This research presents a review of an analytical simulation of heat and mass transmission features of steady, non-Newtonian Casson fluid motion across a permeable medium through a stretching surface. The effects of heat production and thermal emission are put into discussion. Mathematically, the governing model is manipulated by a series of nonlinear partial equations, which are then modified into ordinary differential equations with the assistance of appropriate conversion. Analytical results for such equations are then achieved by invoking the notable technique of the homotopy analysis method (HAM), and its solution sounds good while achieving the convergence guaranteed in the convergence table. Some achievements have been made. The consequence of raising the value of the Casson parameter is comprehended to be putting down the velocity field while increasing the temperature field. Also, the concentration field falls with an increase in the Schmidt number, while it rises with an enhancement in the Soret number. The electric parameter due to Lorentz’s force is capable of accelerating the temperature of the fluid but downsizing the velocity.