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.

The influence of variable surface temperature and concentration on MHD stagnation point flow towards a stretching sheet plays an important role in wire coating, film blowing, fiber spinning and coating. In this work an attempt has been made to study the ramification of thermal radiation on MHD chemically reacting liquid past a stretching surface with nonlinear temperature and concentration. The nonlinear coupled governing equations are changed into a set of nonlinear ordinary differential equations by adopting similarity transformations. The set of nonlinear equations together with the boundary conditions are solved computationally by employing shooting technique. The influence of various flow field parameters (magnetic parameter, suction/injection parameter, velocity ratio parameter, heat absorption, radiation, chemical reaction parameter, Schmidt number) on momentum, heat measure, diffusion, skin friction coefficient, rate of heat transfer and rate of mass transfer is depicted and discussed in detail. The outcomes disclosed that the fluid temperature accelerates on rising the thermal radiation and reverse trend with heat absorption parameter. Species concentration diminishes on enhancing the chemical reaction parameter. A comparison has been made with the published results as a particular case and found to be in fair agreement. Keywords Power law form of surface temperature and concentration • MHD • Thermal radiation • Chemical reaction List of symbols B 0 Uniform magnetic field a, b, c, n Constants c fx Skin-friction coefficient c p Specific heat at constant pressure (J kg −1 K) C w (x) =C ∞ + cx n Concentration of the sheet f ′ Dimensionless velocity k Thermal conductivity of fluid (W m −1 k −1

A numerical investigation on MHD fluid flow in parabolic mode has been performed to point out its significant properties. Thermal radiation, porous medium, heat generation, chemical reaction, and thermal diffusion along with variable temperature and concentration are taken into consideration in the analysis. The novelty of the work is the inclusion of heat generation and thermal diffusion along with exponentially varying temperature and concentration. The constituent governing equations are solved by using finite difference schemes in explicit form. The fluctuations in velocity, concentration, and temperature are observed and discussed with the help of graphs as well as numerical data. Their gradients are also calculated and analyzed the flow properties by using numerical tables. The existence of heat generation, as well as viscous dissipation, creates an increment in the temperature. The gradient of heat transfer rises with the impact of Prandtl number and decay in it is examined under the existence of a source of heat and viscous dissipation.

Unsteady magneto hydrodynamic (MHD) free convection flow of a viscous, incompressible and electrically conducting, well known non-Newtonian fluid named as Kuvshinski fluid past an infinite vertical porous plate in the presence of homogeneous chemical reaction, radiation absorption and heat source/sink is studied analytically. The plate is assumed to move with a constant velocity in the direction of fluid flow. A magnetic field of uniform strength is applied perpendicular to the plate, which absorbs the fluid with a suction that varies with time. The dimensionless governing equations are solved analytically using two terms harmonic and non-harmonic functions. The expressions for the fields of velocity, temperature and concentration are obtained. With the aid of these the expressions for skin friction, Nusselt number and Sherwood number are derived. The effects of various physical parameters on the flow quantities are studied through graphs and tables. For the validity, we have checked our results with previously published work and found in good agreement. Velocity decreases for an increase in visco elastic parameter α2, heat absorption coefficient φ, the chemical reaction parameter γ , the magnetic field parameter M, the Prandtl number Pr, the Schmidt number Sc, and increases for increase in Grashof number Gm, the radiation absorption parameter Q1

This manuscript presents a detailed numerical study on the influence of radiation absorption and chemical reaction on unsteady magneto