An analytical expression of the current generated from the electrochemical reaction in a porous rotating disk electrode (PRDE) is derived when the reactant transport is dominated by advection and diffusion. Simple algebraic expressions for the concentration of reactant and the current response are obtained as a function of the rotation rate, reaction rate, permeability of the porous medium, diffusion coefficients, kinematic viscosity, and geometry of the porous film. Upon comparison, the analytical expression of current in this work coincides with the existing results for the limiting case of low rotation rates. Also the concentration/current expressions here derived are in satisfactory agreement with numerical results.
<abstract><p>This paper develops the combined effects of free convection magnetohydrodynamic (MHD) flow past a vertical plate embedded in a porous medium. The dimensionless coupled non-linear equations are solved to get the approximate analytical expression for the concentration by using the homotopy perturbation method. For all possible values of parameters, skin lubrication, Nusselt number and Sherwood number are derived.</p></abstract>
An analytical approach has been used to study the heat and mass transfer from a vertical plate embedded in a porous medium experiencing a first-order chemical reaction and exposed to a transverse magnetic field. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved analytically a highly accurate and thoroughly tested using Homotopy Perturbation Method. The effects of Biot number, thermal Grashof number, permeability parameter, Hartmann number, Eckert number, Sherwood number and Schmidt number on the velocity, temperature, and concentration profiles are illustrated graphically. Proportional to the plate surface temperature, the local skin-friction coefficient, the local Nusselt number and the local Sherwood number were also presented analytically. The discussion focuses on the physical interpretation of the results as well their comparison with the results of previous studies.
In this paper, some properties of semi-regular graphs have been studied. The energy of graphs has many mathematical properties, which are being investigated for some of the semi-regular graphs. Also, the Laplacian Energy of these types of the graph has been defined has also been studied. We give examples of semi-regular graphs, describe the barbell class, and describe how the property of semi regularity relates to other properties of graphs.
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