Document Type : Full article

Authors

1 Chemical Engineering Shiraz university of thechnology

2 Shiraz University of Technology

Abstract

The main objective of this research is to analyze optimization and the thermal performance of circular porous fins with four different profiles, rectangular, convex, triangular and concave under fully wet conditions. In this research, a linear model was used for the relationship between humidity and temperature. Also, modeling is assumed one-dimensional and the temperature changes only in the direction of the radius of the fin. Moreover, the thermal conductivity and heat transfer coefficient are a function of porosity and temperature, respectively. The governing equations are solved using the Galerkin method and the finite difference method and the use of the Gauss-Seidel algorithm. In this study, the effect of different parameters including relative humidity, Darcy number and Rayleigh number and porosity on temperature distribution, fin efficiency, and fin effectiveness was investigated. The results showed that the efficiency, effectiveness, and heat transfer rate to the base for the rectangular profile is higher than other profiles.
In this research, the Nelder-Mead algorithm is used for optimization. The results showed that to maintain optimal conditions, the ratio of thickness to fin length should be increased by increasing relative humidity or decreasing the Darcy number, Rayleigh number and porosity.

Keywords

[1]     Sharqawy, M. H. and Zubair, S. M., “Efficiency and optimization of straight fins with combined heat and mass transfer–An analytical solution”, Applied Thermal Engineering, 28 (17), 2279 (2008).
[2]     Sabbaghi, S., Rezaii, A., Shahri, G. R. and Baktash, M., “Mathematical analysis for the efficiency of a semi-spherical fin with simultaneous heat and mass transfer”, International Journal of Refrigeration, 34 (8), 1877 (2011).
[3]     Hatami, M., Ahangar, G. R. M., Ganji, D. and Boubaker, K., “Refrigeration efficiency analysis for fully wet semi-spherical porous fins”, Energy Conversion and Management, 84, 533 (2014).
[4]     McQuiston, F., “Fin efficiency with combined heat and mass transfer”, ASHRAE Transactions, 81 (1), 350 (1975).
[5]     Wu, G. and Bong, T. Y., “Overall efficiency of a straight fin with combined heat and mass transfer”, ASHRAE Transactions, 100 (1), 367 (1994).
[6]     Razelos, P. and Imre, K., “The optimum dimensions of circular fins with variable thermal parameters”, Journal of Heat Transfer, 102 (3), 420 (1980).
[7]     Kim, S. Paek, J. and Kang, B., “Flow and heat transfer correlations for porous fin in a plate-fin heat exchanger”, Journal of Heat Transfer, 122 (3), 572 (2000).
[8]     Kiwan, S. and Al-Nimr, M., “Using porous fins for heat transfer enhancement”, Journal of Heat Transfer, 123 (4), 790 (2001).
[9]     Kundu, B. and Das, P., “Performance analysis and optimization of straight taper fins with variable heat transfer coefficient”, International Journal of Heat and Mass Transfer, 45 (24), 4739 (2002).
[10]  Abu-Hijleh, B. A/K, “Natural convection heat transfer from a cylinder with high conductivity permeable fins”, Journal of Heat Transfer, 125 (2), 282 (2003).
[11]  Arslanturk, C., “Simple correlation equations for optimum design of annular fins with uniform thickness”, Applied Thermal Engineering, 25 (14), 2463 (2005).
[12]  Naphon, P., “Study on the heat transfer characteristics of the annular fin under dry-surface, partially wet-surface, and fully wet-surface conditions”, International Communications in Heat and Mass Transfer, 33 (1), 112 (2006).
[13]  Sharqawy, M. H. and Zubair, S. M., “Efficiency and optimization of an annular fin with combined heat and mass transfer–An analytical solution”, International Journal of Refrigeration, 30 (5), 751 (2007).
[14]  Kiwan, S., “Thermal analysis of natural convection porous fins”, Transport in Porous Media, 67 (1), 17 (2007).
[15]  Gorla, R. S. R. and Bakier, A., “Thermal analysis of natural convection and radiation in porous fins”, International Communications in Heat and Mass Transfer, 38 (5), 638 (2011).
[16]  Kundu, B., Bhanja, D. and Lee, K. S., “A model on the basis of analytics for computing maximum heat transfer in porous fins”, International Journal of Heat and Mass Transfer, 55 (25), 7611 (2012).
[17]  Moradi, A., Hayat, T. and Alsaedi, A., “Convection-radiation thermal analysis of triangular porous fins with temperature-dependent thermal conductivity by dtm”, Energy Conversion and Management, 77, 70 (2014).
[18]  Darvishi, M. T., Khani, F. and Gorla, R. S. R., “Natural convection and radiation in a radial porous fin with variable thermal conductivity”, International Journal of Applied Mechanics and Engineering, 19 (1) 27 (2014).
[19]  Darvishi, M. T., Gorla, R. S. R., Khani, F. and Aziz, A., “Termal performance of a porous radial fin with natural convection and radiative heat losses”, Thermal Science, 9 (2), 669 (2015).
[20]  Sobamowo, M. G., “Heat transfer study in porous fin with temperature dependent thermal conductivity and internal heat generation using Legendre wavelet collocation method”, Communication in Mathematical Modeling and Applications, 2 (3), 16 (2017).
[21]  Jooma, R. and Harley, C., “Heat transfer in a porous radial fin: Analysis of numerically obtained solutions” Advances in Mathematical Physics, Article ID: 1658305, 20 pages, (2017). (https://doi.org/10.1155/2017/1658305).
[22]  Daradji, N. and Bouaziz, M. N., “Modelling a spiral porous fin with temperature dependent and independent thermal conductivity”, International Journal of Applied Engineering Research, 13 (7), 5522 (2018).
[23]  Alhumoud, J. M., “Non-equilibrium natural convection flow through a porous medium”, Mathematical Modeling of Engineering Problems, 6 (2), 136 (2019).
[24]  Kiwan, S., “Effect of radiative losses on the heat transfer from porous fins”, International Journal of Thermal Sciences, 46 (10), 1046 (2007).
[25]  Vahabzadeh, A., Ganji, D. and Abbasi, M., “Analytical investigation of porous pin fins with variable section in fully-wet conditions”, Case Studies in Thermal Engineering, 5, 1 (2015).
[26]  Hatami, M. and Ganji, D., “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 (2014).
[27]  Nield, D. A. and Bejan, A., Convection in porous media, 3rd ed., Springer, USA, p. 121 (2006).
[28]  Hazarika, S. A., Bhanja, D., Nath, S. and Kundu, B., “Geometric optimization and performance study of a constructal t-shaped fin under simultaneous heat and mass transfer”, Applied Thermal Engineering, 109, 162 (2016).
[29]  Chilton, T. H. and Colburn, A. P., “Mass transfer (absorption) coefficients prediction from data on heat transfer and fluid friction”, Industrial & Engineering Chemistry, 26 (11), 1183 (1934).
[30]  Grandin, H., Jr., Fundamentals of the finite element method, Macmillan Publishing Company, p. 50 (1986).
[31]  Cicelia, J. E., “Solution of weighted residual problems by using Galerkin's method”, Indian Journal of Science and Technology, 7 (3S), 52 (2014).
[32]  Kundu, B. and Bhanja, D. “An analytical prediction for performance and optimum design analysis of porous fins”, International Journal of Refrigeration, 34 (1), 337 (2011).
[33]  Nelder, J. A. and Mead, R., “A simplex method for function minimization”, The Computer Journal, 7 (4), 308 (1965).