Unsteady boundary layer flow and heat transfer past a porous stretching sheet in presence of variable viscosity and thermal diffusivity (original) (raw)
Meccanica, 2010
The present paper deals with the study of heat transfer characteristics in the laminar boundary layer flow of an incompressible viscous fluid over an unsteady stretching sheet which is placed in a porous medium in the presence of viscous dissipation and internal absorption or generation. Similarity transformations are used to convert the governing time dependent nonlinear boundary layer equations into a system of non-linear ordinary differential equations containing Prandtl number, Eckert number, heat source/sink parameter, porous parameter and unsteadiness parameter with appropriate boundary conditions. These equations are solved numerically by applying shooting method using Runge-Kutta-Fehlberg method. Comparison of numerical results is made with the earlier published results under limiting cases. The effects of the parameters which determine the velocity and temperature fields are discussed in detail.
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.
Unsteady Mixed Convection Slip Flow around a Stretching Sheet in Porous Medium
Journal of Applied Mathematics and Physics
The heat and mass transfer of unsteady MHD two-dimensional mixed convection boundary layer flow over an exponentially porous stretching sheet is presented in this paper. Multiple slip conditions, radiation, suction or blowing, heat generation or absorption along with magnetism and porous medium are incorporated. We reduce the leading equations which are partial differential equations into a family of ordinary differential equations that are non-linear using a set of similarity transformations. The resulting equations with coupled boundary conditions are solved numerically with the aid of bvp4c solver with MATLAB package. The impacts of several non-dimensional governing parameters on the flow fields such as velocity, temperature and concentration profiles along with friction coefficient, temperature gradient and concentration gradient are portrayed graphically and discussed in detail. The result indicates that the magnetic parameter decreases the skin friction coefficient. Thermal boundary layer thickness reduces with increasing radiation parameters and enhances with increasing Prandtl number. It is also observed that the thermal slip parameter depreciates the heat transfer rate and the mass slip parameter diminishes the mass transfer rate. A comparison has been made between the current results and the numerical results of previous studies and observed a very close good agreement.
Thermal Science, 2014
In this article unsteady three dimensional MHD boundary layer flow and heat transfer analysis with constant temperature (CT) and constant heat flux (CH) in a porous medium is considered. The boundary layer flow is governed by a bidirectional stretching sheet. Similarity transformations are used to transform the governing non-linear partial differential equations to ordinary differential equations. Analytical solutions are constructed using homotopy analysis method (HAM). Convergence analysis is also presented through tabular data. The quantities of interest are the velocity, temperature, skin friction coefficient and Nusselt number. The obtained results are validated by comparisons with previously published work in special cases. The results of this parametric study are shown graphically and the physical aspects of the problem are discussed.
ijame, 2013
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...
Three dimensional boundary layer flow due to a permeable shrinking sheet with viscous dissipation and heat generation/absorption, has been studied in the present paper. The governing equations are transformed to ordinary differential equations by using suitable similarity transformations and then solved numerically on computer by standard technique. Numerical results of velocity and temperature profiles are obtained with the effects of various parameters involved such as suction, shrinking, Prandtl number, Eckert number and heat generation coefficient etc. and discussed them graphically in suitable manner such that interesting aspects of the solution can be adopted. Also, the comparison of results of two dimensional case and axisymmetric shrinking sheet case is considered.
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.
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.
Force convective flow over a porous and stretching (shrinking) sheet of variable thickness
Journal of Thermal Analysis and Calorimetry, 2020
The classical problems of natural and forced convection flows are reformulated and combined into a single model by introducing new variables for the field quantities. The proposed model is characterized by additional features of physical interest. A generalized problem of force convection flow and heat transferred is solved for a vertical stretching (shrinking) and porous (impermeable) sheet of variable thickness. The generalization gives rise to new problems, which are obtained in the next fourth section. It is assumed that the stretching/shrinking and porous velocities are variable such that both suction and injection can take place through the porous surface. The variable surface velocity may have linear, nonlinear, exponential and power law forms. Analysis of viscous flow and heat transfer is accomplished by considering force convection boundary layer flow over a stretching (shrinking) and porous surface of variable thickness. The nonlinear problem of partial differential equation is simplified by considering the boundary layer approximations and reduced it into nonlinear ODEs. The ODEs are obtained by introducing unusual and generalized similarity transformations for the stream function and similarity variables. Final ODEs are characterized by suction (injection), stretching (shrinking), convection parameters and Prandtl number. The ODEs are solved numerically, and effects of all existing parameters are studied on flow and heat transfer characteristics. Comparisons of the new problem and its solutions are established with the studies to demonstrate the applicability, validity and high accuracy of the present approach. Keywords Generalized similarity transformations • Forced convection • Stretching/shrinking and porous sheet List of symbols V Velocity of the flow T Temperature field Apparent viscosity Thermal diffusivity U w (x) Sheet stretching (shrinking) velocity x, y Cartesian coordinates Pr Prandtl number Thermal diffusivity 3 Suction (injection) parameter c p Specific heat k, k 1 , c, c 2 Controlling parameters Thermal expansion T ∞ Free stream temperature w Wall shear stress Dynamic viscosity Density of the fluid Kinematic velocity Stream function V w (x) Suction (injection) velocity ∇T Variation between wall temperature and local temperature B Stretching(shrinking) parameter Controlling parameter Gr Modified Grashof number A 1 , A 2 , d 0 , d 1 Controlling parameters A, B Surface controlling parameters T w (x) Heat transfer coefficient T 0 Constant temperature d 2 Controlling parameter
World Journal of Mechanics, 2012
An unsteady boundary layer flow of viscous incompressible fluid over a stretching plate has been considered to solve heat flow problem with variable thermal conductivity. First, using similarity transformation, the velocity components have been obtained, and then the heat flow problem has been attempted in the following two ways: 1) prescribed stretching surface temperature (PST), and 2) prescribed stretching surface heat flux (PHF) Flow and temperature fields have been analyzed through graphs. The expressions for skin friction and coefficient of convective heat transfer Nusselt number in PST and PHF cases have been derived.