I. A. Hassanien

Fourth-order finite difference method for solving Burgers’ equation

Abstract In this paper, we present fourth-order finite difference method for solving nonlinear one-dimensional Burgers’ equation. This method is unconditionally stable. The convergence analysis of the present method is studied and an upper bound for the error is derived. Numerical comparisons are made with most of the existing numerical methods for solving this equation.

GLOBAL STABILITY OF HIV INFECTION MODELS WITH INTRACELLULAR DELAYS

In this paper, we study the global stability of two mathemat- ical models for human immunodeciency virus (HIV) infection with intra- cellular delays. Therst model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4 + T cells and macrophages taking into account the saturation infec- tion rate. The second model generalizes therst one by assuming that the infection rate is given by Beddington-DeAng functional response. Two time delays are used to describe the time periods between viral entry the two classes of target cells and the production of new virus particles. Lyapunov functionals are constructed and LaSalle-type theorem for delay differential equation is used to establish the global asymptotic stability of the uninfected and infected steady states of the HIV infection models. We have proven that if the basic reproduction number R0 is less than

Mixed Convection Effect on Melting from a Vertical Plate in a Porous Medium

In the present work, the effect of mixed convection about vertical surfaces on the phenomenon of melting process in a fluid-saturated porous medium is analyzed on the basis of boundary layer approximations. Similarity solutions are obtained for aiding external flow. The final similarity equations are integrated numerically by use of the fourth-order Runge–Kutta method. Results are reported for the flow and thermal fields in the melt region. The melting phenomenon decreases the local Nusselt number at the solid–liquid interface.

Combined forced and free convection in stagnation flows of micropolar fluids over vertical non-isothermal surfaces

Abstract Boundary layer solutions are presented to study the effects of buoyancy on forced convective micropolar fluid flow and heat transfer in stagnation flows using the theory of micropolar fluids formulated by Eringen. Numerical solutions are given for the governing momentum, angular momentum and energy equations. Missing values of the velocity, angular velocity and thermal functions are tabulated for a range of values of the material parameters. Two flow regions, namely, the buoyancy-assisting and buoyancy-opposed cases are analyzed. The boundary conditions of isothermal as well as linear variation of wall temperature are considered. It is observed that the wall shear stress and surface heat transfer rate increase or decrease with the buoyancy force parameter depending upon the flow regime being buoyancy-assisted or buoyancy-opposed, respectively.

Chebyshev solution of laminar boundary layer flow

An expansion procedure using the Chebyshev polynomials is proposed by using El-Gendi method [1], which yields more accurate results than those computed by P. M. Beckett [2] and A. R. Wadia and F. R. Payne [6] as indicated from solving the Falkner-Skan equation, which uses a boundary value technique. This method is accomplished by starting with Chebyshev approximation for the highest-order derivative and generating approximations to the lower-order derivatives through integration of the highest-order derivative.

Influence of variable permeability on combined convection along a nonisothermal wedge in a saturated porous medium

Mixed convection along a vertical nonisothermal wedge embedded in a fluid-saturated porous media incorporating the variation of permeability and thermal conductivity is studied. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter ζ and a pseudo-similarity variable η are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The entire mixed convection regime is covered by the single nonsimilarity parameter ζ=[1+(Rax/Pex)1/2]−1 from pure forced convection (ζ=1) to pure free convection (ζ=0). The problem is solved using nonsimilarity solution for the case of variable wall temperature. Velocity and temperature profiles as well as local Nusselt number are presented. The wedge angle geometry parameter is ranged from 0 to 1.

Unsteady natural convection from a heated vertical plate in micropolar fluid

An analysis is presented for the unsteady natural convection from a heated semi-infinite vertical plate placed in a micropolar fluid in the presence of internal heat generation or absorption. Numerical solutions of the unsteady boundary layer equations have been obtained at any station along the vertical plate using the finite difference method. Details of the velocity and temperature fields are presented for various values of time.

Local nonsimilarity solutions for mixed convection boundary layer flow of a micropolar fluid on horizontal flat plates with variable surface temperature

An analysis is performed to study the heat transfer characteristics of laminar mixed convection boundary layer flow of a micropolar fluid over a semi-infinite horizontal flat plate with nonuniform surface temperatures. The surface temperature is assumed to vary as a power of the axial coordinate measured from the leading edge of the plate. A nonsimilar mixed convection parameter @x and a pseudo-similarity variable @h are introduced to cast the governing boundary layer equations into a system of dimensionless equations which are solved numerically using finite difference method. The mixed convection parameter is chosen to cover the entire regime of mixed convection from the pure forced convection limit to the pure free convection limit. The effect of material parameter, the exponent for the power-law variation in wall temperature and the nonsimilar mixed convection parameter are considered. The micropolar fluids are observed to display drag reduction and reduce surface heat transfer rate when compared to Newtonian fluid. The effect of the buoyancy force results in the enhancements of friction factor, heat transfer rate and wall couple stress. The local heat transfer rate is found to increase with increase in the exponent value of the power-low variation in wall temperature.

Mixed convection boundary layer flow of a micropolar fluid near a stagnation point on a horizontal cylinder

Abstract The theory of micropolar fluids due to Eringen is used to formulate a set of boundary layer equations for the mixed convective flow of an incompressible micropolar fluid in the vicinity of the front stagnation point on an isothermal circular cylinder. The governing conservation equations have been solved numerically. Missing values of the velocity, angular velocity and thermal functions are tabulated for a wide range of the material parameters of the fluid, the buoyancy parameter and the Prandtl number of the fluid. Micropolar fluids display drag reduction and reduced surface heat transfer rate as compared with Newtonian fluids.

Flow and Heat Transfer on a Continuous Flat Surface Moving in a Parallel Free Stream with Variable Fluid Properties

Boundary layer flow and heat transfer on a continuous flat surface moving in a parallel free stream with variable fluid properties are investigated. The similarity solution is used to transform the problem under consideration into a boundary value problem of coupled ordinary differential equations. Numerical results are carried out for various values of the dimensionless parameters of the problem. The results have demonstrated that the assumption of constant properties may introduce severe errors in the prediction of surface friction factor and heat transfer rate. For the same Reynolds numbers, Prandtl numbers, heating parameter, temperature exponents for viscosity and thermal conductivity parameters, and the same velocity difference |U w - U∞|, larger skin friction, and heat transfer coefficient results for U w > U∞ than for U w < U∞.