Eur. Phys. J. Plus (2020) 135: 120
https://doi.org/10.1140/epjp/s13360-020-00206-0

Regular Article

A new analytical solution of longitudinal fin with variable heat generation and thermal conductivity using DRA

¹ Mechanical Engineering Department, University of 20 aout 1955, El Hadaiek Road, B. O. 26, 21000, Skikda, Algeria
² Physical Engineering Department, University of 20 aout 1955, El Hadaiek Road, B. O. 26, 21000, Skikda, Algeria
³ Department of Mathematics, Faculty of Science, New Valley University, El-Kharga, Al-Wadi Al-Gadid, 72511, Egypt
⁴ Department of Mathematics, Faculty of Science, Northern Border University, Arar, 1321, Saudi Arabia

^* e-mail: m_r_eid@yahoo.com

Received: 12 November 2019
Accepted: 30 November 2019
Published online: 23 January 2020

Abstract

Abstract

In this paper, nonlinear differential equation for a longitudinal fin (LF) heat transfer with thermal conductivity and heat generation that depends on temperature is solved numerically by employing Runge–Kutta technique of fourth-order (RK4) featuring shooting technique and analytically via a new modified analytical technique called Duan–Rach method. The physical model of the heat transfer was utilized to examine the influences of the thermogeometric parameters, heat transfer rate and variable thermal conductivity on the temperature profile and efficiency of LF. The obtained outcomes show that the temperature profile of fin, heat transfer and the efficiency of the fin are considerably impacted by the fin factor of thermogeometric. The analytical outcomes by a new efficient algorithm are compared with the numerical computations of the RK4 featuring shooting techniques and various available literature outcomes to achieve the precision of the proposed technique. Obtained results show obviously the fidelity of the suggested approach.

Graphic abstract

Flow model of longitudinal fin and the effect of thermogeometric parameter on dimensionless temperature distribution.