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This study is a study of three‐dimensional couple stress Casson fluid flow with nonlinear thermal radiation and heat source effects. The convective heat and mass transfer analysis is applied to a porous stretching sheet. In fluid flow direction, a uniform magnetic field can be applied. Using the similarity transformations, nondimensional expressions are achieved. The obtained equations are found numerically via the shooting technique as well as Runge‐Kutta‐Fehlberg method in MATLAB software. The contribution of different physical parameters is explored and discussed. Such parameters are porous parameter, couple stress parameter, heat source parameter, nonlinear thermal radiation, temperature parameter, and Lewis number. We found, the decreasing rate of heat transfer in the case of couple stress fluid motion when comparing Casson fluid flow with various values of Γ1 ${\Gamma }_{1}$ and Pr $\text{Pr}$.

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In this study, the impact of thermal radiation and partial slip on magnetohy-drodynamic flow of Jeffrey nanofluid comprising motile gyrotactic microorganisms via vertical stretching surface is analysed. The governing partial differential equations are reformed to a system of coupled ordinary differential equations by utilizing the similarity transformations. The transformed equations are of order four which are complex to solve analytically hence, the coupled system is solved computationally by using shooting technique along Runge-Kutta integrated scheme. The ramifications of different thermo-physical parameters on the density of gyrotactic microorganisms, Jeffrey nanofluid velocity, nanoparticles concentration, temperature, Sherwood number and Nusselt number are illustrated graphically. Comparing the current study with the results already published favours the validity of this work. It is established that the Nusselt number is boosted on enhancing the thermal radiation parameter and the reverse trend has been observed on raising the Richardson number, whereas the gyrotactic microorganisms density is more in case of viscous nanofluid compared to Jeffrey nanofluid.