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Convective flow is a self-sustained flow with the effect of the temperature gradient. The density is non-uniform due to the variation of temperature. The effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in a different field, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of MHD unsteady second-grade fluid in the presence of ramped boundary conditions near a porous surface. The dynamical analysis of heat transfer is based on classical differentiation with no memory effects. The non-dimensional form of the governing equations of the model is developed. These are solved by the classical integral (Laplace) transform technique/method with the convolution theorem and closed-form solutions are attained for temperature, concentration, and velocity. The physical aspects of distinct parameters are discussed  via  graph to see the influence on the fluid concentration, velocity, and temperature. Our results suggest that the velocity profile decrease by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness of momentum and enlargement of thermal conductivity. Furthermore, to validate our results, some results are recovered from the literature.

Dynamical Analysis of Radiation and Heat Transfer on MHD Second Grade Fluid