An unconditionally stable third order scheme for mixed convection flow between parallel plates with oscillatory boundary conditions

Abstract

This work proposes an unconditionally stable third-order multistep technique for time-dependent partial differential equations. Its unconditional stability is proved by employing von Neumann stability analysis, and constructed Matlab code is another solid proof of the existence of the such scheme. The scheme is constructed on three consecutive time levels, and a compact fourth-order scheme is considered for spatial discretization. The convergence conditions are found when applied to the system of parabolic equations. The scheme is tested on two examples of flow between parallel plates. The mathematical model of heat and mass transfer of flow between parallel plates under the effects of viscous dissipation, thermal radiations, and chemical reaction is given and solved by the proposed scheme. The impact of some parameters, including radiation and reaction rate parameters, on velocity, temperature, and concentration profiles is also illustrated by graphs. The proposed scheme is also compared with the existing scheme, providing faster convergence than an existing one. The fundamental benefit of the proposed scheme is that it can give a compact fourth-order solution to parabolic equations.

A two‐stage reliable computational scheme for stochastic unsteady mixed convection flow of Casson nanofluid

“…The appearance of high‐powered multiprocessing processors and intuitive cluster management software has revitalized this strategy. More research is required to address the gap in the literature on stochastic computational analysis of non‐Newtonian fluid 24–29 . The present investigation might be strengthened by applying a higher‐order computational method and Casson fluid.…”

“…More research is required to address the gap in the literature on stochastic computational analysis of non-Newtonian fluid. [24][25][26][27][28][29] The present investigation might be strengthened by applying a higher-order computational method and Casson fluid.…”