Application of Collocation Spectral Method to Solve a Convective-Radiative Longitudinal Fin with Temperature Dependent Internal Heat Generation, Thermal Conductivity and Heat Transfer Coefficient

2015 ◽  
Vol 12 (9) ◽  
pp. 2851-2860
Author(s):  
Yasong Sun ◽  
Jing Ma
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Spectral Method ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Collocation Spectral Method

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 Volume Method for Analysis of Convective Longitudinal Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation

2017 ◽  
Vol 374 ◽  
pp. 106-120 ◽  
Author(s):  
Gbeminiyi M. Sobamowo ◽  
Bayo Y. Ogunmola ◽  
Gaius Nzebuka
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Temperature Distribution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Volume Method

In this study, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation has been analyzed using finite volume method. The numerical solution was validated with the exact solution for the linear problem. The developed heat transfer models were used to investigate the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity (non-linear) parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. From the results, it shows that the fin temperature distribution, the total heat transfer, and the fin efficiency are significantly affected by the thermo-geometric of the fin. Therefore, the results obtained in this analysis serve as basis for comparison of any other method of analysis of the problem and they also provide platform for improvement in the design of fin in heat transfer equipment.

Heat Transfer in Plane with Temperature Dependent Thermal Variables

2018 ◽  
Vol 387 ◽  
pp. 23-36 ◽  
Author(s):  
Marcio Lourenco ◽  
Raseelo Joel Moitsheki ◽  
Adewunmi Gideon Fareo ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Exact Solution ◽  
Exact Solutions ◽  
Heat Generation ◽  
Heat Conductivity ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Bench Mark ◽  
Temperature Dependent

In this paper we consider heat transfer in a wall with temperature dependent heat conductivity and internal heat generation. It turns out the model considered is non-linear. We employ the classical Lie point symmetry analysis to determine the exact solutions. A number of cases for thermal conductivity and internal heat generation are considered. In some cases the exact solutions are not possible to construct. However, we first use the obtained exact solution as a bench mark for the quasilinear method. Since confidence is established, we then use the quasilinear method to solve some other applicable problem.

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