Thermal performance of a longitudinal fin under the influence of magnetic field using Sumudu transform method with pade approximant (STM‐PA)

Abstract

Temperature distribution, and efficiency of a rectangular profiled longitudinal fin are examined in this investigation with the impact of the magnetic field. By exploiting appropriate non‐dimensional terms, the heat transfer equation incorporating temperature‐dependent thermal conductivity, heat transfer coefficient, and Maxwell expression for the effect of the magnetic field yield a dimensionless nonlinear ordinary differential equation (ODE) with corresponding boundary conditions (BCs). Sumudu transform method with Pade approximant (STM‐PA) has been employed to obtain an analytical solution for the temperature profile of a longitudinal rectangular fin subjected to a uniform magnetic field under multi‐boiling heat transfer. The STM‐PA results are compared to the Runge‐Kutta Fehlberg's fourth‐fifth (RKF‐45) order technique for computational verification and are observed to be in good accordance. The behavior of dimensionless temperature profile has been explicated graphically for diverse values of non‐dimensional parameters such as thermal conductivity parameter, Hartmann number, and thermogeometric parameter. The results of this study show that as the thermal conductivity parameter enriches, the temperature profile of the longitudinal fin improves, whereas it declines for the Hartmann number and thermogeometric parameter. Under multi‐boiling heat transference, fin efficiency varies significantly depending on the impact of pertinent variables.

A mathematical study on non-linear temperature-dependent thermal conductivity

“…For Case 2: Figures 5 and 6 demonstrate the dimensionless temperature  (X) with the dimensionless axial coordinate X using Eqn. (23) for several physical parameters N, G,  C and  G . As seen in Figure 5, the temperature increases as the value of  C raises.…”

“…With the help of DTM and the modified residual power series method (MRPSM), Sowmya et al [22] address the temperature feature of a convective-radiative rectangular patterned annular fin regarding the presence of a magnetic field. Sowmya et al [23] adopted the Sumudu transform technique with Pade approximant (STM-PA) and the differential transform approach with Pade approximation (DTM-PA)…”

“…All of the aforementioned studies make the assumption that thermal conductivity is either a constant or an exponential function of temperature, or linearly temperature-dependent [25]. Furthermore, the temperature distribution can be derived by a lengthy computation process using a variety of analytical and numerical techniques that have been used in numerous investigations [20][21][22][23][24][25][26]. Thus, the aim of this work is to offer a simple calculation-based solution for the temperature distribution of a longitudinal fin in both linear and non-linear cases and to demonstrate the effectiveness of the technique.…”