Thermal stabilities of slabs and hollow spheres with internal heat generation and variable thermal conductivity—I. thermal stability of Landau slabs with linearly varying thermal conductivity

1987 ◽  
Vol 323 (1) ◽  
pp. 33-42 ◽  
Author(s):  
C.K. Liu
Keyword(s):  
Thermal Conductivity ◽  
Thermal Stability ◽  
Heat Generation ◽  
Hollow Spheres ◽  
Internal Heat ◽  
Variable Thermal Conductivity ◽  
Internal Heat Generation ◽  
Thermal Stabilities ◽  
Thermal Stability Of

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.

Finite element thermal analysis of a moving porous fin with temperature-variant thermal conductivity and internal heat generation

2020 ◽  
Vol 1 (1) ◽  
pp. 110
Author(s):  
Gbeminiyi Sobamowo ◽  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element ◽  
Heat Generation ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Péclet Number ◽  
Porous Fin

This paper focuses on finite element analysis of the thermal behaviour of a moving porous fin with temperature-variant thermal conductivity and internal heat generation. The numerical solutions are used to investigate the effects of Peclet number, Hartmann number, porous and convective parameters on the temperature distribution, heat transfer and efficiency of the moving fin. The results show that when the convective and porous parameters increase, the adimensional fin temperature decreases. However, the value of the fin temperature is amplified as the value Peclet number is enlarged. Also, an increase in the thermal conductivity and the internal heat generation cause the fin temperature to fall and the rate of heat transfer from the fin to decrease. Therefore, the operational parameters of the fin must be carefully selected to avoid thermal instability in the fin.

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