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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 138573 Total View: 1744268
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
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Article http://dx.doi.org/10.26855/jamc.2020.09.005

Exact Solutions for Nonlinear Transient Heat Transfer of Porous Fin Subjected to Magnetic Field with Variable Internal Heat Generation

M. G. Sobamowo

Department of Mechanical Engineering, Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.

*Corresponding author: M. G. Sobamowo

Published: August 19,2020

Abstract

This work establishes an exact analytical solution for the nonlinear transient thermal model of porous fin subjected to magnetic field with tempera-ture-dependent internal heat generation. With the aid of Laplace transform method, the developed exact analytical model is used to study the impacts of the model parameters on the thermal performance of the fin. Through the developed symbolic heat transfer models using the exact analytical method, parametric studies show that increase in porosity, convective, radiative and magnetic parameters increase the rate of heat transfer from the fin and consequently improve the efficiency of the fin. It is established that the exact analytic solution can serve as basis for comparison of any other method of analysis of the problem and it can also provide platform for improvement in the design of porous fin in heat transfer equipment.

References

[1] S. Kiwan, A. Al-Nimr. (2001). Using Porous Fins for Heat Transfer Enhancement. ASME J. Heat Transfer, 2001, 123: 790-5.

[2] S. Kiwan. (2007a). Effect of radiative losses on the heat transfer from porous fins. Int. J. Therm. Sci., 46, 1046-1055.

[3] S. Kiwan. (2007b). Thermal analysis of natural convection porous fins. Tran. Porous Media, 67, 17-29.

[4] S. Kiwan, O. Zeitoun. (2008). Natural convection in a horizontal cylindrical annulus using porous fins. Int. J. Numer. Heat Fluid Flow, 18(5), 618-634.

[5] R. S. Gorla, A. Y. Bakier. (2011). Thermal analysis of natural convection and radiation in porous fins. Int. Commun. Heat Mass Transfer, 38, 638-645.

[6] B. Kundu, D. Bhanji. (2011). An analytical prediction for performance and optimum design analysis of porous fins. Int. J. Refri-geration, 34, 337-352.

[7] B. Kundu, D. Bhanja, K. S. Lee. (2012). A model on the basis of analytics for computing maximum heat transfer in porous fins. Int. J. Heat Mass Transfer, 55(25-26), 7611-7622.

[8] A. Taklifi, C. Aghanajafi, H. Akrami. (2010). The effect of MHD on a porous fin attached to a vertical isothermal surface. Transp Porous Med., 85, 215-31.

[9] D. Bhanja, B. Kundu. (2011). Thermal analysis of a constructal T-shaped porous fin with radiation effects. Int J Refrigerat, 34, 1483-96.

[10] B. Kundu. (2007). Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer. Int. J. Heat Mass Transfer, 50, 1545-1558.

[11] S. Saedodin, S. Sadeghi. (2013). Temperature distribution in long porous fins in natural convection condition. Middle-east J. Sci. Res., 13(6), 812-817.

[12] S. Saedodin, M. Olank. (2011). Temperature Distribution in Porous Fins in Natural Convection Condition. Journal of American Science, 7(6), 476-481.

[13] M. T. Darvishi, R. Gorla, R. S., Khani, F., Aziz, A.-E. (2015). Thermal performance of a porus radial fin with natural convection and radiative heat losses. Thermal Science, 19(2), 669-678.

[14] M. Hatami, D. D. Ganji. (2013). Thermal performance of circular convective-radiative porous fins with different section shapes and materials. Energy Conversion and Management, 76, 185-193.

[15] M. Hatami, D. D. Ganji. (2014). Thermal behavior of longitudinal convective-radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4). International of J. Ceramics International, 40, 6765-6775.

[16] M. Hatami, A. Hasanpour, D. D. Ganji. (2013). Heat transfer study through porous fins (Si3N4 and AL) with tempera-ture-dependent heat generation. Energ. Convers. Manage, 74, 9-16.

[17] M. Hatami, D. D. Ganji. (2014). Investigation of refrigeration efficiency for fully wet circular porous fins with variable sections by combined heat and mass transfer analysis. International Journal of Refrigeration, 40, 140-151.

[18] M. Hatami, G. H. R. M. Ahangar, D. D. Ganji, K. Boubaker. (2014). Refrigeration efficiency analysis for fully wet semi-spherical porous fins. Energy Conversion and Management, 84, 533-540.

[19] R. Gorla, R. S., Darvishi, M. T. Khani, F. (2013). Effects of variable Thermal conductivity on natural convection and radiation in porous fins. Int. Commun. Heat Mass Transfer, 38, 638-645.

[20] A. Moradi, T. Hayat and A. Alsaedi. (2014). Convective-radiative thermal analysis of triangular fins with temperature-dependent thermal conductivity by DTM. Energy Conversion and Management, 77, 70-77.

[21] S. Saedodin. M. Shahbabaei. (2013). Thermal Analysis of Natural Convection in Porous Fins with Homotopy Perturbation Method (HPM). Arab J Sci Eng., 38: 2227-2231.

[22] H. Ha, Ganji D. D., and Abbasi M. (2005). Determination of Temperature Distribution for Porous Fin with Tempera-ture-Dependent Heat Generation by Homotopy Analysis Method. J Appl Mech Eng., 4(1).

[23] H. A. Hoshyar, I. Rahimipetroudi, D. D. Ganji, A. R. Majidian. (2015). Thermal performance of porous fins with tempera-ture-dependent heat generation via Homotopy perturbation method and collocation method. Journal of Applied Mathematics and Computational Mechanics, 14(4), 53-65.

[24] Y. Rostamiyan, D. D. Ganji, I. R. Petroudi, and M. K. Nejad. (2014). Analytical Investigation of Nonlinear Model Arising in Heat Transfer Through the Porous Fin. Thermal Science, 18(2), 409-417.

[25] S. E. Ghasemi, P. Valipour, M. Hatami, D. D. Ganji. (2014). Heat transfer study on solid and porous convective fins with tem-perature-dependent heat-generation using efficient analytical method. J. Cent. South Univ., 21, 4592-4598. 

[26] I. R. Petroudi, D. D. Ganji, A. B. Shotorban, M. K. Nejad, E. Rahimi, R. Rohollahtabar and F. Taherinia. (2012). Semi-Analytical Method for Solving Nonlinear Equation Arising in Natural Convection Porous fin. Thermal Science, 16(5), 1303-1308.

[27] M. G. Sobamowo. (2016). Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering, 99, 1316-1330.

[28] S. Abbasbandy, E. Shivanian, and I. Hashim. (2011). Exact analytical solution of a forced convection in porous-saturated duct. Comm. Nonlinear Sci Numer Simulat. 16, 3981-3989.

How to cite this paper

Exact Solutions for Nonlinear Transient Heat Transfer of Porous Fin Subjected to Magnetic Field with Variable Internal Heat Generation

How to cite this paper: M. G. Sobamowo. (2020) Exact Solutions for Nonlinear Transient Heat Transfer of Porous Fin Subjected to Magnetic Field with Variable Internal Heat Generation. Journal of Applied Mathematics and Computation, 4(3), 94-103.

DOI: https://dx.doi.org/10.26855/jamc.2020.09.005