Heat and mass transfer on a stretching/shrinking and porous sheet of variable thickness with suction and injection

Heat and mass transfer in a viscous flow over a non-uniform porous plate of variable thickness is investigated in this paper. The variably heated plate is stretched/shrunk in a stagnant fluid with variable velocity and has the non-uniform species concentration. The governing partial differential equations are simplified and solved numerically. The transport of heat and mass in the flow regime is governed by a set of PDE’s satisfying certain necessary boundary conditions. The governing PDE’s are simplified by using boundary layer approximations and transformed into a set of ODE’s by invoking a set of new transformations. The system of ODE’s contains several dimensionless numbers (parameters) which demonstrates the behavior of all field quantities. All the unknown variables, rates of heat and mass transfer are evaluated and effects of the existing parameters are seen on them, whereas, they are significantly changed with the variation of these dimensionless quantities. New solutions and results are presented in graphs and tables, whereas, they are thoroughly examined and discussed. In addition to that the modeled problem and its solutions are exactly matched with the classical problems and their corresponding solutions for specific numerical values of the governing parameters involved in the current modeled problem. The engineering applications of heat and mass transfer problems are very famous in many industrial processes. Therefore, these two phenomena are widely discussed and analyzed, whereas, they are frequently utilized for the formation of metallic devices/objects while using additive manufacturing processes, cryogenics, formation of reasonable and suitable heat exchangers, falling film evaporation and the steam boilers. However, most of the engineering systems with or without magnetized and electrically conducting surfaces cannot be expressed in usual coordinates i.e. cartesian coordinate system, moreover, most of the engineering processes involve fluids of different nature and kinds, whereas, sometime they also require different physical and environmental conditions. Therefore, in such situations we need, to upgrade and modify the present modeled problem according to prevailing situations.