Modelling and numerical computation for flow of micropolar fluid towards an exponential curved surface: a Keller box method

The numerical analysis of MHD boundary layer non-Newtonian micropolar fluid due to an exponentially curved stretching sheet is developed in this study. In the energy equation effects of viscous dissipation are included. For the mathematical description of the governing equations curvilinear coordinates are used. By utilizing exponential similarity variables, the modelled partial differential equations (PDEs) are reduced into ordinary ones. The resultant non-linear ODEs are numerically solved with two methods shooting and Keller box method. The study reveals that the governing parameters, namely, radius of curvature, material parameter, magnetic parameter, Prandtl number and Eckert number have major effects on the fluid velocity, micro-rotation velocity, surface friction, couple stress and heat transfer rate. The results indicate that the magnetic field diminishes the fluid velocity inside the hydrodynamics boundary layer whereas it enhances the temperature inside the thermal boundary layer. Microrotation profile decreases near the surface, as the magnetic parameter and radius of curvature increases but far away behavior is opposite. The material parameter enhances the velocity and microrotation profile whereas, opposite behaviors is noticed for the temperature distribution. Obtained outcomes are also compared with the existing literature and the comparison shows a good agreement with existing studies.

Modeling and numerical simulation of micropolar fluid over a curved surface: Keller box method

BACKGROUND

This paper examines the flow behavior of micropolar liquid over a curved surface. MHD fluid is considered. The surface inducing the fluid motion has a prescribed temperature different from the ambient fluid moreover the heat transfer mechanism is investigated. Curvilinear coordinates are used for the mathematical formulation of the flow equation. Similarity variables are derived and are utilized to alter the governing expressions for the flow of momentum and heat transfer characteristic.

METHOD

The resulting non-linear ODEs are resolved systematically by two numerically approaches namely; the Keller box method and the shooting method.

RESULTS

The numerical results for the temperature and velocity fields has been presented through tables and graphs against the independent parameters and non-dimensional numbers i.e., material parameter, power law index, radius of curvature, magnetic parameter, Prandtl and Eckert numbers, skin friction (drag force) and Nusselt number. Physical explanation of the graph presented is given to understand the performance of fluid flow and heat transport phenomena in different emerging situation.

CONCLUSION

The main outcomes in the presence of various flow variables on the skin friction velocity, Nusselt number, temperature are highlighted via graphical sketch and Tables. Velocity field displays a decreasing trend with magnetic parameter, power law index and radius of curvature of the stretching velocity whereas, opposite behavior observed for the material parameter. Near the surface curvature and magnetic parameter shows an enhancement in microrotation profile whereas, it shows reverse behavior when it is far away. Material parameter increases for large values of microrotation profile on the other hand power-law index decreases for large values. For higher values magnetic parameter, radius of curvature and Eckert number temperature profile increases. But temperature reduces subject to material parameter and Prandtl number.