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The implanted porous media plays a key role in the performance of the fluid flow. To study the novelty of porous media in a two‐dimensional fluid motion associated with thermophoretic forces, viscous dissipative heat, and variable thermal conductivity over a permeable horizontal surface, we have adopted appropriate similarity transformation to convert the prominent partial differential equations to nonlinear ordinary differential equations in nondimensional form. MATLAB Bvp4c code is employed for the conservation of equations with the appropriate converted boundary conditions and this finite difference scheme is found stable. Furthermore, we have performed a comparison test for validity and accuracy test and established a satisfactory agreement with former literature. The effect of porosity and thermal conductivity in presence of suction/blowing over the fluid velocity and temperature are significant. In this study, the fluid velocity is enhanced for heat generation and thermal conductivity in presence of blowing. The importance of porous media and such study can be experienced in various branches like petroleum engineering, hydrogeology, biophysics, material science, and so forth.

The impact of heat transfer in micropolar fluid may be developed due to its various promising applications in engineering, bio-medical sciences, geo-thermal progression, spherical storage tanks, nuclear power plants, automobile sectors etc. Motivated by such significance, the current study is to expound the influences of micropolar Casson fluid flow over a solid sphere with Brownian motion, thermophoretic force and buoyancy force surrounded by porous medium. The adopted model having complex PDE’s are reduced to dimensionless ODE’s by utilizing proper similarity solutions. A numerical approach have been carried out for velocity, micro rotation, temperature and concentration, the solutions are procured by Matlab Bvp4c code and plotted graphs for diverse involved parameters. An adequate result is acquired by an assessment with earlier available work. The effects of key parameters on surface drag coefficient, surface thermal flux and particles concentration flux are examined and displayed in tabular form. Grash of number raises the profiles of thermal flux and concentration flux where the buoyancy force is more dominant. Further, the obtained results indicate that the angular velocity is elevated near the surface of the sphere, and they behaves asymptotically far away from the surface due to the effect of micropolar parameter. Moreover, temperature and molar species concentration are enriched with upper values of micropolar factor. It is perceived that, augmented values of Casson parameter amplifies the velocity outline.

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