Blasius flow and heat transfer of fourth-grade fluid with slip

International audienceThis investigation deals with the effects of slip, magnetic field, and non-Newtonian flow parameters on the flow and heat transfer of an incompressible, electrically conducting fourth-grade fluid past an infinite porous plate. The heat transfer analysis is carried out for two heating processes. The system of highly non-linear differential equations is solved by the shooting method with the fourth-order Runge-Kutta method for moderate values of the parameters. The effective Broyden technique is adopted in order to improve the initial guesses and to satisfy the boundary conditions at infinity. An exceptional cross-over is obtained in the velocity profile in the presence of slip. The fourth-grade fluid parameter is found to increase the momentum boundary layer thickness, whereas the slip parameter substantially decreases it. Similarly, the non-Newtonian fluid parameters and the slip have opposite effects on the thermal boundary layer thickness

Optimal Homotopy Asymptotic Solution for Thermal Radiation and Chemical Reaction Effects on Electrical MHD Jeffrey Fluid Flow Over a Stretching Sheet through Porous Media with Heat Source

In this paper, the problem of thermal radiation and chemical reaction effects on electrical MHD Jeffrey fluid flow over a stretching surface through a porous medium with the heat source is presented. We obtained the approximate analytical solution of the nonlinear differential equations governing the problem using the Optimal Homotopy Asymptotic Method (OHAM). Comparison of results has been made with the numerical solutions from the literature, and a very good agreement has been observed. Subsequently, effects of governing parameters of the velocity, temperature and concentration profiles are presented graphically and discussed

Temperature Dependent Viscosity of a Third Order Thin Film Fluid Layer on a Lubricating Vertical Belt

This paper aims to study the influence of heat transfer on thin film flow of a reactive third order fluid with variable viscosity and slip boundary condition. The problem is formulated in the form of coupled nonlinear equations governing the flow together with appropriate boundary conditions. Approximate analytical solutions for velocity and temperature are obtained using Adomian Decomposition Method (ADM). Such solutions are also obtained by using Optimal Homotopy Asymptotic Method (OHAM) and are compared with ADM solutions. Both of these solutions are found identical as shown in graphs and tables. The graphical results for embedded flow parameters are also shown

Analysis of Unsteady Axisymmetric Squeezing Fluid Flow with Slip and No-Slip Boundaries Using OHAM

In this manuscript, An unsteady axisymmetric flow of nonconducting, Newtonian fluid squeezed between two circular plates is studied with slip and no-slip boundaries. Using similarity transformation, the system of nonlinear partial differential equations is reduced to a single fourth order ordinary differential equation. The resulting boundary value problems are solved by optimal homotopy asymptotic method (OHAM) and fourth order explicit Runge-Kutta method (RK4). It is observed that the results obtained from OHAM are in good agreement with numerical results by means of residuals. Furthermore, the effects of various dimensionless parameters on the velocity profiles are investigated graphically

Numerical Study of the Casson Non-Newtonian Fluid Flow over a Nonlinear Stretching Sheet

In this paper, numerical study of Casson non-Newtonian fluid over a nonlinear stretching sheet using shooting method will be presented. The governing nonlinear partial differential equation is converted to an ordinary differential equation  by using similarity transformations. This ordinary differential equation is handled numerically with the use of well-known shooting technique aided by Runge-Kutta method. For comparison of the results, MATLAB in-built solver BVP4C is used. The discussion of the results is provided in the forms of tables as well as graphically

Closed-Form Solutions for a Nonlinear Partial Differential Equation Arising in the Study of a Fourth Grade Fluid Model

The unsteady unidirectional flow of an incompressible fourth grade fluid bounded by a suddenly moved rigid plate is studied. The governing nonlinear higher order partial differential equation for this flow in a semiinfinite domain is modelled. Translational symmetries in variables and are employed to construct two different classes of closed-form travelling wave solutions of the model equation. A conditional symmetry solution of the model equation is also obtained. The physical behavior and the properties of various interesting flow parameters on the structure of the velocity are presented and discussed. In particular, the significance of the rheological effects are mentioned

Analytical modeling of MHD flow over a permeable rotating disk in the presence of soret and dufour effects: Entropy analysis.

The main concern of the present article is to study steady magnetohydrodynamics (MHD) flow, heat transfer and entropy generation past a permeable rotating disk using a semi numerical/analytical method named Homotopy Analysis Method (HAM). The results of the present study are compared with numerical quadrature solutions employing a shooting technique with excellent correlation in special cases. The entropy generation equation is derived as a function of velocity, temperature and concentration gradients. Effects of flow physical parameters including magnetic interaction parameter, suction parameter, Prandtl number, Schmidt number, Soret and Dufour number on the fluid velocity, temperature and concentration distributions as well as entropy generation number are analysed and discussed in detail. Results show that increasing the Soret number or decreasing the Dufour number tends to decrease the temperature distribution while the concentration distribution is enhanced. The averaged entropy generation number increases with increasing magnetic interaction parameter, suction parameter, Prandtl number, and Schmidt number