Muhammad Hamid

Wavelets solution of MHD 3-D fluid flow in the presence of slip and thermal radiation effects

This article is devoted to analyze the magnetic field, slip, and thermal radiations effects on generalized three-dimensional flow, heat, and mass transfer in a channel of lower stretching wall. We supposed two various lateral direction rates for the lower stretching surface of the wall while the upper wall of the channel is subjected to constant injection. Moreover, influence of thermal slip on the temperature profile beside the viscous dissipation and Joule heating is also taken into account. The governing set of partial differential equations of the heat transfer and flow are transformed to nonlinear set of ordinary differential equations (ODEs) by using the compatible similarity transformations. The obtained nonlinear ODE set tackled by means of a new wavelet algorithm. The outcomes obtained via modified Chebyshev wavelet method are compared with Runge-Kutta (order-4). The worthy comparison, error, and convergence analysis shows an excellent agreement. Additionally, the graphical representation for var...

Gegenbauer wavelets collocation-based scheme to explore the solution of free bio-convection of nanofluid in 3D nearby stagnation point

In the current article, we investigated a three-dimensional nanofluid bio-convection model near a stagnation attachment. The set of governing equations, with a set of similarity variables, expressing the conservation of momentum, total mass, microorganisms, thermal energy and nanoparticles are reduced to nonlinear ODEs set. The obtained nonlinear system is tackled via collocation-based Gegenbauer wavelets technique. The purpose of this extension is to reduce the computational work as compared to the traditional Gegenbauer wavelets method. Additionally, the suggested trial solutions must satisfy the boundary conditions. Convergence analysis shows an excellent agreement. The graphical plots for various physical parameters are illustrated. Additionally, the significant physical quantities of viable interests and the impact of different physical parameters on the dissemination of the motile microorganisms are also included in our study. The error and convergence analyses are endorsing that the proposed method is well efficient and could be extended to other nonlinear problems.

Fluid flow and heat transfer investigation of blood with nanoparticles through porous vessels in the presence of magnetic field

In this study, the blood flow was investigated involving nanoparticles through porous blood vessels in the presence of magnetic field by means of collocation and least squares techniques. Blood was assumed to be non-Newtonian fluid having nanoparticles in which different models were used to determine the viscosity of the nanofluids. Vogel’s, Reynolds, variable, and constant viscosity models were discussed by using the two aforementioned techniques. Hence, we compared our results with a numerical technique RK-4 and already existing results to show the credibility of our solutions. Further, some physical parameters and their effects are also stated in this research. Increase in the thermophoresis parameter and pressure gradient along with the decrease in the Brownian motion parameter provide a rapid change in the velocity profile, which has been disclosed by results. Additionally, a dramatic change in the velocity has been realized by using Vogel’s model.