Hill Publishing Group | contact@hillpublisher.com
Join Us

Hill Publishing Group

Location：Home / Journals / Journal of Applied Mathematics and Computation /

Journal of Applied Mathematics and Computation

DOI：http://dx.doi.org/10.26855/jamc.2022.06.008

Impacts of Magnetic Field, Internal Heat Generation, Ambient and Fin Surface Temperatures on the Thermal Performance of Radiating Fin with Variable Thermal Conductivity

Date: June 7,2022 |Hits: 1773 Download PDF How to cite this paper

M. G. Sobamowo1,*, O. A. Adeleye2, A. A. Yinusa1, B. O. Adesoye1, O. C. Osih1

1Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria.

2Department of Biomedical Engineering, University of Lagos, Akoka, Lagos, Nigeria.

*Corresponding author: M. G. Sobamowo

Abstract

Radiating fins are commonly used in radiators to augment the heat transfer between a primary surface and the environment. However, the thermal performance of such passive device is significantly influenced by several internal and external factors. Therefore, in this work, the impacts of internal heat generation, magnetic field, ambient and fin surface temperatures on the thermal response of a radiating fin with temperature-dependent thermal conductivity is examined using differential transformation method. The results of the power series solutions are verified numerically, and very good agreements are established. The symbolic solutions are used to examine the effects of the internal and external conditions on the thermal performance of the passive device. It is found that as the conductive-radiative and magnetic field parameters increase, the fin temperature distribution in the fin decreases which the heat transfer rate through the fin is augmented and hence, the fin thermal efficiency is improved. The temperature distribution in the fin increases through the fin as the nonlinear thermal conductivity parameter increases. When the value of the internal heat generation increases, the temperature distribution through the extended surface increases. The ambient temperature increases, the fin temperature decreases. However, an increase in the radiation sink temperature causes the radiative heat loss to decrease but the temperature within the fin to increase. The developed analytical solutions provide a good platform for the nonlinear thermal analysis of the fin and proper design of the extended surfaces in thermal systems.

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

[3] S. Kiwan. (2007). Thermal analysis of natural convection porous fins. Tran. Porous Media, 67(2007), 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), (2008), 618-634.

[5] R. S. Gorla, A. Y. Bakier. (2001). Thermal analysis of natural convection and radiation in porous fins. Int. Commun. Heat Mass Transfer, 38(2011), 638-645.

[6] B. Kundu, D. Bhanji. (2011). 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. (2012). 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. (2010). 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. (2011). Thermal analysis of a constructal T-shaped porous fin with radiation effects. Int J Refrigerat, 34(2011), 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(2007), 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), (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. (2010). 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. (2013). 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. (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(2014), 6765-6775.

[16] M. Hatami, A. Hasanpour, D. D. Ganji. (2013). 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. (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(2014), 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(2014), 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(2013), 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(2014), 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., (2013), 38: 2227-2231.

[22] H. Ha, Ganji, D. D., and Abbasi, M. (2005). 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. (2014). 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. (2014). 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. (2014). Heat transfer study on solid and porous convective fins with temper-ature-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. (2012). 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. (2011). 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. (2015). 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. (2015). 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. (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(2016), 1316-1330.

[31] H. A. Hoshyar, D. D. Ganji, M. R. Majidian. (2016). 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. (2018). On the effect of magnetic field on thermal performance of convec-tive-radiative fin with temperature-dependent thermal conductivity. Karbala International Journal of Modern Science, 4(2018), 1-11.

[33] T. Patel and R. Meher. (2017). Thermal Analysis of porous fin with uniform magnetic field using Adomian decomposition Sumudu transform method. De Gruyter Nonlinear Engineering, 2017, 1-10.

[34] M. G. Sobamowo. (2019). 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, p. 19.

How to cite this paper

Impacts of Magnetic Field, Internal Heat Generation, Ambient and Fin Surface Temperatures on the Thermal Performance of Radiating Fin with Variable Thermal Conductivity

How to cite this paper:  M. G. Sobamowo, O. A. Adeleye, A. A. Yinusa, B. O. Adesoye, O. C. Osih. (2022) Impacts of Magnetic Field, Internal Heat Generation, Ambient and Fin Surface Temperatures on the Thermal Performance of Radiating Fin with Variable Thermal Conductivity. Journal of Applied Mathematics and Computation, 6(2), 235-245.

DOI: http://dx.doi.org/10.26855/jamc.2022.06.008

More Articles

Open for Discovery

Volumes & Issues

Free HPG Newsletters

Add your e-mail address to receive free newsletters from Hill Publishing Group.

More Journals

Contact us

Hill Publishing Group

8825 53rd Ave

Elmhurst, NY 11373, USA

E-mail: contact@hillpublisher.com

Home　|　Journals　|　Books　|　For Authors and Reviewers　|　Online Submission　|　Contact Us　|　About Us
Copyright © 2019 Hill Publishing Group Inc. All Rights Reserved.