On the study of viscous fluid due to exponentially shrinking sheet in the presence of thermal radiation (original) (raw)
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Ain Shams Engineering Journal, 2014
The aim of this paper was to examine the steady boundary layer flow of an Eyring-Powell model fluid due to an exponentially shrinking sheet. In addition, the heat transfer process in the presence of thermal radiation is considered. Using usual similarity transformations the governing equations have been transformed into non-linear ordinary differential equations. Homotopy analysis method (HAM) is employed for the series solutions. The convergence of the obtained series solutions is carefully analyzed. Numerical values of the temperature gradient are presented and discussed. It is observed that velocity increases with an increase in mass suction S. In addition, for the temperature profiles opposite behavior is observed for increment in suction. Moreover, the thermal boundary layer thickness decreases due to increase in Prandtl number Pr and thermal radiation R.
Indian Journal of Pure & Applied Physics, 2018
In the present analysis, we have investigated the effects of thermal radiation on an unsteady three-dimensional boundary layer flow of an incompressible viscous fluid and heat transfer due to a permeable axisymmetric shrinking sheet with suction and power-law variation in wall temperature. The similarity transformations have been used to convert the governing partial differential equations into non-linear ordinary differential equations and then solved numerically by shooting technique. The conditions of the existence, non-existence and duality of the similarity solution have been explored by the investigation where the solution depends not only on suction parameter but on unsteadiness parameter also. Further, it has been emerged that the range of the suction parameter S , where the similarity solution exists, is increased with the increase of unsteadiness parameter A . Also, the graphs of velocity profile, temperature profile, skin-friction coefficient and rate of heat transfer at ...
2016
In this present article, we have analyzed MHD boundary layer flow of a viscous incompressible fluid over an exponentially porous stretching sheet in presence of thermal radiation. Using a similarity transformation, the governing equations are transformed into a system of nonlinear ordinary differential equations, which are then solved by homotopy analysis method (HAM). The effects of various parameters, namely the magnetic field parameter, radiation parameter, suction parameter, permeability parameter, Prandtl number on the velocity and temperature are analyzed through graphically. Moreover, a comparative study between the previously published and the present study is made. MSC: 76S05 • 76M55
Boundary Layer Flow and Heat Transfer over an Exponentially Shrinking Sheet
Chinese Physics Letters, 2011
An analysis is made to study boundary layer flow and heat transfer over an exponentially shrinking sheet. Using similarity transformations in exponential form, the governing boundary layer equations are transformed into self-similar nonlinear ordinary differential equations, which are then solved numerically using a very efficient shooting method. The analysis reveals the conditions for the existence of steady boundary layer flow due to exponential shrinking of the sheet and it is found that when the mass suction parameter exceeds a certain critical value, steady flow is possible. The dual solutions for velocity and temperature distributions are obtained. With increasing values of the mass suction parameter, the skin friction coefficient increases for the first solution and decreases for the second solution.
2013
This work presents a boundary-layer analysis of an incompressible viscous steady flow and forced convection over a horizontal flat plate. The solution for velocity and temperature are calculated by applying the Homotopy perturbation method (HPM). A special technique is attempted by which one is able to obtain solutions that are close to the exact solution of the equation. The obtained results are compared to the exact solution and another results provided by previous works so that the high accuracy of the obtained results is clear. Also, the results reveal that this method is effective, simple, and can be applied for other nonlinear problems in different fields of science and engineering, especially some fluid mechanics and heat transfer equations. doi: 10.14456/WJST.2014.47
Heat transfer analysis for a hydromagnetic viscous fluid over a non-linear shrinking sheet
International Journal of Heat and Mass Transfer, 2011
The boundary layer flow and heat transfer analysis of electrically conducting viscous fluid over a nonlinearly shrinking sheet is investigated. A similarity transformation is used to reduce the governing equations to a set of nonlinear ordinary differential equations. The system of equations is solved numerically employing an implicit finite difference scheme known as Keller-box method. It is found that dual solutions exist for this particular problem. The numerical results for the velocity, temperature, wall skin friction coefficient and local rate of heat transfer through the surface for various values of physical parameters both in case of stretching and shrinking sheet are analyzed and discussed for both the solutions. Present results in the hydrodynamic case (M = 0) are compared with existing numerical results in case of stretching flow and found in good agreement.
Physics Letters A, 2008
This Letter endeavours to complete an earlier numerical analysis for flow and heat transfer in a viscous fluid over a sheet nonlinearly stretched by extending the investigation in two directions. On one side, the effects of thermal radiation are included in the energy equation, and, on the other hand, the prescribed wall heat flux case (PHF case) is also analyzed. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation. The variations of dimensionless surface temperature as well as flow and heat-transfer characteristics with the governing dimensionless parameters of the problem, which include a nonlinearly stretching sheet, thermal radiation, viscous dissipation and power-law index of the wall temperature parameters, are graphed and tabulated.
MHD flow over exponential radiating stretching sheet using homotopy analysis method
Journal of King Saud University - Engineering Sciences, 2014
An analytical solution for MHD boundary layer flow of a viscous incompressible fluid over an exponentially stretching sheet is developed in this study. The effect of thermal radiation is included in the energy equation. Through suitable similarity transformations, the governing equations are transformed into a system of nonlinear ordinary differential equations. Homotopy analysis method (HAM) has been used to get accurate and complete analytic solution. This study reveals that the governing parameters, namely, the magnetic and the radiation parameters have major effects on the flow field, skin friction coefficient, and the heat transfer rate. The magnetic field enhances the dimensionless temperature inside the thermal boundary layer whereas reduces the dimensionless velocity inside the hydrodynamic boundary layer. Heat transfer rate becomes low with magnetic and radiation parameters while the friction factor is increased with magnetic field. Moreover, a comparative study between the previously published and the present results in special cases is conducted and an excellent agreement is found between them.
American Journal of Computational Mathematics, 2015
In this paper, the analytical solution of a viscous and incompressible fluid towards an exponentially stretching porous sheet with surface heat flux in porous medium, for the boundary layer and heat transfer flow, is presented. The equations of continuity, momentum and the energy are transformed into non-linear ordinary differential by using similarity transformation. The solutions of these highly non-linear ordinary differential equations are found analytically by means of Homotopy Analysis Method (HAM). The result obtained by HAM is compared with numerical results presented in the literature. The accuracy of the HAM is indicated by close agreement of the two sets of results. By this method, an expression is obtained which is admissible for all values of effective parameters. This method has the ability to control the convergence of the solution.