Similarity Solution of Heat and Mass Transfer for Natural Convection over a Moving Vertical Plate with Internal Heat Generation and a Convective Boundary Condition in the Presence of Thermal Radiation, Viscous Dissipation, and Chemical Reaction
Steady laminar natural convection flow over a semi-infinite moving vertical plate with internal heat generation and convective surface boundary condition in the presence of thermal radiation, viscous dissipation, and chemical reaction is examined in this paper. In the analysis, we assumed that the left surface of the plate is in contact with a hot fluid while the cold fluid on the right surface of the plate contains a heat source that decays exponentially with the classical similarity variable. We utilized similarity variable to transform the governing nonlinear partial differential equations into a system of ordinary differential equations, which are solved numerically by applying shooting iteration technique along fourth-order Runge-Kutta method. The effects of the local Biot number, Prandtl number, buoyancy forces, the internal heat generation, the thermal radiation, Eckert number, viscous dissipation, and chemical reaction on the velocity, temperature, and concentration profiles are illustrated and interpreted in physical terms. A comparison with previously published results on the similar special cases showed an excellent agreement. Finally, numerical values of physical quantities, such as the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number, are presented in tabular form. 1. Introduction Convective flows with simultaneous heat and mass transfer under the influence of the chemical reaction arise in many transport processes both naturally and artificially in many branches of science and engineering applications. This phenomenon plays an important role in the chemical industry, power and cooling industry for drying, chemical vapour deposition on surfaces, cooling of nuclear reactors, and petroleum industries. Natural convection flow occurs frequently in nature. It occurs due to temperature differences, as well as due to concentration differences or the combination of these two; for example, in atmospheric flows, there exist differences in water concentration, and hence the flow is influenced by such concentration difference. Changes in fluid density gradients may be caused by nonreversible chemical reaction in the system as well as by the differences in the molecular weight between values of the reactants and the products. Chemical reactions can be modeled as either homogenous or heterogeneous processes. This depends on whether they occur at an interface or as a single phase value reaction. A homogeneous reaction is one that occurs uniformly throughout a given phase. On the other hand, a heterogeneous reaction
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