Document Type : Original Article


1 Department of Mechanical Engineering, University of Lagos, Nigeria

2 Department of Biomedical Engineering, University of Lagos, Nigeria

3 Department of Mechanical Engineering, Federal University of Agriculture, Ogun State, Nigeria.


In this paper, unsteady thermal scrutiny of radiative-convective moving fin considering the influences of magnetic field and time-dependent boundary conditions is explored via Laplace transform method. The analytical solutions obtained are employed in the investigation of the impacts of Hartmann number, Peclet number, radiative and convective parameters on the transient thermal performance and effectiveness in the moving fin. The research outcomes establish that an increase in convective and porosity terms generates a corresponding increase in the fin’s heat transfer rate. This consequently augments the fin’s efficiency. Correspondingly, an increase in increases the magnitude of temperature distribution within the fin. It is also found that increasing the results in an increase in material mobility rate. Meanwhile, the exposure period of the material to its surrounding environmental conditions diminishes while fin losses more surface heat, hence the temperature of the fin intensifies. Finally, an increase in the fin’s internal heat generation and thermal conductivity reduces heat transfer rate. Thus, the controlling terms of the fin during operation should be prudently selected to make sure that it retains its principal function of heat removal from the main surface.


[1]. S. Kiwan, A. Al-Nimr. Using Porous Fins for Heat Transfer Enhancement. ASME J. Heat Transfer 2001; 123:790–5.
[2]  S. Kiwan, Effect of radiative losses on the heat transfer from porous fins. Int. J. Therm. Sci. 46(2007a)., 1046-1055
[3] S. Kiwan. Thermal analysis of natural convection porous fins. Tran. Porous Media 67(2007b), 17-29.
[4] S. Kiwan, O. Zeitoun, Natural convection in a horizontal cylindrical annulus using porous fins. Int. J. Numer. Heat Fluid Flow 18 (5)(2008), 618-634.
[5] R. S. Gorla, A. Y. Bakier. Thermal analysis of natural convection and radiation in porous fins. Int. Commun. Heat Mass Transfer 38(2011), 638-645.
[6] B. Kundu, D. Bhanji. An analytical prediction for performance and optimum design analysis of porous fins. Int. J. Refrigeration 34(2011), 337-352.
[7] B. Kundu, D. Bhanja, K. S. Lee. A model on the basis of analytics for computing maximum heat transfer in porous fins. Int. J. Heat Mass Transfer 55 (25-26)(2012) 7611-7622.
[8] A. Taklifi, C. Aghanajafi, H. Akrami. The effect of MHD on a porous fin attached to a vertical isothermal surface. Transp Porous Med. 85(2010) 215–31.
[9] D. Bhanja, B. Kundu. Thermal analysis of a constructal T-shaped porous fin with radiation effects. Int J Refrigerat 34(2011) 1483–96.
[10] B. Kundu,  Performance and optimization analysis of SRC profile fins subject to simultaneous heat and mass transfer. Int. J. Heat Mass Transfer 50(2007) 1545-1558.
[11] S. Saedodin, S. Sadeghi, S. Temperature distribution in long porous fins in natural convection condition. Middle-east J. Sci. Res. 13 (6)(2013) 812-817.
[12] S. Saedodin, M. Olank, 2011. Temperature Distribution in Porous Fins in Natural Convection Condition, Journal of American Science 7(6)(2011) 476-481.
[13] A. Taklifi, C. Aghanajafi, H. Akrami, The effect of MHD on a porous fin attached to a vertical isothermal surface, Transp. Porous Media 85 (1) (2010) 215-231.
[14] M. Hatami , D. D. Ganji. Thermal performance of circular convective-radiative porous fins with different section shapes and materials. Energy Conversion and Management, 76(2013)185−193.
[15] M. Hatami , D. D. Ganji. Thermal behavior of longitudinal convective–radiative porous fins with different section shapes and ceramic materials (SiC and Si3N4). International of J. Ceramics International, 40(2014), 6765−6775.
[16] M. Hatami, A. Hasanpour, D. D. Ganji, Heat transfer study through porous fins (Si3N4 and AL) with temperature-dependent heat generation. Energ. Convers. Manage. 74(2013) 9-16.
[17] M. Hatami , D. D. Ganji. 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(2014) 140−151.
[18] M. Hatami, G. H. R. M. Ahangar, D. D. Ganji,, K. Boubaker. Refrigeration efficiency analysis for fully wet semi-spherical porous fins. Energy Conversion and Management, 84(2014) 533−540.
[19] R. Gorla, R.S., Darvishi, M. T. Khani, F.  Effects of variable Thermal conductivity on natural convection and radiation in porous fins. Int. Commun. Heat Mass Transfer 38(2013), 638-645.
[20] A. Moradi, T. Hayat and A. Alsaedi, Convective-radiative thermal analysis of triangular fins with temperature-dependent thermal conductivity by DTM. Energy Conversion and Management 77 (2014) 70–77
[21] S. Saedodin. M. ShahbabaeiThermal Analysis of Natural Convection in Porous Fins with Homotopy Perturbation Method (HPM). Arab J Sci Eng (2013) 38:2227–2231.
[22] H. Ha, Ganji D. D and Abbasi M. Determination of Temperature Distribution for Porous Fin with Temperature-Dependent Heat Generation by Homotopy Analysis Method. J Appl Mech Eng., 4(1) (2005).
[23] S. Rezazadeh Amirkolaei1, D.D. Ganji, H. Salarian, Determination of temperature distribution for porous fin which is exposed to uniform magnetic field to a vertical isothermal surface by homotopy analysis method and collocation method, Indian J. Sci. Res. 1 (2) (2014) 215-222.
[24] Y. Rostamiyan,, D. D. Ganji , I. R. Petroudi, and M. K. Nejad. Analytical Investigation of Nonlinear Model Arising in Heat Transfer Through the Porous Fin. Thermal Science. 18(2)(2014), 409-417.
[25] S. E. Ghasemi, P. Valipour, M. Hatami, D. D. Ganji.. Heat transfer study on solid and porous convective fins with temperature-dependent heat -generation using efficient analytical method J. Cent. South Univ. 21(2014), 4592−4598. 
[26] I. R. Petroudi, D. D. Ganji, A.  B. Shotorban, M. K. Nejad, E. Rahimi, R. Rohollahtabar and F. Taherinia.  Semi-Analytical Method for Solving Nonlinear Equation Arising in Natural Convection Porous fin. Thermal Science, 16(5) (2012), 1303-1308.
[27] S. Abbasbandy, E. Shivanian and I. Hashim. Exact analytical solution of a forced convection in porous-saturated duct. Comm. Nonlinear Sci Numer Simulat. 16(2011), 3981–3989.
[28] M. T. Darvishi, R. Gorla, R.S., Khani, F., Aziz, A.-E. Thermal performance of a porous radial fin with natural convection and radiative heat losses. Thermal Science, 19(2) (2015)  669-678.
[29] H. A. Hoshyar,  I. Rahimipetroudi, D. D. Ganji, A. R. Majidian. Thermal performance of porous fins with temperature-dependent heat generation via Homotopy perturbation method and collocation method. Journal of Applied Mathematics and Computational Mechanics. 14(4) (2015), 53-65.
[30] M. G. Sobamowo. Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering 99(2016), 1316–1330.
[31] H.A. Hoshyar, D.D. Ganji, M.R. Majidian, Least square method for porous fin in the presence of uniform magnetic field, J. Appl. Fluid Mech. 9 (2) (2016) 661-668.
[32] G. Oguntala, R. Abd-Alhameed, M. G. Sobamowo. On the effect of magnetic field on thermal performance of convective-radiative fin with temperature-dependent thermal conductivityKarbala International Journal of Modern Science 4 (2018) 1-11
[33] T.  Patel and R.  Meher. Thermal Analysis of porous fin with uniform magnetic fieldu sing Adomian decomposition Sumudu transform method. De Gruyter NonlinearEngineering 2017, 1-10.
[34] M. G.Sobamowo. Optimum Design and Performance Analyses of Convective-Radiative Cooling Fin under the Influence of Magnetic Field Using Finite Element Method. Hindawi Journal of Optimization Volume 2019, Article ID 9705792, 19 pages.
[35] M. Torabi, H. Yaghoobi and A. Aziz Analytical Solution for Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity Int. J. Thermophysics (2012) 33: 924-941.
[36] A. Aziz and R. J. Lopez , Convection -radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing, I. J. of Thermal Sciences 50 (2011),  1523-1531.
[37] A. Aziz, F. Khani, Convection-radiation from a continuously moving fin of variable thermal conductivity, J. of Franklin Institute, 348 (2011), 640-651.
[38] S. Singh, D. Kumar ,K. N. Rai. Wavelet Collocation Solution for Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity. International Journal of Engineering and Advanced Technology, 2(4), 2013.
[39] A. Aziz, M. Torabi, Covective-radiative fins with simultaneous variation of thermal conductivity, heat transfer coef ficient and surface emissivity with temperature, Heat transfer Asian Research 41 (2) (2012).
[40] J. Ma, Y. Sun, B. W. Li, H. Chen Spectral collocation method for radiative–conductive porous fin with temperature dependent properties. Energy Conversion and Management 111 (2016) 279–288.
[41] Y. Sun J. Ma, B. W.  Li, H. Spectral collocation method for convective-radiative transfer of a moving rod with variable thermal conductivity. International Journal of Thermal Sciences 90 (2015) 187-196.
[42] A. Aziz, F. Khani. Convection-radiation from a continuous moving fin of variable thermal conductivity. J Franklin Inst 2011;348:640–651
[43] A. Aziz, Lopez R. J. Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing. Int.  J Therm Sci.  2011;50:1523–1531.
[44] M. Torabi, H. Yaghoobi,   A. Aziz. Analytical solution for convective-radiative continuously moving fin with temperature-dependent thermal conductivity. Int. J Thermophys, 33(2012), 924– 941.
[45] A.S.V. R.  Kanth and N. U.  Kumar. Application of the Haar Wavelet Method on a Continuously Moving Convective-Radiative Fin with Variable Thermal Conductivity. Heat Transfer—Asian Research. DOI. 42(4), 1-17.
[46] R. K. Singla and D.  Ranjan. Application of decomposition method and inverse parameters in a moving fin, Energy Conversion and Management, 84(2014), 268-281
[47] A. Moradi and R. Rafiee. Analytical Solution to Convection-Radiation of a Continuously Moving Fin with Temperature-Dependent thermal conductivity, Thermal Science, 17(2003), 1049-1060.
[48] A. S. Dogonchi and D. D. Ganji. Convection-Radiation heat transfer study of moving fin with temperature dependent thermal conductivity, heat transfer coefficient and heat generation, Applied Thermal Engineering, 103(2016), 705-712
[49] Y. S. Sun and J. Ma. Application of Collocation Spectral Method to Solve a Convective – Radiative Longitudinal Fin with Temperature Dependent Internal Heat Generation, Thermal Conductivity and Heat Transfer Coefficient,  Journal of Computational and Theoretical Nano-science, volume12(2015), 2851- 2860.
[50]. S. Singh, D. Kumar, K. N. Rai. Wavelet Collocation Solution for Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity. International Journal of Engineering and Advanced Technology (IJEAT). vol. 2(4), 2013.
[51] D. Ranjan. A simplex search method for a conductive-convective fin with variable conductivity. Int J Heat Mass Transf 2011;54:5001–5009.
[52] Yinusa, Ahmed and Sobamowo, Gbeminiyi (2019) "Analysis of Dynamic Behaviour of a Tensioned Carbon Nanotube in Thermal and Pressurized Environments," Karbala International Journal of Modern Science: Vol. 5 : Iss. 1, Article 2. DOI: 10.33640/2405-609X.1015
[53] Oguntala G, Sobamowo G, Ahmed Y. Transient analysis of functionally graded material porous fin under the effect of Lorentz force using the integral transform method for improved electronic packaging. Heat Transfer. 2020;1–18.