Nonlinear Stretching Sheet Research Articles

Magnetohydrodynamic Flow of Viscous Fluid over a Non-Linearly Stretching Sheet

In this paper, the Magnetohydrodynamic (MHD) Flow of Viscous Fluid over a Nonlinear Stretching Sheet is investigated numerically. The partial differential equations governing the flow are reduced to a non linear ordinary differential equations by using similarity transformations. The resulting transformed equations are numerically solved by an explicit finite difference scheme known as the Keller Box Method. The velocity profiles are determined and the effects of the magnetic parameter and non linear stretching parameter on the flow characteristics are investigated. In addition to this the numerical results for the local skin friction coefficients are computed. Comparison with the exact solution and previously reported analytic solutions is made and excellent agreement is noted. Moreover, the velocity profile obtained by Keller box method is in a better agreement to the exact solution than by the Homotopy Analysis Method. It is also found that, an increase in the magnetic parameter or non-linearity parameter causes a decrease in the velocity profile and velocity distribution.

A STUDY ON MHD BOUNDARY LAYER FLOW OVER A NONLINEAR STRETCHING SHEET USING IMPLICIT FINITE DIFFERENCE METHOD

The problem of the MHD boundary layer flow of an in compressible viscous fluid over a non-linear stretc hing sheet is discussed. Using similarity transformation governing equations are transformed in to nonlinear ordinary different ial equation. The Implicit finite difference Keller box method is applied to find the numerical solution of nonlinear differential equat ion. Graphical results of fluid velocity have been presented and discussed for the related parameters.

Flow and Mass Transfer of Second Grade Fluid in a Porous Medium Over a Nonlinear Stretching Sheet with Chemically Reactive Species and Suction

Flow and Mass Transfer of Second Grade Fluid in a Porous Medium Over a Nonlinear Stretching Sheet with Chemically Reactive Species and Suction

Heat Transfer of Viscoelastic Fluid Flow due to Nonlinear Stretching Sheet with Internal Heat Source

In the present paper, a viscoelastic boundary layer flow and heat transfer over an exponentially stretching continuous sheet in the presence of a heat source/sink has been examined. Loss of energy due to viscous dissipation of the non-Newtonian fluid has been taken into account in this study. Approximate analytical local similar solutions of the highly non-linear momentum equation are obtained for velocity distribution by transforming the equation into Riccati-type and then solving this sequentially. Accuracy of the zero-order analytical solutions for the stream function and velocity are verified by numerical solutions obtained by employing the Runge-Kutta fourth order method involving shooting. Similarity solutions of the temperature equation for non-isothermal boundary conditions are obtained in the form of confluent hypergeometric functions. The effect of various physical parameters on the local skin-friction coefficient and heat transfer characteristics are discussed in detail. It is seen that the rate of heat transfer from the stretching sheet to the fluid can be controlled by suitably choosing the values of the Prandtl number Pr and local Eckert number E, local viscioelastic parameter k<sup>*</sup><sub>1</sub> and local heat source/ sink parameter β<sup>*</sup>

Effect of Viscous Dissipation and Thermal Radiation on Heat Transfer over a Non-Linearly Stretching Sheet Through Porous Medium

In this present paper, we have discussed the effects of viscous dissipation and thermal radiation on heat transfer over a non-linear stretching sheet through a porous medium. Usual similarity transformations are considered to convert the non-linear partial differential equation of motion and heat transfer into ODE’s. Solutions of motion and heat transfer are obtained by the Runge-Kutta integration scheme with most efficient shooting technique. The graphical results are presented to interpret various physical parameters of interest. It is found that the velocity profile decreases with an increase of the porous parameter asymptotically. The temperature field decreases with an increase in the parametric values of the Prandtl number and thermal radiation while with an increase in parameters of the Eckert number and porous parameter, the temperature field increases in both PST (power law surface temperature) and PHF (power law heat flux) cases. The numerical values of the non-dimensional wall temperature gradient and wall temperature are tabulated and discussed.

Heat Transfer Analysis for Couple Stress Fluid over a Nonlinearly Stretching Sheet

An investigation has presented to analyze the heat transfer in a boundary layer flow of an incompress- ible couple stress fluid over a nonlinear stretching sheet. The heat transfer problem have been analyzed for the two heating processes, 1) PST (prescribed surface temperature case) and 2) PHF (prescribed heat flux case). The govern- ing partial differential equations for flow and heat transfer are transformed to ordinary differential equations. The nu- merical solutions have been obtained by using fourth order Runge-Kutta method coupled with shooting method. The effects of dimensionless surface temperature, couple stress parameter , Prandtl number Pr , Eckert number Ec, non- linear stretching sheet parameter n and 1; 2 have been observed by graphical illsurations. Chen (8) described the effects of viscous dissipation on heat transfer in a non-Newtonian liquid film over an unsteady stretching sheet. Alinejad (9) investigate the flow and heat transfer characteristics of viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation, Khan et al. (10) presented an analysis of the axisymmet- ric flow of a non-Newtonian fluid over a radially stretch- ing sheet, Mehmood et al. (11) investigates the theoretical study of steady stagnation point flow with heat transfer of a second grade nano fluid towards a stretching surface, Khan et al. (12) gives an analytical study for the effects of slip factors on unsteady stagnation point flow and heat transfer towards a stretching sheet. Asghar (13) reveals all possible similarity transformations for the flow of power-law fluid over a stretching surface by a Lie group analysis. The rota- tion of the fluid particles and its effect has studied under the theory of couple stresses which describes the rotation field in specification of the velocity field. The examples of cou- ple stress fluids include blood, rheologically complex flu- ids, lubricant oil with long chain additives, polymeric sus- pensions, etc. Stokes (14) considered the effects of couple stresses in fluids. Soundalgekar (15) carried out an analysis for the dispersion of a solute in a channel flow of fluid with

Thermal Radiation, Heat Source/Sink and Work Done by Deformation Impacts on MHD Viscoelastic Fluid over a Nonlinear Stretching Sheet

This work is focused on the effects of heat source/sink, viscous dissipation, radiation and work done by deformation on flow and heat transfer of a viscoelastic fluid over a nonlinear stretching sheet. The similarity transformations have been used to convert the governing partial differential equations into a set of nonlinear ordinary differential equations. These equations are then solved numerically using a very efficient implicit finite difference method. Favorable comparison with previously published work is performed and it is found to be in excellent agreement. The results of this parametric study are shown in several plots and tables and the physical aspects of the problem are highlighted and discussed.

Stagnation-Point Flow toward a Vertical, Nonlinearly Stretching Sheet with Prescribed Surface Heat Flux

An analysis is carried out to study the steady two-dimensional stagnation-point flow of an incompressible viscous fluid towards a stretching vertical sheet. It is assumed that the sheet is stretched nonlinearly, with prescribed surface heat flux. This problem is governed by three parameters: buoyancy, velocity exponent, and velocity ratio. Both assisting and opposing buoyant flows are considered. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically by finite difference Keller-box method. The flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Dual solutions are found in the opposing buoyant flows, while the solution is unique for the assisting buoyant flows.

Mixed Convection Flow of a Non-Newtonian Nanofluid Over a Non-Linearly Stretching Sheet

Mixed Convection Flow of a Non-Newtonian Nanofluid Over a Non-Linearly Stretching Sheet

Variational Iteration Method for the Magneto-Hydrodynamic Nanoflow Over a Nonlinear Stretching Sheet Using He's Polynomials

Variational Iteration Method for the Magneto-Hydrodynamic Nanoflow Over a Nonlinear Stretching Sheet Using He's Polynomials

Viscous Flow over Nonlinearly Stretching Sheet with Effects of Viscous Dissipation

The flow and heat transfer characteristics of incompressible viscous flow over a nonlinearly stretching sheet with the presence of viscous dissipation is investigated numerically. The similarity transformation reduces the time‐independent boundary layer equations for momentum and thermal energy into a set of coupled ordinary differential equations. The obtained equations, including nonlinear equation for the velocity field f and differential equation by variable coefficient for the temperature field θ, are solved numerically by using the fourth order of Runge‐Kutta integration scheme accompanied by shooting technique with Newton‐Raphson iteration method. The effect of various values of Prandtl number, Eckert number and nonlinear stretching parameter are studied. The results presented graphically show some behaviors such as decrease in dimensionless temperature θ due to increase in Pr number, and curve relocations are observed when heat dissipation is considered.

A New Analytical Approach to Solve Magnetohydrodynamics Flow Over a Nonlinear Porous Stretching Sheet by Laplace Padé Decomposition Method

The aspire of this article is to bring in a new approximate method, that is to say the Laplace Pade decomposition method which is a mixture of Laplace decomposition and Pade approximation to offer an analytical approximate way out to magnetohydrodynamics flow over a nonlinear porous stretching sheet. This new iteration approach provides us with a convenient way to approximate solution. A closed agreement between the obtained solution and some well-known results has been established. The proposed procedure can be applied to handle other nonlinear problems.

Non-Perturbative Solution of the Magnetohydrodynamic Flow over a Nonlinear Stretching Sheet by Homotopy Perturbation Method-Padé Technique

In this study, we investigate the magnetohydrodynamic (MHD) boundary layer flow by employing the homotopy perturbation method (HPM) and Pad´e approximation. The series solution of the governing nonlinear problem is developed. Generally, the truncated series solution is adequate only in a small region when the exact solution is not reached. We overcame this limitation by using the Pad´e techniques, which have the advantage in turning the polynomials approximation into a rational function, and applied it to the series solution to improve the accuracy and enlarge the convergence domain. A comparison of the present solution with the existing solution is made and excellent agreement is noted.

Flow and Diffusion of Chemically Reactive Species over a Nonlinearly Stretching Sheet Immersed in a Porous Medium

The flow and mass transfer of a chemically reactive species over a nonlinearly stretching sheet in a porous medium is considered. The boundary layer theory and the similarity procedure are used to obtain a system of nonlinear ordinary differential equations. A feasible approximate analytical solution for the system is obtained and the influences of the physical parameters on the flow and mass transfer characteristics are analyzed. The permeability parameter reduces the velocity profiles and increases the momentum and concentration boundary layers thickness. The destructive chemical reaction reduces the concentration boundary layers.