Improve Analytical Solutions for Trapezoidal, Rectangular and Dovetail Shapes of Inclined Longitudinal Porous Fin
DOI:
https://doi.org/10.37934/cfdl.17.1.140161Keywords:
Natural convection, Fully wet fin, Galerkin method, least squares method, differential transform methodAbstract
This study improved the approximate analytical solutions of the heat distribution and transport of inclined longitudinal porous fin in the presence of radiative and convective environments with rectangular, trapezoidal, and dovetail profiles. The model of Darcy, which mimics the interaction of fluids and solids, is utilized to obtain the equation of governing the heat transfer of the porous fin. To investigate the rectangular, trapezoidal, and dovetail profiles, a single equation has been solved through analysis of the mathematical model by using the optimal differential transform method (ODTM) which consist least squares differential transform method (LSDTM), and the Galerkin differential transform method (GDTM) while the BVP4c presents the numerical solution. A comparison is made between the approximate analytical and numerical solutions for different parameters. It results in that the solutions produced from LSDTM and GDTM are closer to the numerical solution than the solutions of DTM, nonlinear autoregressive exogenous-levenberg marquardt algorithm (NARX-LMA) and cascade feedforward backpropagated-levenberg marquardt algorithm (CFB-LMA). A comprehensive graphic analysis was conducted to examine the effect of variation in inclination angles, tapering at the tip, wet porous parameters, internal heat generation, progressive natural convection parameters, and dimensionless radiation parameters on the thermal profile and thermal transfer rate of the porous longitudinal fin. The split fin design achieves the greatest heat transfer rate, trailed by rectangular and trapezoidal fin profiles, assuming that internal heat generation is maintained to a minimum.
Downloads
References
Vafai, K .“Heat Transfer of Nanofluids in Porous Media.” In Handbook of Porous Media, Third Edition, 491–92. CRC Press, 2015. DOI: https://doi.org/10.1201/b18614-18
Nield, Donald A., and Adrian Bejan. “Mechanics of Fluid Flow through a Porous Medium.” In Convection in Porous Media, 1–35. Cham: Springer International Publishing, 2017. DOI: https://doi.org/10.1007/978-3-319-49562-0_1
Panchal, Hitesh, and Ravishankar Sathyamurthy. "Experimental analysis of single-basin solar still with porous fins." International Journal of Ambient Energy 41, no. 5 (2020): 563-569. https://doi.org/10.1080/01430750.2017.1360206. DOI: https://doi.org/10.1080/01430750.2017.1360206
Queipo, Nestor V., and Efrain Nava. "A gradient boosting approach with diversity promoting measures for the ensemble of surrogates in engineering." Structural and Multidisciplinary Optimization 60, no. 4 (2019): 1289-1311. https://doi.org/10.1007/s00158-019-02325-4. DOI: https://doi.org/10.1007/s00158-019-02325-4
Kiwan, Suhil. "Effect of radiative losses on the heat transfer from porous fins." International journal of thermal sciences 46, no. 10 (2007): 1046-1055. https://doi.org/10.1016/j.ijthermalsci.2006.11.013. DOI: https://doi.org/10.1016/j.ijthermalsci.2006.11.013
Kundu, Balaram, and Dipankar Bhanja. "An analytical prediction for performance and optimum design analysis of porous fins." International Journal of Refrigeration 34, no. 1 (2011): 337-352. https://doi.org/10.1016/j.ijrefrig.2010.06.011. DOI: https://doi.org/10.1016/j.ijrefrig.2010.06.011
Gorla, Rama Subba Reddy, and A. Y. Bakier. "Thermal analysis of natural convection and radiation in porous fins." International Communications in Heat and Mass Transfer 38, no. 5 (2011): 638-645. https://doi.org/10.1016/j.icheatmasstransfer.2010.12.024. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2010.12.024
Petroudi, Rahimi Iman, Domairry Davood Ganji, Bahram Amir Shotorban, Khazayi Mehdi Nejad, Ehsan Rahimi, Reza Rohollahtabar, and Fatemeh Taherinia. "Semi-analytical method for solving non-linear equation arising of natural convection porous fin." Thermal Science 16, no. 5 (2012): 1303-1308. https://doi.org/10.2298/tsci1205303p. DOI: https://doi.org/10.2298/TSCI1205303P
Kundu, Balaram, Dipankar Bhanja, and Kwan-Soo Lee. "A model on the basis of analytics for computing maximum heat transfer in porous fins." International Journal of Heat and Mass Transfer 55, no. 25-26 (2012): 7611-7622. https://doi.org/10.1016/j.ijheatmasstransfer.2012.07.069. DOI: https://doi.org/10.1016/j.ijheatmasstransfer.2012.07.069
Abdulridah, Saja Isam, and Abeer Majeed Jasim. "New Analytical Study of Heat Transfer Analysis of Jeffery–Hamel Nanofluid Flow Problem with Porous Medium." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 103, no. 1 (2023): 105-132. https://doi.org/10.37934/arfmts.103.1.105132. DOI: https://doi.org/10.37934/arfmts.103.1.105132
Aziz, A., and Mohsen Torabi. "Convective‐radiative fins with simultaneous variation of thermal conductivity, heat transfer coefficient, and surface emissivity with temperature." Heat Transfer—Asian Research 41, no. 2 (2012): 99-113. https://doi.org/10.1002/htj.20408. DOI: https://doi.org/10.1002/htj.20408
Patel, Trushit, and Ramakanta Meher. "Thermal Analysis of porous fin with uniform magnetic field using Adomian decomposition Sumudu transform method." Nonlinear Engineering 6, no. 3 (2017): 191-200. https://doi.org/10.1515/nleng-2017-0021.
Patel, Trushit, and Ramakanta Meher. "Thermal Analysis of porous fin with uniform magnetic field using Adomian decomposition Sumudu transform method." Nonlinear Engineering 6, no. 3 (2017): 191-200. https://doi.org/10.1515/nleng-2017-0021. DOI: https://doi.org/10.1515/nleng-2017-0021
Jawairia, Shahzadi, and Jawad Raza. “Optimization of Heat Transfer Rate in a Moving Porous Fin under Radiation and Natural Convection by Response Surface Methodology: Sensitivity Analysis.” Chemical Engineering Journal Advances 11, no. 100304 (2022): 100304. https://doi.org/10.1016/j.ceja.2022.100304. DOI: https://doi.org/10.1016/j.ceja.2022.100304
Roy, Pranab Kanti, Hiranmoy Mondal, and Bipattaran Raj. "Analytical and numerical solution of the longitudinal porous fin with multiple power‐law‐dependent thermal properties and magnetic effects." Heat Transfer 51, no. 3 (2022): 2702-2722. https://doi.org/10.1002/htj.22421. DOI: https://doi.org/10.1002/htj.22421
Jasim, Abeer Majeed. "Exploration of No-Slip and Slip of Unsteady Squeezing Flow Fluid Through a Derivatives Series Algorithm." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 100, no. 1 (2022): 11-29. https://doi.org/10.37934/arfmts.100.1.1129. DOI: https://doi.org/10.37934/arfmts.100.1.1129
Zhou, J. K. "Differential transformation and its applications for electrical circuits." (1986).
Kundu, Balaram, Ranjan Das, and Kwan-Soo Lee. "Differential transform method for thermal analysis of exponential fins under sensible and latent heat transfer." Procedia Engineering 127 (2015): 287-294. https://doi.org/10.1016/j.proeng.2015.11.370. DOI: https://doi.org/10.1016/j.proeng.2015.11.370
Sowmya, G., and Bijjanal Jayanna Gireesha. "Analysis of heat transfer through different profiled longitudinal porous fin by differential transformation method." Heat Transfer 51, no. 2 (2022): 2165-2180. https://doi.org/10.1002/htj.22394. DOI: https://doi.org/10.1002/htj.22394
Khudair, Ayad R., and S. A. M. Haddad. "Restricted fractional differential transform for solving irrational order fractional differential equations." Chaos, Solitons & Fractals 101 (2017): 81-85. https://doi.org/10.1016/j.chaos.2017.05.026. DOI: https://doi.org/10.1016/j.chaos.2017.05.026
Hussin, Che Haziqah Che, Arif Mandangan, Amirah Azmi, and Adem Kilicman. "Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 99, no. 2 (2022): 197-206. https://doi.org/10.37934/arfmts.99.2.197206.
Varun Kumar, R. S., G. Sowmya, Fadl A. Essa, B. C. Prasannakumara, M. Alsehli, and B. Saleh. "RETRACTED: Thermal analysis of an annular fin under multi-boiling heat transfer coefficient using differential transform method with Pade approximant (DTM-Pade)." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering (2022): 09544089221076255. https://doi.org/10.1177/09544089221076255. DOI: https://doi.org/10.1177/09544089221076255
Sabdin, Abdul Rahman Farhan, Che Haziqah Che Hussin, Arif Mandangan, Graygorry Brayone Ekal, and Jumat Sulaiman. "Approximate Analytical Solutions for Non-linear Telegraph Equations with Source Term." Journal of Advanced Research in Applied Sciences and Engineering Technology 31, no. 3 (2023): 238-248. DOI: https://doi.org/10.37934/araset.31.3.238248
Yaghoobi, Hessameddin, and Mohsen Torabi. "The application of differential transformation method to nonlinear equations arising in heat transfer." International Communications in Heat and Mass Transfer 38, no. 6 (2011): 815-820. https://doi.org/10.1016/j.icheatmasstransfer.2011.03.025. DOI: https://doi.org/10.1016/j.icheatmasstransfer.2011.03.025
Beleri, Joonabi, and S. Kotnurkar Asha. "Peristaltic transport of Ellis fluid under the influence of viscous dissipation through a non-uniform channel by multi-step differential transformation method." Journal of Advanced Research in Numerical Heat Transfer 9 (2022): 1-18.
Hussin, Che Haziqah Che, Arif Mandangan, Amirah Azmi, and Adem Kilicman. "Solitary Wave Solutions for Forced Nonlinear Korteweg-de Vries Equation by Using Approximate Analytical Method." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 99, no. 2 (2022): 197-206. https://doi.org/10.37934/arfmts.99.2.197206. DOI: https://doi.org/10.37934/arfmts.99.2.197206
Kiwan, Suhil. "Thermal analysis of natural convection porous fins." Transport in porous media 67 (2007): 17-29. https://doi.org/10.1007/s11242-006-0010-3. DOI: https://doi.org/10.1007/s11242-006-0010-3
Ghasemi, S. E., P. Valipour, M. Hatami, and D. D. Ganji. "Heat transfer study on solid and porous convective fins with temperature-dependent heat generation using efficient analytical method." Journal of Central South University 21 (2014): 4592-4598. https://doi.org/10.1007/s11771-014-2465-7. DOI: https://doi.org/10.1007/s11771-014-2465-7
Eshan, Abdul Rauf, and Wah Yen Tey. "Investigation of Shape Parameter for Exponential Weight Function in Moving Least Squares Method." Progress in Energy and Environment (2017): 17-24.
Qayyum, Mubashir, Hamid Khan, M. Tariq Rahim, and Inayat Ullah. "Analysis of unsteady axisymmetric squeezing fluid flow with slip and no-slip boundaries using OHAM." Mathematical Problems in Engineering 2015 (2015). https://doi.org/10.1155/2015/860857. DOI: https://doi.org/10.1155/2015/860857
Meher, Ramakanta, and Nirav D. Patel. "Analytical Investigation of MHD Jeffery–Hamel flow problem with heat transfer by differential transform method." SN Applied Sciences 1, no. 7 (2019): 656. https://doi.org/10.1007/s42452-019-0632-z. DOI: https://doi.org/10.1007/s42452-019-0632-z
Patel, N., and Ramakanta Meher. "Analytical investigation of Jeffery-Hemal flow with magnetic field by differential transform method." Int. J. Adv. Appl. Math. Mech 6 (2018): 1-9.
Khan, Naveed Ahmad, Muhammad Sulaiman, and Fahad Sameer Alshammari. "Heat transfer analysis of an inclined longitudinal porous fin of trapezoidal, rectangular and dovetail profiles using cascade neural networks." Structural and Multidisciplinary Optimization 65, no. 9 (2022): 251. https://doi.org/10.1007/s00158-022-03350-6 DOI: https://doi.org/10.1007/s00158-022-03350-6
Downloads
Published
How to Cite
Issue
Section
