Exact Solutions of Chemically Reactive Solute Distribution in MHD Boundary Layer Flow over a Shrinking Surface

Abstract

An analytical study of the distribution of a reactant solute undergoing a first-order chemical reaction in the boundary layer flow of an electrically conducting incompressible fluid over a linearly shrinking surface is presented. The flow is permeated by an externally applied magnetic field normal to the plane of the flow. The equations governing the flow and concentration field are reduced into a set of nonlinear ordinary differential equations using similarity variables. Closed form exact solutions of the reduced concentration equation are obtained for both prescribed power-law surface concentration (PSC) and power-law wall mass flux (PMF) as boundary conditions. The study reveals that the concentration over a shrinking sheet is significantly different from that of a stretching surface. It is found that the solute boundary layer thickness is enhanced with the increasing values of the Schmidt number and the power-law index parameter, but decreases with enhanced values of magnetic and reaction rate parameters for the PSC case. For the PMF case, the solute boundary layer thickness decreases with the increase of the Schmidt number, magnetic and reaction rate parameter for power-law index parameter n = 0. Negative solute boundary layer thickness is observed for the PMF case when n = 1 and 2, and these facts may not be realized in real-world applications.

On the Comparison between Compact Finite Difference and Pseudospectral Approaches for Solving Similarity Boundary Layer Problems

“…We first consider a steady one-dimensional laminar flow of a viscous incompressible electrically conducting fluid over a continuously shrinking sheet. The governing equation is given (see, e.g., [29,30]) in similarity form as…”

“…We first consider the flow of a viscous incompressible electrically conducting fluid over a continuously shrinking sheet which is governed by a third-order nonlinear differential equation. The known exact analytical solution [29,30] of this problem is used as a benchmark to validate the accuracy of the proposed algorithm discussed in this work. We also consider a a three-equation system that models the problem of unsteady free convective heat and mass transfer on a stretching surface in a porous medium in the presence of a chemical reaction [23,31].…”

Effect of Chemical Reaction on Convective Heat Transfer of Boundary Layer Flow in Nanofluid over a Wedge with Heat Generation/Absorption and Suction

“…A chemical reaction is said to be first-order when a reaction rate depends on a single substance and the value of the exponent is one. Midya (2012) observed from their study that the first-order chemical reaction is very important in chemical engineering where the chemical reactions take place between a foreign mass and the working fluid. Bhuvaneswari et al (2009) used Lie group analysis to solve the natural convection heat and mass transfer in an inclined surface with first-order homogenous chemical reaction.…”

Effects of transpiration on unsteady MHD flow of an upper convected Maxwell (UCM) fluid passing through a stretching surface in the presence of a first order chemical reaction

“…It is known that several chemical reactions can be approximated by the first-order or pseudo first-order reaction. [46] Even zeroth and second-order reactions can be approximated satisfactorily by the first order reaction up to 60% conversion if we are concerned mainly with the changes of compositions with the reaction time. [46] Therefore, the first-order chemical reaction plays a significant role in chemical engineering.…”