In this study we analyzed the flow, heat and mass transfer behavior of Casson fluid past an exponentially permeable stretching surface in presence of thermal radiation, magneticfield, viscous dissipation, heat source and chemical reaction. We presented dual solutions by comparing the results of the Casson fluid with the Newtonian fluid. The governing partial nonlinear differential equations of the flow, heat and mass transfer are transformed into ordinary differential equations by using similarity transformation and solved numerically by using Matlab bvp4c package. The effects of various non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed and presented graphically. Also, the friction factor, Nusselt and Sherwood numbers are analyzed and presented in tabular form for both Casson and Newtonian fluids separately. Under some special conditions the results of the present study have an excellent agreement with existing studies for both Casson and Newtonian fluid cases

In this study, we inquired the cross-diffusion effects on the magnetohydrodynamic Williamson fluid flow across a variable thickness stretching sheet by viewing velocity slip. With the aid of Runge-Kutta based shooting process, we resolved the transformed differential equations numerically. The effects of different dimensionless parameters on three usual profiles (velocity, temperature, concentration) along with skin friction coefficient, heat transfer rate and mass transfer rate are examined with the support of plots and tables. Dual solutions are exhibited for two cases i.e., Newtonian fluid and non-Newtonian fluid. Results reveal that the Soret and Dufour numbers have drift to control the thermal and concentration boundary layers. We also found a good agreement of the present results by comparing with the published results

In this study we investigated the effect of space and temperature dependent heat generation/absorption on three-dimensional magnetohydrodynamic nanofluid flow over a nonlinearly permeable stretching sheet. After using appropriate self-similarity transformation the governing equations are solved numerically using bvp4c Matlab package. The effects of the non-dimensional governing parameters on velocity, temperature and concentration profiles are discussed with the help of graphs. Also, coefficient of skin friction and Nusselt number is analyzed and presented through tables. It is found that present results have an excellent agreement with the existed studies under some special cases. Results indicate that an increase in space and temperature dependent heat source or sink increases the temperature and concentration profiles of the flow. Dual solutions exist only for certain range of power-law index

The current study covers the relative study of non-aligned magnetohydrodynamic stagnation point flow of a nanofluid comprising gyrotactic microorganisms across a stretching sheet in the presence of nonlinear thermal radiation and variable viscosity. The governing equations transitioned as nonlinear ordinary differential equations with suited similarity transformations. With the assistance of Runge-Kutta based shooting method, we derived solutions. Results for oblique and free stream flow cases are exhibited through plots for the parameters of concern. In tabular form, heat and mass transfer rate along with the local density of the motile microorganisms are analyzed for some parameters. It is found that local density of the motile microorganisms is highly influenced by the Biot and Peclet numbers. Rising values of the magnetic field parameter, Biot number, thermal radiation parameter and thermophoresis parameter increase the thermal boundary layer. Bioconvection Peclet number and bioconvection Lewis number have tendency to reduce the density of the motile microorganisms. It is also found that thermal and concentration boundary layers become high in free stream flow when compared with the oblique flow

Squeezing flow is a flow where the material is squeezed out or disfigured within two parallel plates. Such flow is beneficial in various fields, for instance, in welding engineering and rheometry. The current study investigates the squeezing flow of a hybrid nanofluid (propylene glycol–water mixture combined with paraffin wax–sand) between two parallel plates with activation energy and entropy generation. The governing equations are converted into ordinary differential equations using appropriate similarity transformations. The shooting strategy (combined with Runge–Kutta fourth order method) is applied to solve these transformed equations. The results of the conducted parametric study are explained and revealed in graphs. This study uses a statistical tool (correlation coefficient) to illustrate the impact of the relevant parameters on the engineering parameters of interest, such as the surface friction factor at both plates. This study concludes that the squeezing number intensifies the velocity profiles, and the rotating parameter decreases the fluid velocity. In addition, the magnetic field, rotation parameter, and nanoparticle volumetric parameter have a strong negative relationship with the friction factor at the lower plate. Furthermore, heat source has a strong negative relationship with heat transfer rate near the lower plate, and a strong positive correlation with the same phenomena near the upper plate. In conclusion, the current study reveals that the entropy generation is increased with the Brinkman number and reduced with the squeezing parameter. Moreover, the results of the current study verify and show a decent agreement with the data from earlier published research outcomes.