In this research paper, a numerical investigation of effects of Reynolds number and Elastic number, using MATLAB built in bvp4c solver technique has been done on Walter B fluid flow past a vertical channel. The suitable similarity transformation has been adopted to convert the boundary layer governing equations (Partial Differential Equations) into its corresponding solvable ordinary differential equations and these equations are solved using MATLAB bvp4c scheme. The normal and tangential velocity profiles are drawn for various values of parameter such as Reynolds number (Re) and Elastic number (S) and results are analysed graphically. It is perceived that with enhance of Reynolds number as well as Elastic number the normal velocity profile enhances. Further an error analysis has been done by comparing the work with the results obtained from Homotopy Perturbation Method and the comparison is found to be in very good agreement.

An analysis has been done to scrutinize the existence of dual solutions of the Casson nanofluid caused due to an exponential form of stretching surface which is situated in porous medium and second order velocity slip. An uniform magnetic field is considered in the transverse dirction of the flow. A suitable similarity transformation is employed to amend the model equations into solvable form and hence solved by adopting the MATLAB built-in bvp4c solver scheme. Results are discussed through both graphical mode and tabulations with respect to some novel flow parameters. The stability analysis has been studied and found two solutions, one is stable in nature and physically tractable. From the study, we have seen that the flow parameters associated with nanofluid enhance the heat transfer of the fluid. The Casson fluid parameter has also a power to increase temperature of the system.