On solution existence of MHD Casson nanofluid transportation across an extending cylinder through porous media and evaluation of priori bounds.

It is a theoretical exportation for mass transpiration and thermal transportation of Casson nanofluid over an extending cylindrical surface. The Stagnation point flow through porous matrix is influenced by magnetic field of uniform strength. Appropriate similarity functions are availed to yield the transmuted system of leading differential equations. Existence for the solution of momentum equation is proved for various values of Casson parameter [Formula: see text], magnetic parameter M, porosity parameter [Formula: see text] and Reynolds number Re in two situations of mass transpiration (suction/injuction). The core interest for this study aroused to address some analytical aspects. Therefore, existence of solution is proved and uniqueness of this results is discussed with evaluation of bounds for existence of solution. Results for skin friction factor are established to attain accuracy for large injection values. Thermal and concentration profiles are delineated numerically by applying Runge-Kutta method and shooting technique. The flow speed retards against M, [Formula: see text] and [Formula: see text] for both situations of mass injection and suction. The thermal boundary layer improves with Brownian and thermopherotic diffusions.