An Explicit Fourth-Order Compact Numerical Scheme for Heat Transfer of Boundary Layer Flow

Yasir Nawaz, Muhammad Shoaib Arif, Wasfi Shatanawi and Amna Nazeer
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Yasir Nawaz: Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad Capital Territory 44000, Pakistan
Muhammad Shoaib Arif: Department of Mathematics, Air University Islamabad, PAF Complex E-9, Islamabad Capital Territory 44000, Pakistan
Wasfi Shatanawi: Department of Mathematics and General Sciences, Prince Sultan University Riyadh, Riyadh 12435, Saudi Arabia
Amna Nazeer: Department of Mathematics, Comsats University, Islamabad Capital Territory 45550, Pakistan

Energies, 2021, vol. 14, issue 12, 1-17

Abstract: The main contribution of this article is to propose a compact explicit scheme for solving time-dependent partial differential equations (PDEs). The proposed explicit scheme has an advantage over the corresponding implicit compact scheme to find solutions of nonlinear and linear convection–diffusion type equations because the implicit existing compact scheme fails to obtain the solution. In addition, the present scheme provides fourth-order accuracy in space and second-order accuracy in time, and is constructed on three grid points and three time levels. It is a compact multistep scheme and conditionally stable, while the existing multistep scheme developed on three time levels is unconditionally unstable for parabolic and considered a type of equations. The mathematical model of the heat transfer in a mixed convective radiative fluid flow over a flat plate is also given. The convergence conditions of dimensionless forms of these equations are given, and also the proposed scheme solves equations, and results are compared with two existing schemes. It is hoped that the results in the current report are a helpful source for future fluid-flow studies in an industrial environment in an enclosure area.

Keywords: compact explicit scheme; nonlinear PDEs; flow over the plate; mixed convection; thermal radiation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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