Utilization of modified fluxes on thermal and mass transportation in Williamson material

Due to numerous applications, stretched flows got much attention now days. Current inspection discusses the involvement of thermal and mass transport in Williamson material past over a bi-directional surface. The surface in stretched along x- and y- axies and flow occupies the region z >= 0. Heat transport is modeled via modified heat flux model (MHFM), whereas, generalized mass flux has been used in transportation of mass. The theory of boundary layer (BL) has been utilized on modeling the conservation laws with certain important considerations. Afterwards, the obtained ODEs have been approximated after transformation via optimal homotopy analysis procedure (OHAP). The convergence of used scheme is shown through error analysis table. Efficiency and authenticity of the code is shown by comparative study. Applications of magnetic field (variable), Williamson number, and index number make reduction in flow. The maximum amount of production in thermal energy is obtained using large values of Brownian motion and thermophoresis. Such considered model is used in the applications like improvement in thermal energy, recovery in petroleum, adjusting cooling (devices), and energy devices.