Exact solutions involving special functions for unsteady convective flow of magnetohydrodynamic second grade fluid with ramped conditions

Muhammad Bilal Riaz,Ali Akgül,Kashif Ali Abro,Aziz Ur Rehman,Muhammad Abbas,Khadijah M Abualnaja,Y S Hamed

doi:10.1186/s13662-021-03562-y

Abstract

A number of mathematical methods have been developed to determine the complex rheological behavior of fluid’s models. Such mathematical models are investigated using statistical, empirical, analytical, and iterative (numerical) methods. Due to this fact, this manuscript proposes an analytical analysis and comparison between Sumudu and Laplace transforms for the prediction of unsteady convective flow of magnetized second grade fluid. The mathematical model, say, unsteady convective flow of magnetized second grade fluid, is based on nonfractional approach consisting of ramped conditions. In order to investigate the heat transfer and velocity field profile, we invoked Sumudu and Laplace transforms for finding the hidden aspects of unsteady convective flow of magnetized second grade fluid. For the sake of the comparative analysis, the graphical illustration is depicted that reflects effective results for the first time in the open literature. In short, the obtained profiles of temperature and velocity fields with Laplace and Sumudu transforms are in good agreement on the basis of numerical simulations.

Highlights

The natural convection heat transfer from a vertical plate to a fluid has implementations in many industrial processes
Seth et al [4, 5] have obtained the exact solutions of the MHD natural convection flow
5 Results and discussion From Eqs. (34) and (41), we observe that the temperature profile has two different solution expressions calculated by Sumudu transformation in (34) and by Laplace transformation method in (41)

Summary

Introduction

The natural convection heat transfer from a vertical plate to a fluid has implementations in many industrial processes. The implementations of the Sumudu transform method of the partial differential equations have been discussed in the literature [8]. Integro-differential equations have been investigated by Sumudu transform in [10]. To get the Sumudu transformation for the second order derivative of the function r(t), proceeding in the same way, we obtain d2r(t) 1 dr(t)

Results

Conclusion