Hybrid solution for the flow and heat transfer of a second-grade viscoelastic fluid on a stretching sheet with injection or suction (original) (raw)
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Numerical Solution of Heat Transfer in a Viscoelastic Boundary Layer Flow over a Stretching Sheet
Proceedings of the International …, 2012
This paper presents a study on visco elastic boundary layer flow and heat transfer over a stretching sheet in the presence of viscous dissipation and non-uniform heat source. A quasilinearization technique is used to solve velocity and temperature profiles. Two cases are considered, namely, (i) Prescribed surface temperature (PST) and (ii) Prescribed wall heat flux (PHF). The effect of various parameters on velocity and temperature profiles is depicted in graphs and discussed.
Analysis on Viscoelastic Fluid Flow and Heat Transfer Over A Stretching Sheet
International Journal for Computational Methods in Engineering Science and Mechanics, 2011
In this article, the problem of flow and heat transfer of an incompressible homogeneous second-grade fluid over a non-isothermal stretching sheet in the presence of non-uniform internal heat generation/absorption will be solved by the Homotopy Analysis Method (HAM). The governing partial differential equations are converted into ordinary differential equations by a similarity transformation. The effects of viscous dissipation, work due to deformation, internal heat generation/absorption, and thermal radiation are considered in the energy equation and the variations of dimensionless surface temperature as well as the heat transfer characteristics with various values of non-dimensional viscoelastic parameter k 1 , Prandtl number σ , Eckert number E c (E c ), radiation parameter N R , and the coefficients of space-dependent (A * ) and temperaturedependent (B * ) internal heat generation/absorption are graphed and tabulated. Two cases have been studied: (i) the sheet with prescribed surface temperature (PST case); and (ii) the sheet with prescribed heat flux (PHF case). The results reveals that HAM is very effective, convenient, and quite accurate to both linear and nonlinear problems. It is predicted that this method can be widely applied in engineering applications. Some plots and numerical results have been presented to indicate the reliability and simplicity of this method.
Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity
International Journal of Non-linear Mechanics, 2002
This paper deals with the study of boundary layer #ow and heat transfer of a visco-elastic #uid immersed in a porous medium over a non-isothermal stretching sheet. The #uid viscosity is assumed to vary as a function of temperature. The presence of variable viscosity of the #uid leads to the coupling and the non-linearity in the boundary value problem. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge}Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. An analysis has been carried out for two di!erent cases namely (1) prescribed surface temperature (PST), and (2) prescribed heat #ux (PHF), to get the e!ect of #uid viscosity, permeability parameter and visco-elastic parameter for various situations. The important "nding of our study is that the e!ect of #uid viscosity parameter is to decrease the wall temperature pro"le signi"cantly when #ow is through a porous medium. Further, the e!ect of permeability parameter is to decrease the skin friction on the sheet.
Heat Transfer in Boundary Layer Viscolastic Fluid Flow Over Anexponentially Stretching Sheet
2013
The paper presents the study of momentum and heat transfer characteristics in a visco-elastic boundary layer fluid flow over an exponentially stretching continuous sheet with non-uniform heat source. The flow is generated solely by the application of two equal and opposite forces along the x-axis such that stretching of the boundary surface is of exponential order in x and influenced by uniform magnetic field applied vertically. The non-linear boundary layer equation for momentum is converted into ordinary differential equation by means of similarity transformation. Approximate analytical similarity solutions is obtained for the dimensionless stream function and velocity distribution function after transforming the boundary layer equation into Riccati type and solving it sequentially. Heat transfer equation is then solved using Runge-Kutta fourth order method. The accuracy of the analytical solutions is also verified by comparing the solutions obtained to those in literature when Ha...
Frontiers in Heat and Mass Transfer, 2020
A numerical study of fluid flow over stretching sheet with temperature dependent properties has been performed induced by mixed convection. The significant variation of the Prandtl number and viscosity in the temperature is observed [see table 1]. Viscosity and Prandtl number are vary in inverse of the linear function. The physical problem modeled in the mathematical equations in dimension form, which is converted to the non-dimensional equations by applying similarity transformations and suitable boundary conditions. The mathematical modelling problem is transformed PDE's are numerically solved using Quasilinearization technique and FDM. The current numerical data has been presented in terms of velocity and heat transfer profiles and including the appropriate physical reason. The graphically represented the temperature and velocity distribution has been analyzed in detail. It has been found that the temperature and velocity profiles increases with decrease of m. The various parameter values of buoyancy force, Ratio between free stream velocity and the reference velocity and stream function are increases with higher value m = 1 acting in near to the plate on the velocity profile but temperature profile acting on away from the plate. The skin friction and heat transfer fluid flow enhance the buoyancy force. In particular 82 percentage and 2 percentage increment in skin friction and heat transfer is observed that buoyancy force increases from 2 to 3 at other parameters are fixed. The stretching sheet fluid flow behaviors enrich the solution and understand the boundary layers.
Heat Transfer of Viscoelastic Fluid Flow due to Nonlinear Stretching Sheet with Internal Heat Source
International Journal of Applied Mechanics and Engineering, 2013
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. ...
International Journal of Heat and Mass Transfer
In this paper, visco-elastic boundary layer flow and heat transfer over a stretching sheet in presence of viscous dissipation and non-uniform heat source have been discussed. Analytical solutions of highly non-linear momentum equation and confluent hypergeometric similarity solution of heat transfer equations are obtained. Here two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The effect of various parameters like visco-elastic parameter, Eckert number, Prandtl number, and non-uniform heat source/sink parameter on temperature distribution are analyzed and effect of all these parameters on wall temperature gradient and wall temperature are tabulated and discussed.
Mixed Convection in Viscoelastic Boundary Layer Flow and Heat Transfer Over a Stretching Sheet
Advances in Applied Mathematics and Mechanics
An investigation is carried out on mixed convection boundary layer flow of an incompressible and electrically conducting viscoelastic fluid over a linearly stretch-ing surface in which the heat transfer includes the effects of viscous dissipation, elastic deformation, thermal radiation, and non-uniform heat source/sink for two general types of non-isothermal boundary conditions. The governing partial differential equa-tions for the fluid flow and temperature are reduced to a nonlinear system of ordi-nary differential equations which are solved analytically using the homotopy analysis method (HAM). Graphical and numerical demonstrations of the convergence of the HAM solutions are provided, and the effects of various parameters on the skin friction coefficient and wall heat transfer are tabulated. In addition it is demonstrated that pre-viously reported solutions of the thermal energy equation given in [1] do not converge at the boundary, and therefore, the boundary derivatives report...
2013
In this study, asteady three dimensionalviscoelas tic fluid flow and heat transfer due to a stretchin g sheet with an applied magnetic field is considered for an alysis. The fluid far away from the surface is ambi ent and the motion in the flow field is caused by the stretchin g surface in two lateral directions.The heat tran sfer analysis has been carried out for two heating processes, v iz. the constant wall temperature (CWT) and the constant heat flux (CHF). An analytical solution in the form of series expansionfor the velocity and temperature di stribution is obtained employing homotopyanalysis method (HAM). The quantities of interest are velocity and tempera ture distribution as well as the skin-friction andthe wa ll heat flux. These are determined for various valu es of the parameters such as viscoelastic parameter, non-dime nsional magnetic parameter, stretching ratio and th e Prandtl number. The results obtained are presented in the form of graphs and tabulated data. It isob...
In this paper two dimensional flow of a viscoelastic fluid due to stretching surface is considered. Flow analysis is carried out by using closed form solution of fourth order differential equation of motion of viscoelastic fluid. Further (Walters' liquid B' model) heat transfer analysis is carried out using convective surface condition. The governing equations of flow and heat transfer are non-linear partial differential equations which are unable to solve analytically hence are solved using Runge-Kutta Numerical Method with efficient shooting technique. The flow and heat transfer characteristics are studied through plots drawn. Numerical values of Wall temperature are calculated and presented in the table and compared with earlier published results which are in good agreement