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We proposed a mathematical model for an incompressible, viscous, natural convection, and stagnation point slip flow of MHD Prandtl fluid over an infinite plate. The governing flow equations are constructed using the Prandtl rheological model. In account of physical relevance, we investigated the Soret and Dufour effects on the flow field. The complex natured flow equations are transformed to a set of PDEs using a suitable similarity variables. The non-dimensionalized ruling problem together with physical boundary conditions is numerically analyzed via Crank-Nicolson scheme. The velocity, temperature and concentration of the diffusing species distributions are enhanced for higher values of unsteadiness parameter. It is noted that velocity is slightly decreasing for higher values of Reynolds number while smaller values of Re providing more dominant effects on the velocity, temperature and concentration of the diffusing species profiles and enhanced heat and mass transfer rates is noticed. The physical behavior of reduced Nusselt and Sherwood numbers, friction factor, for distinct values of emerging parameters is examined and representative set of graphs are presented. Highlights Flow model is presented for MHD Prandtl fluid flow over an infinite plate. Mathematical model is performed for unsteady flow with Soret and Dufour effects. The proposed model is solved via crank Nicolson finite difference scheme. Simulations are performed for skin friction, Nusselt and Sherwood numbers.

This study investigates the heat augmentation and hydromagnetic flow of water-based carbon nanotubes (CNTs) inside a partially heated rectangular fin-shaped cavity. A thin heated rod is placed within the cavity to create a resistance or to provide a source for heat transfer. The obstacle is tested for the heated case, while the right side of the horizontal tip is tested for three different temperatures (adiabatic, cold, and heated). The left vertical side of the cavity is partially heated with temperature Th, and the rest of the sides are kept cold at temperature Tc except the right tip. Two different thermal boundary conditions (prescribed temperature and adiabatic) are employed on the fin tip. The CNTs and water are assumed to be in thermal equilibrium with no-slip velocity. The magnetic field and thermal radiation are introduced in the momentum and energy equations, respectively. The governing equations are obtained in dimensionless form by means of dimensionless variables. The numerical computation is performed via the finite element method using the Galerkin approach. The substantial effects of emerging parameters on the streamlines, isotherms, dimensionless velocities, and temperature are reported graphically and discussed. In the case of a cold or adiabatic fin-tip, a drop to minimum is found in the dimensionless temperature. The components of velocity are perceived maximum at a vertical corner while minimum at the horizontal corner. It is demonstrated that the local Nusselt numbers are increased by introducing both solid volume fraction of CNTs and radiation effects, while the Nusselt number noticed maximum at the corners.