Numerical solution of magnetohydrodynamics radiative flow of Oldroyd-B nanofluid toward a porous stretched surface containing gyrotactic microorganisms

In this article, we explore an incompressible steady flow of Oldroyd-B nanofluid near a plan porous stretched surface considering the influence of thermophoresis, Brownian motion, and thermal radiation. Moreover, the constant magnetic field of intensity B₀ is implemented with a low Reynolds number as well as the induced magnetic effect and the electric fields are ignored. The suitable similarity variables are applied to the governing partial differential equations (PDEs) which yield the dimensionless ordinary differential equations (ODEs). The MATLAB function bvp4c has been used to resolve the resulting ODEs. The attributes of various flow parameters on the transfer rate of mass, heat, density number of motile microorganisms, motile density, temperature, velocity, and nanoparticles concentration have been explored. It is determined that the boosting values of Prandtl number, solutal stratified, and the radiation parameter supports the boosting of heat transfer rate, and their reduction is assisted by the boosting values of thermal stratified and Brownian motion parameter. Moreover, the higher values of Brownian motion parameters and Schmidt number are more effective in the boosting of Sherwood number, although an opposite behavior is spotted for the boosting values of the thermophoresis and solutal stratified parameter. In the same way, the fluid velocity declines with the escalation of Deborah numbers, Hartmann number, and porosity parameter as well as the fluid temperature minimizes for the inclination of Prandtl number and thermal stratified parameter although it is magnified for the inclination of radiation parameter.