Exact closed-form unique and dual solutions to the longitudinal fin with temperature-dependent properties and internal heat generation

2019 ◽  
Vol 97 (1) ◽  
pp. 23-29 ◽  
Author(s):  
E. Shivanian ◽  
M.R. Ansari ◽  
M. Shaban
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Heat Generation ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Full Discussion ◽  
Study Heat Transfer ◽  
Temperature Dependent Properties

In this study, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is revisited. The advanced heat transfer models have been used to study the effects of thermo-geometric parameters, coefficient of heat transfer, and thermal conductivity parameters on the temperature distribution, heat transfer, and thermal performance of the longitudinal rectangular fin. It is shown that its governing nonlinear differential equation with proper boundary conditions is exactly solvable. With this aim, we reduce the order of the differential equation to first and then convert it into a total differential equation by multiplying by a convenient integrating factor. A full discussion and exact analytical solution in the implicit form is given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, or the solutions are dual, depending on the values of the parameters of the model.

Thermal Analysis of Longitudinal Fin with Temperature-Dependent Properties and Internal heat Generation by a Novel Intelligent Computational Approach Using Optimized Chebyshev Polynomials

2019 ◽  
Vol 20 (2) ◽  
pp. 153-166 ◽  
Author(s):  
Elyas Shivanian ◽  
Ramin Kazemi ◽  
Mahdi Keshtkar
Keyword(s):  
Heat Transfer ◽  
Heat Generation ◽  
Chebyshev Polynomials ◽  
Optimization Problem ◽  
Mathematical Formulation ◽  
Internal Heat ◽  
Computational Approach ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Temperature Dependent Properties

AbstractIn this work, heat transfer in a longitudinal rectangular fin with temperature-dependent thermal properties and internal heat generation is studied and more accurate results obtained in respect of the previous investigations. The advanced heat transfer models have been used to study the effects of thermo-geometric parameters, coefficient of heat transfer and thermal conductivity parameters on the temperature distribution, heat transfer and thermal performance of the longitudinal rectangular fin. It is applied a novel intelligent computational approach for searching the solution. In order to achieve this aim, the governing equation is transformed into an equivalent problem whose boundary conditions are such that they are convenient to apply reformed version of Chebyshev polynomials of the first kind. These Chebyshev polynomials based functions construct approximate series solution with unknown weights. The mathematical formulation of optimization problem consists of an unsupervised error which is minimized by tuning weights via interior point method. The trial approximate solution is validated by imposing tolerance constrained into optimization problem.

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.

Heat Transfer of Thin Fins With Temperature-Dependent Thermal Properties and Internal Heat Generation

1967 ◽  
Vol 89 (2) ◽  
pp. 155-162 ◽  
Author(s):  
H. M. Hung ◽  
F. C. Appl
Keyword(s):  
Heat Transfer ◽  
Thermal Properties ◽  
Temperature Distribution ◽  
Heat Generation ◽  
Analytical Study ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Numerical Examples

An analytical study of the temperature distribution along thin fins with temperature-dependent thermal properties and internal heat generation is presented. The analysis utilizes a recently published bounding procedure which yields analytical and continuous bounding functions for the temperature distribution. Several numerical examples are considered. Tabular and graphical results are given. The effects of variable thermal properties and internal heat generation are also shown.

The exact closed solution in the analysis of a natural convection porous fin with temperature-dependent thermal conductivity and internal heat generation

2019 ◽  
Vol 97 (5) ◽  
pp. 566-575
Author(s):  
S. Abbasbandy ◽  
E. Shivanian
Keyword(s):  
Thermal Conductivity ◽  
Natural Convection ◽  
Thermal Behaviour ◽  
Heat Generation ◽  
Exact Analytical Solution ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Porous Fin ◽  
Temperature Dependent Thermal Conductivity

In the current work, thermal behaviour analysis of a natural convection porous fin with internal heat generation and temperature-dependent thermal conductivity is studied. The developed symbolic heat transfer models are for the purpose of the investigation of the effects of various parameters on the thermal behaviour of the porous fin. It is shown that its governing nonlinear differential with proper boundary conditions is exactly solvable. To this aim, we reduce the order of differential equations first and then convert into a total differential equation by multiplying a convenient integrating factor. A full discussion and exact analytical solution in the implicit form is given for further physical interpretation and it is proved that a solution to the problem may not exist or the solution is mathematically unique depending on the values of the parameters of the model.

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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