Bani Singh

Finite-element simulation of mixed convection flow of micropolar fluid over a shrinking sheet with thermal radiation

An analysis is carried out to investigate the effect of thermal radiation on mixed convection flow of a msicropolar fluid over a shrinking sheet with prescribed surface heat flux. The velocity of the shrinking sheet and the surface heat flux are assumed to vary as a linear function of the distance from the origin. Using the boundary layer approximation and similarity transformations, the governing partial differential equations are transformed into a system of nonlinear coupled ordinary differential equations which are solved numerically by using a variational finite element method. The effects of suction, radiation, and buoyancy parameters on velocity, microrotation, and temperature functions are examined in detail. The skin-friction coefficient, local couple stress, and the local Nusselt number have also been computed. Under special conditions, an analytical solution is obtained only for the flow velocity, which is compared with the numerical results obtained by finite element method. An excellent agreement of the two sets of solutions is observed, which confirms the validity of the finite element method employed herein. Also, in order to check the convergence of numerical solutions, the calculations are executed by reducing the mesh size. The sensitivity of the solution as a function of suction through the permeable sheet has also been examined. The current study has important applications in industrial polymeric materials processing.

Finite Element Solution of Unsteady Mixed Convection Flow of Micropolar Fluid over a Porous Shrinking Sheet

The objective of this investigation is to analyze the effect of unsteadiness on the mixed convection boundary layer flow of micropolar fluid over a permeable shrinking sheet in the presence of viscous dissipation. At the sheet a variable distribution of suction is assumed. The unsteadiness in the flow and temperature fields is caused by the time dependence of the shrinking velocity and surface temperature. With the aid of similarity transformations, the governing partial differential equations are transformed into a set of nonlinear ordinary differential equations, which are solved numerically, using variational finite element method. The influence of important physical parameters, namely, suction parameter, unsteadiness parameter, buoyancy parameter and Eckert number on the velocity, microrotation, and temperature functions is investigated and analyzed with the help of their graphical representations. Additionally skin friction and the rate of heat transfer have also been computed. Under special conditions, an exact solution for the flow velocity is compared with the numerical results obtained by finite element method. An excellent agreement is observed for the two sets of solutions. Furthermore, to verify the convergence of numerical results, calculations are conducted with increasing number of elements.

Effect of chemical reaction and viscous dissipation on MHD nanofluid flow over a horizontal cylinder: Analytical solution

An analytical study of the MHD boundary layer flow of electrically conducting nanofluid over a horizontal cylinder with the effects of chemical reaction and viscous dissipation is presented. Similarity transformations have been applied to transform the cylindrical form of the governing equations into the system of coupled ordinary differential equations and then homotopy analysis method has been implemented to solve the system. Homotopy analysis method (HAM) does not contain any small or large parameter like perturbation technique and also provides an easiest approach to ensure the convergence of the series of solution. The effects of chemical reaction parameter, magnetic parameter and other important governing parameters with no flux nanoparticles concentration is carried out to describe important physical quantities.

Unsteady electromagnetic radiative nanofluid stagnation-point flow from a stretching sheet with chemically reactive nanoparticles, Stefan blowing effect and entropy generation

This article investigates the combined influence of nonlinear radiation, Stefan blowing and chemical reactions on unsteady electro-magneto-hydrodynamic stagnation-point flow of a nanofluid from a horizontal stretching sheet. Both electrical and magnetic body forces are considered. In addition, the effects of velocity slip, thermal slip and mass slip are considered at the boundaries. An analytical method named as homotopy analysis method is applied to solve the non-dimensional system of nonlinear partial differential equations which are obtained by applying similarity transformations on governing equations. The effects of emerging parameters such as Stefan blowing parameter, electric parameter and magnetic parameter on the important physical quantities are presented graphically. In addition, an entropy generation analysis is provided in this article for thermal optimization. The flow is observed to be accelerated both with increasing magnetic field and electrical field. Entropy generation number is markedly enhanced with greater magnetic field, electrical field and Reynolds number, whereas it is reduced with increasing chemical reaction parameter.

Finite Element Analysis of MHD Flow of Micropolar Fluid over a Shrinking Sheet with a Convective Surface Boundary Condition

This paper presents a numerical solution for the steady mixed convection magnetohydrodynamic (MHD) flow of an electrically conducting micropolar fluid over a porous shrinking sheet. The velocity of shrinking sheet and magnetic field are assumed to vary as power functions of the distance from the origin. A convective boundary condition is used rather than the customary conditions for temperature, i.e., constant surface temperature or constant heat flux. With the aid of similarity transformations, the governing partial differential equations are transformed into a system of nonlinear ordinary differential equations, which are solved numerically, using the variational finite element method (FEM). The influence of various emerging thermophysical parameters, namely suction parameter, convective heat transfer parameter, magnetic parameter and power index on velocity, microrotation and temperature functions is studied extensively and is shown graphically. Additionally the skin friction and rate of heat transfer, which provide an estimate of the surface shear stress and the rate of cooling of the surface, respectively, have also been computed for these parameters. Under the limiting case an analytical solution of the flow velocity is compared with the present numerical results. An excellent agreement between the two sets of solutions is observed. Also, in order to check the convergence of numerical solution, the calculations are carried out by reducing the mesh size. The present study finds applications in materials processing and demonstrates excellent stability and convergence characteristics for the variational FEM code.

Numerical study of steady dissipative mixed convection optically-thick micropolar flow with thermal radiation effects

The objective of this paper is to study theoretically and numerically the effect of thermal radiation on mixed convection boundary layer flow of a dissipative micropolar non-Newtonian fluid from a continuously moving vertical porous sheet. The governing partial differential equations are transformed into a set of non-linear differential equations by using similarity transformations. These equations are solved iteratively with the Bellman-Kalaba quasi-linearization algorithm. This method converges quadratically and the solution is valid for a large range of parameters. The effects of transpiration (suction or injection) parameter, buoyancy parameter, radiation parameter and Eckert number on velocity, microrotation and temperature functions have been studied. Under a special case comparison of the present numerical results is made with the results available in the literature and an excellent agreement is found. Additionally skin friction and rate of heat transfer have also been computed. The study has appli...

Wavelet optimized finite difference mesh for MHD flow in a circular duct

Abstract There is a large class of important problems in scientific and engineering applications where the solution shows very little variation in the core region but very rapid changes close to the boundary of the domain of interest. Magnetohydrodynamic flow problems belong to this category. Treatment of such problems numerically, therefore, requires a non-uniform mesh, which is very fine near the boundary. The determination of the size of the grid in different parts of the domain is, therefore, a challenging problem. Some recent studies suggest that wavelet methods can be effectively applied to create an optimized mesh. The method has mostly been used for one dimensional problems. The present paper investigates the problem for fully developed MHD duct flow problems which are basically two dimensional. The boundary layer character is more pronounced in one direction as compared to the other. The governing equations comprise a coupled system of two partial differential equations with Dirichlet boundary conditions. Wavelet based adaptive mesh is first created and then the system is discretized over this mesh. Computations have been carried out at different precision levels for various Hartmann numbers for a pipe of circular section. Contours are also drawn to depict the core and the boundary layer region.