In this work, we have studied analytically the heat and mass transfer of unsteady MHD natural convective flow past a motioning plate with binary chemical reaction. The flow surface spontaneously moves with unvaried velocity in the flow direction or opposite under the influence of magnetic field. We studied both frequency-dependent effects and "long-time" effects that would require non-practically long channels to be observed in steady flow. We also explored mathematically the important aspects of reactive fluid flow, especially the residence time flow behaviour, scale-up and scale-down procedures. From the present study, it is seen amongst others that temperature is enhanced as the fluid angular velocity rises which leads to maximum temperature in the body of the liquid. It is discovered that mean velocity decrease with a rise in the species reaction and reaction order. The graphical results representing the governing flow parameters effect were presented and discussed. The flow conditions at the wall were also investigated, presented and described.

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A theoretical investigation on the flow of nonlinear magnetohydrodynamic (MHD), laminar, viscous, incompressible boundary layer fluid with thermal radiative heat transfer and variable properties past a stretching plate was carried out. The liquid is taken to be gray, absorbing, emitting but with non-scattering medium. The main nonlinear equations governing the flow are reduced to ordinary differential equations by using appropriate similarity variables and quantities. The obtained nonlinear equations are computationally solved by applying shooting techniques coupled with Nachtsheim-Swigert method for asymptotic satisfaction of boundary conditions by fourth order Runge-Kutta scheme. The computational results for momentum and heat distribution are obtained for various values of the emerging parameters. The results for the coefficient of skin friction and dimensionless heat gradient are likewise obtained for different physical parameters values. From the study, it was observed that the parameters which enhanced the heat source terms decreased the fluid viscosity and caused increase in the flow rate. Also, parameter that reduced heat source terms encouraged viscosity which resulted in retardation of the fluid velocity.

An unsteady flow of heat and species transport through a porous medium in an infinite movable vertical permeable flat surface is considered. The hydromagnetic chemical reactive fluid flow is stimulated by the thermal and solutant convection, and propelled by the movement of the surface. The formulated nonlinear flow equations in time space are solved analytically by asymptotic expansions to obtain solutions for the flow momentum, energy and chemical concentration for various thermo-physical parameters. The existence of flow characteristic is defined with the assistance of the flow parameters. In the study, the impact of some pertinent flow terms is reported and discussed. The study revealed that the species boundary layer increases with a generative chemical reaction and decreases with a destructive chemical reaction. Also, arise in the generative species reaction term reduces the flow momentum for the cooling surface. The impact of other flow governing parameters is displayed graphically as well as the fluid wall friction, wall energy and species gradients. The results of this study are important in chemical thermal engineering for monitoring processes to avoid solution blow up.

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