Mohammed S. Alhuthali

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid*

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fouriers law of heat conduction.

A shooting reproducing kernel Hilbert space method for multiple solutions of nonlinear boundary value problems

In this work an iterative method is proposed to predict and demonstrate the existence and multiplicity of solutions for nonlinear boundary value problems. In addition, the proposed method is capable of calculating analytical approximations for all branches of solutions. This method is a combination of reproducing kernel Hilbert space method and a shooting-like technique which takes advantage of two powerful methods for solving nonlinear boundary value problems. The formulation and implementation of this iterative method is discussed for nonlinear second order with two and three-point boundary value problems. Also, the convergence of the proposed method is proved. To demonstrate the computational efficiency, the mentioned method is implemented for some nonlinear exactly solvable differential equations including strongly nonlinear Bratu equation and nonlinear reaction-diffusion equation. It is also applied successfully to two nonlinear three-point boundary value problems with unknown exact solutions. In the last example a new branch of solutions is found which shows the power of the method to search for multiple solutions and indicates that the method may be successful in cases where purely analytic methods are not.

Mixed convection flow of jeffrey nanofluid with thermal radiation and double stratification

This article addresses the two-dimensional laminar boundary layer flow of magnetohydrodynamic (MHD) Jeffrey nanofluid with mixed convection. Effects of thermal radiation, thermophoresis, Brownian motion and double stratifications are taken into account. Rosseland’s approximation is utilized for the thermal radiation phenomenon. Convergent series solutions of velocity, temperature and nanoparticle concentration are developed. Graphs of dimensionless temperature and nanoparticle concentration are presented to investigate the influences of different emerging parameters. The values of skin-friction coefficient, local Nusselt and Sherwood numbers are computed and discussed for both Jeffrey and viscous fluids cases. We have observed that the temperature profile retarded for the larger values of Deborah number while an enhancement is noticed with the increasing values of ratio of relaxation to retardation times. Increasing values of thermal and nanoparticle concentration stratifications lead to a reduction in the temperature and nanoparticle concentration. The values of local Nusselt and Sherwood numbers are larger for the viscous fluid case when compared with Jeffrey fluid.

Application of the operational matrix of fractional-order Legendre functions for solving the time-fractional convection-diffusion equation

The operational matrix of fractional-order Legendre functions method are considered.The fractional order convection-diffusion problem is solved.The problem can be used extensively in science and engineering as in oil reservoir simulations.Problems which, an initially discontinuous profile is propagated by diffusion and convection. In this paper, the application of the operational matrix of fractional-order Legendre functions (FLFs) to solve the time-fractional convection-diffusion equation has been investigated. Fractional calculus has been applied to model the engineering and physical processes which are best described with other mathematical tools. The time variable of the time-fractional convection-diffusion equation and its space variable have been approximated by FLFs and shifted Legendre polynomials, respectively. The fractional derivatives together with product matrices of FLFs are employed to convert the solution of this problem to the solution of a system of algebraic equations.

Newtonian heating effects in three-dimensional flow of viscoelastic fluid

A mathematical model is constructed to investigate the three-dimensional flow of a non-Newtonian fluid. An incompressible viscoelastic fluid is used in mathematical formulation. The conjugate convective process (in which heat the transfer rate from the bounding surface with a finite capacity is proportional to the local surface temperature) in three-dimensional flow of a differential type of non-Newtonian fluid is analyzed for the first time. Series solutions for the nonlinear differential system are computed. Plots are presented for the description of emerging parameters entering into the problem. It is observed that the conjugate heating phenomenon causes an appreciable increase in the temperature at the stretching wall.