convective Boundary Condition in the Presence of Thermal Radiation, Viscous Dissipation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. Mohammed Ibrahim ◽  
N. Bhashar Reddy
Keyword(s):  
Boundary Condition ◽  
Natural Convection ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Heat Generation ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation

Steady laminar natural convection flow over a semi-infinite moving vertical plate with internal heat generation and convective surface boundary condition in the presence of thermal radiation, viscous dissipation, and chemical reaction is examined in this paper. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. We utilized similarity variable to transform the governing nonlinear partial differential equations into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique along fourth-order Runge-Kutta method. The effects of the local Biot number, Prandtl number, buoyancy forces, the internal heat generation, the thermal radiation, Eckert number, viscous dissipation, and chemical reaction on the velocity, temperature, and concentration profiles are illustrated and interpreted in physical terms. A comparison with previously published results on the similar special cases showed an excellent agreement. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, are presented in tabular form.

scholarly journals Similarity Solutions for an Internal Heat Generation, Thermal Radiation and Free Convection Unsteady Boundary Layer Flow over a Vertical Plate

2016 ◽  
Vol 8 (3) ◽  
pp. 341-353 ◽  
Author(s):  
M. Y. Ali ◽  
N. M. R. Zahed ◽  
M. N. Uddin ◽  
M. J. Uddin
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Heat Generation ◽  
Boundary Layer Flow ◽  
Vertical Plate ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Unsteady Boundary Layer ◽  
Layer Flow

The present paper deals with possible similarity solution of unsteady boundary layer flow over a vertical plate in the presence of internal heat generation, thermal radiation and buoyancy force. Under suitable similarity transformations, the non-linear partial differential equations are transformed into a set of ordinary differential equations. The transformed ordinary differential equations with boundary conditions are then solved numerically by using sixth order Runge-Kutta integration scheme. The effects of the governing parameters on the flow and thermal fields are investigated and shown graphically for various parameters in the velocity and the temperature distributions. The most essential case is discussed in this paper.

scholarly journals Non-similar solutions for natural convection from a moving vertical plate with a convective thermal boundary condition

2016 ◽  
Vol 20 (6) ◽  
pp. 1847-1853
Author(s):  
Asterios Pantokratoras
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Thermal Expansion ◽  
Heat Generation ◽  
Wall Temperature ◽  
Vertical Plate ◽  
Internal Heat ◽  
Thermal Boundary Condition ◽  
Internal Heat Generation ◽  
Wall Heat Transfer

In a recent paper by Makinde (Thermal Science, 2011, Vol. 15, Suppl. 1, pp. S137-S143.) the effect of thermal buoyancy along a moving vertical plate with internal heat generation was considered. The plate thermal boundary condition was a convective condition with a heat transfer coefficient proportional to x-1/2 . The fluid thermal expansion coefficient was proportional to 1-x and the internal heat generation was assumed to decay exponentially across the boundary layer and proportional to x-1 in order that the problem accepts a similarity solution. In the present work, the same problem without heat generation is considered, with constant heat transfer coefficient and constant thermal expansion coefficient which is more realistic and has much more practical applications. The present problem is non-similar and results are obtained with the direct numerical solution of the governing equations. The problem is governed by the Prandtl number, the non-dimensional distance along the plate and a convective Grashof number, which is introduced for the first time. It is found that the wall shear stress, the wall heat transfer and the wall temperature, all increase with increasing distance and the wall temperature tends to 1. The influence of the convective Grashof number is to increase the wall shear stress and the wall heat transfer and to reduce the wall temperature.

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