摘要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.
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.
Chandaneswar Midya*. Exact Solutions of Chemically Reactive Solute Distribution in MHD Boundary Layer Flow over a Shrinking Surface[J]. 中国物理快报, 2012, 29(1): 14701-014701.
Chandaneswar Midya*. Exact Solutions of Chemically Reactive Solute Distribution in MHD Boundary Layer Flow over a Shrinking Surface. Chin. Phys. Lett., 2012, 29(1): 14701-014701.
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