Wavelet-based numerical solution for MHD boundary-layer flow due to stretching sheet

In this paper, a two-dimensional steady flow of a viscous fluid due to a stretching sheet in the presence of a magnetic field is considered. We proposed two new numerical schemes based on the Haar wavelet coupled with a collocation approach and quasi-linearization process for solving the Falkner-Skan equation representing the governing problem. The important derived quantities representing the fluid velocity and wall shear stress for various values of flow parameters Mand βare calculated. The proposed methods enable us to obtain the solutions even for negative β, nonlinear stretching parameter, and smaller values of the magnetic parameter ()M1< which was missing in the earlier findings. Numerical and graphical results obtained show an excellent agreement with the available findings and demonstrate the efficiency and accuracy of the developed schemes. Another significant advantage of the present method is that it does not depends on small parameters and initial presumptions unlike in traditional semi-analytical and numerical methods

Investigation of MHD micropolar flow between a stationary and a rotating disc: Keller-box solution

AbstractIn the present investigation, magnetohydrodynamic (MHD) micropolar fluid flow between a stationary disc and a rotating disc with a constant angular velocity is considered. The study investigates the effect of magnetic field and microrotation structure on the flow characteristics. The governing equations of motion are transformed to a system of nonlinear ordinary differential equations (ODEs) in dimensionless form using Von Karman’s similarity transformations. An algorithm based on implicit finite difference method-Keller-box Scheme is employed to solve the resulting similarity equations for various pertinent parameters. Numerical solutions of velocity profiles, pressure gradient and microrotation profiles are discussed, and presented through tables and graphs for various Magnetic parameter. Comparisons are made between the obtained results and previously reported findings in the literature. The successful validation against existing literature supports the effectiveness of the methodology employed in this investigation

Analysis of Magnetohydrodynamic Free Convection in Micropolar Fluids over a Permeable Shrinking Sheet with Slip Boundary Conditions

The convective micropolar fluid flow over a permeable shrinking sheet in the presence of a heat source and thermal radiation with the magnetic field directed towards the sheet has been studied in this paper. The mathematical formulation considers the partial slip condition at the sheet, allowing a realistic representation of the fluid flow near the boundary. The governing equations for the flow, heat, and mass transfer are formulated using the conservation laws of mass, momentum, angular momentum, energy, and concentration. The resulting nonlinear partial differential equations are transformed into a system of ordinary differential equations using suitable similarity transformations. The numerical solutions are obtained using robust computational techniques to examine the influence of various parameters on the velocity, temperature, and concentration profiles. The impact of slip effects, micropolar fluid characteristics, and permeability parameters on the flow features and heat transfer rates are thoroughly analyzed. The findings of this investigation offer valuable insights into the behavior of micropolar fluids in free convection flows over permeable shrinking sheets with slip, providing a foundation for potential applications in various industrial and engineering processes. Key findings include the observation that the velocity profile overshoots for assisting flow with decreasing viscous force and rising magnetic effects as opposed to opposing flow. The thermal boundary layer thickness decreases due to buoyant force but shows increasing behavior with heat source parameters. The present result agrees with the earlier findings for specific parameter values in particular cases