TOTAL VIEWS: 4836

Published: December 29,2021

In this work, heat transfer study of rectangular moving porous fin with temperature-dependent thermal conductivity and internal heat generation is presented using differential transformation and finite difference methods. The results of the two methods are compared and very good agreements are established. However, with the aid of the approximate analytical solution, parametric studies of the effects of thermal-geometric and thermo-physical fin parameters such as the Peclet number, thermal conductivity parameter, convection parameter, porosity parameter and internal heat generation parameter on the temperature distribution, rate of heat transfer and thermal efficiency of the fin are investigated. From the analysis, it is found that increase in porosity, convective, increase the rate of heat transfer from the fin and consequently improve the efficiency of the fin while increase in thermal conductivity and internal heat generation decreases the rate of heat transfer from the fin. It is hoped that the numerical and semi-analytical studies presented in this paper will help in providing good physical insights in practice.

[1] Kraus, A. D., Aziz, A., Welty, J. (2001). Extended surface heat transfer. Wiley; 2001.

[2] 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, volume 99 2016, pp. 1316-1330.

[3] Chiu, C. H., Chen, C. K. (2002). A decomposition method for solving the convective longitudinal fins with variable thermal conductivity. Int J Heat Mass Transf, 2002, 45: 2067-2075.

[4] Arslanturk, C. (2005). A decomposition method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Int Commun Heat Mass Transf, 2005, 32: 831-841.

[5] Rajabi, A. (2007). Homotopy perturbation method for fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Phys Lett A, 2007, 364: 33-37.

[6] Domairry, G., Fazeli, M. (2009). Homotopy analysis method to determine the fin efficiency of convective straight fins with temperature-dependent thermal conductivity. Commun Nonlinear Sci Numer Simul, 2009, 14: 489-499.

[7] Kulkarni, D. B., Joglekar, M. M. (2009). Residue minimization technique to analyze the efficiency of convective straight fins having temperature-dependent thermal conductivity. Appl Math Comput, 2009, 215: 2184-2191.

[8] Bouaziz, M. N., Aziz, A. (2010). Simple and accurate solution for convective-radiative fin with temperature dependent thermal conductivity using double optimal linearization. Energ Convers Manage, 2010, 51: 2276-2782.

[9] Ranjan, D. (2011). A simplex search method for a conductive-convective fin with variable conductivity. Int J Heat Mass Transf, 2011, 54: 5001-5009.

[10] Aziz, A., Khani, F. (2011). Convection-radiation from a continuous moving fin of variable thermal conductivity. J Franklin Inst, 2011, 348: 640-651.

[11] Aziz, A., Lopez, R. J. (2011). Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing. Int J Therm Sci, 2011, 50: 1523-1531.

[12] Torabi, M., Yaghoobi, H., Aziz, A. (2012). Analytical solution for convective-radiative continuously moving fin with temperature-dependent thermal conductivity. Int J Thermophys, 2012, 33: 924-941.

[13] A. S. V. Ravi Kanth and N. Uday Kumar. Application of the Haar Wavelet Method on a Continuously Moving Convective-Radiative Fin with Variable Thermal Conductivity. Heat Transfer—Asian Research . DOI: 10.1002/htj.21038.

[14] Sharqawy, M. H., Zubair, S. M. (2008). Efficiency and optimization of straight fins with combined heat and mass transfer—an analytical solution. Appl Therm Eng, 2008, 28: 2279-2288.

[15] Fouladi, F., Hosseinzadeh, E., Barari, A., Domairry, G. (2010). Highly nonlinear temperature-dependent fin analysis by variational iteration method. Heat Transf Res, 2010, 41: 155-165.

[16] Malekzadeh, P., Rahideh, H., Karami, G. (2006). Optimization of convective-radiative fins by using differential quadrature method. Energy Convers Manag, 2006, 47: 1505-1514.

[17] Kundu, B., Aziz, A. (2010). Performance of a convectively heated rectangular fin with a step change in cross-sectional area and losing heat by simultaneous convection and radiation (step fins under radiation environment). J Heat Transf, 2010, 132: 104502-1.

[18] Ya-song Sun, Jing Ma. (2015). 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, pp. 2851-2860.

[19] Mohsen Torabi, A. Aziz. (2012). Thermal performance and efficiency of convective– radiative T-shaped fins with temperature dependent thermal conductivity, heat transfer coefficient and surface emissivity. International Communications in Heat and Mass Transfer, volume 39, pp. 1018-1029.

[20] Darvishi, M. T., Gorla, R. S. R, Kani, F. (2013). Natural Convection and Radiation in Porous Fins. International Journal for Numerical Methods for Heat & Fluid Flow, volume 23, pp. 1406-1420.

[21] Abdelhalim, E. (2013). On A New Differential Transformation Method for Solving Nonlinear Differential Equation. Asian-European Journal of Mathematics, volume 6.

[22] Maheria, M. G. (2010). Thermal Analysis of Natural Convection and Radiation in Porous Fins. ETD Archive. Paper 447.

[23] Prasad, B. S. (1997). Fin Efficiency and Mechanisms of heat exchange through fins in multi-stream plate-fin heat exchanger: development and application of a rating algorithm. International Journal of Heat Transfer, volume 40, pp. 4279-4288.

[24] Singla, R. K. and Ranjan, D. (2014). Application of decomposition method and inverse parameters in a moving fin. Energy Conversion and Management, volume 84, pp. 268-281.

[25] J. K. Zhou. (1986). Differential Transformation method and its Application for electrical circuits. Hauzhang University Press, Wuhan (China), 1986.

[26] Moradi, A., Rafiee, R. (2013). Analytical Solution to Convection-Radiation of a Continuously Moving Fin with Temperature-Dependent thermal conductivity. Thermal Science, volume 17, pp. 1049-1060.

[27] Dogonchi, A. S., Ganji, D. D. (2016). Convection-Radiation heat transfer study of moving fin with temperature dependent thermal conductivity, heat transfer coefficient and heat generation. Applied Thermal Engineering, 103(2016), pp. 705-712.

[28] A. A. Joneidi, D. D. Ganji, M. Babaelahi. (2009). Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity. International Communications in Heat and Mass Transfer, volume 36, pp. 757-762.

[29] M. Torabi, H. Yaghoobi, and A. Aziz. (2012). Analytical Solution for Convective-Radiative Continuously Moving Fin with Temperature-Dependent Thermal Conductivity Int. J. Thermophysics, (2012), 33: 924-941.

[30] A. Aziz, Robert J. Lopez. (2011). Convection-radiation from a continuously moving, variable thermal conductivity sheet or rod undergoing thermal processing. I. J. of Thermal Sciences, 50(2011), 1523-1531.

[31] A. Aziz, F. Khani. (2011). Convection-radiation from a continuously moving fin of variable thermal conductivity. J. of Franklin Institute, 348(2011), 640-651.

[32] S. Singh, D. Kumar, K. N. Rai. (2013). 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.

[33] A. Aziz, M. Torabi. (2012). 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).

[34] J. Ma, Y. Sun, B. W. Li, H. Chen. (2016). Spectral collocation method for radiative-conductive porous fin with temperature dependent properties. Energy Conversion and Management, 111(2016), 279-288.

[35] Y. Sun, J. Ma, B. W. Li, H. (2015). Spectral collocation method for convective-radiative transfer of a moving rod with variable thermal conductivity. International Journal of Thermal Sciences, 90(2015), 187e196.

**Heat Transfer Analysis of a Rectangular Moving Porous Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation: Comparative and Parametric Studies**

**How to cite this paper:** M. G. Sobamowo, A. A. Yinusa, M. O. Salami, O. C. Osih, B. O. Adesoye. (2021). Heat Transfer Analysis of a Rectangular Moving Porous Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation: Comparative and Parametric Studies. *Engineering Advances*, **1**(**2**), 50-66.

DOI: http://dx.doi.org/10.26855/ea.2021.12.004

- Modeling and Design of a Prototype Footstep Power Generating Machine
- Heat Transfer Analysis of a Rectangular Moving Porous Fin with Temperature-Dependent Thermal Conductivity and Internal Heat Generation: Comparative and Parametric Studies
- Noble Metals Potential of Gudjareti-Khachkovi Ore Field, Georgia
- Performance Analysis of Flameproof Submersible Pump for Mining Application
- Numerical Investigation of Adiabatic Film Cooling Effectiveness over Flat Plate with ESCR Shape Ramp Configuration
- Nanofabrics—The Smart Textile