Heat transfer study on convective–radiative semi-spherical fins with temperature-dependent properties and heat generation using efficient computational methods

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.

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

Canadian Journal of Physics ◽

10.1139/cjp-2018-0109 ◽

2019 ◽

Vol 97 (1) ◽

pp. 23-29 ◽

Cited By ~ 2

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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Internal Laminar Heat Transfer With Gas-Property Variation

Journal of Heat Transfer ◽

10.1115/1.3449842 ◽

1971 ◽

Vol 93 (4) ◽

pp. 432-440 ◽

Cited By ~ 7

Author(s):

T. B. Swearingen ◽

D. M. McEligot

Keyword(s):

Heat Transfer ◽

Numerical Solutions ◽

Bulk Temperature ◽

Parallel Plates ◽

Temperature Dependent ◽

Property Variation ◽

Constant Wall Heat Flux ◽

Mixed Mean ◽

Two Dimensional Flow ◽

Temperature Dependent Properties

The results of a numerical investigation of internal laminar heat transfer to a gas with temperature-dependent properties are reported. In this investigation the authors obtained numerical solutions to the coupled partial differential equations of continuity, energy, momentum, and integral continuity describing the two-dimensional flow of perfect gas between heated parallel plates. A sequence of numerical solutions was obtained for the case of constant wall heat flux with a fully developed velocity profile at the start of the heated section and pure forced convection. The results may be summarized by Nu=Nuconst.prop.+0.024(Q+)0.3(Gzm)0.75f·Rem=24(Twall/Tbulk) where the subscript “m” refers to properties evaluated at the local mixed-mean (or bulk) temperature.

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