Transient thermal analysis of longitudinal fins with internal heat generation considering temperature-dependent properties and different fin profiles

2014 ◽  
Vol 86 ◽  
pp. 365-370 ◽  
Author(s):  
Sobhan Mosayebidorcheh ◽  
Masoud Farzinpoor ◽  
D.D. Ganji
Keyword(s):  
Thermal Analysis ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Temperature Dependent ◽  
Transient Thermal Analysis ◽  
Temperature Dependent Properties ◽  
Transient Thermal

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.

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.

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