Heat transfer study in a convective-radiative fin with temperature-dependent thermal conductivity and magnetic field using variation parameters method

Abstract

Abstract. In this work, a heat transfer study is carried out in a convective-radiative straight fin with temperature-dependent thermal conductivity and a magnetic field using the variation of parameters method. The developed heat transfer model is used to analyze the thermal performance, establish the optimum thermal design parameters and investigate the effects of thermo-geometric parameters and non-linear thermal conductivity parameters on the thermal performance of the fin. The results obtained are compared with the results in literature and good agreements are found. The analysis can serve as basis for comparison of any other method of analysis of the problem and it also provides a platform for improvement in the design of fin in heat transfer equipment. MSC 2010: 35A15

Numerical solution for a porous fin thermal performance problem by application of Sinc collocation method

“…Haar wavelet collocation method 26 Thermal performance analysis of porous fin with temperature-dependent thermal conductivity and internal heat generation Chebyshev spectral collocation method 27 Effects of particles deposition on thermal performance of a convective-radiative heat sink porous fin of an electronic component Spectral collocation method 28 Natural convection and radiation in a radial porous fin with variable thermal conductivity Chebychev spectral collocation method CSCM 29 Analysis of Heat transfer in Porous Fin with Temperature-dependent Thermal Conductivity and Internal Heat Generation Legendre wavelet collocation method 30 Prediction of temperature distribution in straight fin with variable thermal conductivity and internal heat generation using Legendre wavelet collocation method Legendre wavelet collocation method 31 Heat transfer study of porous fin with temperature-dependent thermal conductivity-collocation method Exact analytical solution 43 Exact, analytic temperature distributions of pin fins with constant thermal conductivity and power-law type heat transfer coefficient method, 5,20 and diverse collocation methods, for example, Haar wavelet, 25,26 spectral, 27,28 Chebychev, 29 and Legendre. [30][31][32] Hoseinzadeh et al 33 compared analytical and numerical methods to study of heat transfer though a porous fin with rectangular cross section. Sadeghi et al 34 investigated natural convection for a multifin system.…”

“…The idea of porous fins has first been presented by Kiwan and Al‐Nimr 3 as considering Darcy's model in formulation, finite element code used to solve the problem 4 . Researchers have used many different methods to approach the porous fins problem, for example, CFD solution, 2,4–9 homotopy analysis method, 1,10–19 Runge‐Kutta, 20,21 Galerkin's method of weighted residual, 22 least squares method, 23 Adomian decomposition method, 6,24 differential transform method, 5,20 and diverse collocation methods, for example, Haar wavelet, 25,26 spectral, 27,28 Chebychev, 29 and Legendre 30–32 . Hoseinzadeh et al 33 compared analytical and numerical methods to study of heat transfer though a porous fin with rectangular cross section.…”

Nonlinear Thermal Response Analysis of an Internally Heated Radiative-Convective Porous Fin subjected to Magnetic Fields using Method of Lines

“…In a further analysis, Aziz and Bouaziz [12], Sobamowo [13], Ganji et al [14] and Sobamowo et al [15] employed methods of weighted residual to explore the nonlinear thermal behaviour of fins. In another studies, methods of double decomposition and variation of parameter were used by Sobamowo [16] and Sobamowo et al [17], respectively to study the thermal characteristics of fins. Also, differential transformation method has been used by some researchers such as Moradi and Ahmadikia [18], Sadri et al [19], Ndlovu and Moitsheki [20], Mosayebidarchech et al [21], Ghasemi et al [22] and Ganji and Dogonchi [23] to predict the heat transfer behaviour in the passive devices.…”

Optimum Design and Performance Analyses of Convective-Radiative Cooling Fin under the Influence of Magnetic Field Using Finite Element Method

“…The development of exact analytical solutions for such nonlinear models is very difficult. Consequently, some of the past studies have developed approximate analytical solution in terms of series solutions for the thermal analyses of fins using different approximate 2 Journal of Optimization analytical methods [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Nevertheless, the series solutions involve large number of terms.…”