Thermal Performance Evaluation of Longitudinal Fins with Various Profiles Using Homotopy Perturbation Method
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RESEARCH PAPER
Thermal Performance Evaluation of Longitudinal Fins with Various Profiles Using Homotopy Perturbation Method Arman Irandegani1 • Murteza Sanjaranipour1
•
Faramarz Sarhaddi2
Received: 18 April 2020 / Accepted: 31 August 2020 Shiraz University 2020
Abstract The thermal performance of longitudinal radiative–convective fins with rectangular, trapezoidal, and concave parabolic profiles was analyzed by the homotopy perturbation method (HPM). The governing equation of the problem was obtained by establishing the energy balance for a longitudinal element on the longitudinal radiative–convective fin. In addition, thermal conductivity, convective heat transfer coefficient, and surface emissivity were assumed to change with temperature. Given its nonlinear nature, the governing equation was solved relying on the HPM. Validating the results from this method with those of the differential transform method, a good agreement was achieved between the two. In parametric studies, the fins were compared in terms of heat transfer rate, effectiveness, and efficiency. Further, the effects of changes in thermal conductivity, emissivity, convection–conduction parameter, and the radiation–conduction parameter were also investigated on the fin performance. The results were suggestive of the potentials of HPM as a reliable tool for solving nonlinear equations such as the energy equation for radiative–convective fins without compromising accuracy or speed. Further, the concave parabolic fin was found to have a higher heat transfer rate, efficiency, and effectiveness than its rectangular and trapezoidal counterparts. Keywords Approximated analytical solution Longitudinal radiative–convective fin Homotopy perturbation method Variable thermal properties
1 Introduction In principle, fins improve the rate of heat transfer from a body to a fluid by extending the heat exchange surface area (Cengel 2007; Kraus et al. 2002). Fins are used in a wide range of engineering applications, including but not limited to heat exchangers, internal combustion engines, solar collectors, and electronic coolers. Accordingly, fins are one of the main components of energy consumption systems. In common analyses used for investigating the thermal performance of fins, simplifying assumptions are made, including uniform temperature distribution across fin cross section, constant thermophysical properties, and linear & Murteza Sanjaranipour [email protected]; [email protected] 1
Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
2
Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran
boundary conditions. These assumptions transform the governing energy equations from partial differential equations (PDEs) to ordinary differential equations (ODEs). Under these conditions, the ODE has an analytical solution, which is based on hyperbolic functions, Bessel functions, etc. Provided that thermophysical properties are temperature-
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