Heat transfer and thermodynamic performance of convective–radiative cooling double layer walls with temperature-dependent thermal conductivity and internal heat generation

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.

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A Study on Convective-Radial Fins with Temperature-dependent Thermal Conductivity and Internal Heat Generation

Nonlinear Engineering ◽

10.1515/nleng-2017-0135 ◽

2019 ◽

Vol 8 (1) ◽

pp. 145-156

Author(s):

Trushit Patel ◽

Ramakanta Meher

Keyword(s):

Thermal Conductivity ◽

Temperature Distribution ◽

Fractional Order ◽

Heat Generation ◽

Internal Heat ◽

Internal Heat Generation ◽

Temperature Dependent ◽

Transform Method ◽

Adomian Decomposition ◽

Temperature Dependent Thermal Conductivity

Abstract In this paper, the temperature distribution in a convective radial fins is analyzed through a fractional order energy balance equation with the consideration of internal heat generation and temperature dependent thermal conductivity. Adomian decomposition Sumudu transform method is used to study the influence of temperature distribution and the efficiency of radial fins for different values of thermal conductivity and to determine the role of thermal conductivity, thermo-geometric fin parameter as well as fractional order values in finding the temperature distribution and the fin efficiency of the convective radial fins. Finally, the efficiency of this proposed method has been studied by comparing the obtained results with the classical order results obtained by using numerical method and Variational Iteration Method (Coskun and Atay, 2007).

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

Canadian Journal of Physics ◽

10.1139/cjp-2018-0242 ◽

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.

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