Purpose – The purpose of this paper is to numerically solve the problem of steady mixed convection boundary layer flow past a vertical flat plate embedded in a fluid-saturated porous medium filled by a nanofluid. The non-Darcy equation model along with the mathematical nanofluid model proposed by Tiwari and Das (2007) has been used. Design/methodology/approach – Using appropriate similarity transformations, the basic partial differential equations are transformed into ordinary differential equations. These equations have been solved numerically for different values of the nanoparticle volume fraction, the mixed convection and the non-Darcy parameters using the bvp4c function from Matlab. A stability analysis has been also performed. Findings – Numerical results are obtained for the reduced skin-friction, heat transfer and for the velocity and temperature profiles. The results indicate that dual solutions exist for the opposing flow case (λ<0). The stability analysis indicates that for the opposing flow ca...

Mixed convection boundary layer flow past a vertical flat plate embedded in a non-Darcy porous medium saturated by a nanofluid

Numerical calculation from the full differential equations for convection in an unbounded region is expensive, and hence approximate solutions are important. For small values of the Rayleigh number Ra, perturbation methods are appropriate. At large values of Ra thermal boundary layers are formed, and boundary layer theory is the obvious method of investigation. This approach forms the subject of much of this chapter. We follow to a large extent the discussion by Cheng (1985a).

External Natural Convection

The flow of a steady, incompressible, micropolar fluid between parallel plates is studied in the presence of cross-diffusion effects. The governing non-linear systems of differential equations are solved by the homotopy analysis method. The non-dimensional velocity, temperature and concentration profiles are displayed graphically for different values of Dufour number, Soret number and coupling number. In addition, the skin-friction coefficient, heat and mass transfer rates are shown in a tabular form.

Flow of Micropolar Fluid Between Parallel Plates with Soret and Dufour Effects

In this paper, we develop extended one-step methods for solving optimal control problem for systems governed by delay differential equations(DDEs). The optimal control problem governed by ordinary differential equations have been considered in this paper as a case of the DDEs with the absence of delays. The proposed problem is reduced to either a constrained or unconstrained minimization problem according to the nature of the dynamic system and the given conditions. Pontryagin’s maximum (or minimum) principle is used to characterize the optimal controls. Numerical results with simulations compared with other methods are presented to show the efficiency of the methodology.

Numerical method based on extended one-step schemes for optimal control problem with time-lags

In this article, we study the effect of variable viscosity on the flow and vortex instability of non-Darcian free convection boundary layer flow on a horizontal surface in a saturated porous medium. The wall temperature is a power function of the distance from the origin. The variation of viscosity is expressed as an exponential function of temperature. The transformed boundary layer equations, which are developed using a non similar solution approach, are solved by means of a finite difference method. The analysis of the disturbance flow is based on linear stability theory. The local Nusselt number, critical Rayleigh number and the associated wave number at the onset of vortex instability are presented over a wide range of wall to ambient viscosity ratio parameters μ*= μw/μ∞. The variable viscosity effect is found to enhance the heat transfer rate and destabilize the flow for liquid heating, while the opposite trend is true for gas heating.

/pdf/effect-of-variable-viscosity-on-vortex-instability-of-non-2s7u0kiz07.pdf

Effect of variable viscosity on vortex instability of non-Darcy free convection boundary layer flow adjacent to a non-isothermal horizontal surface in a porous medium

/pdf/effect-of-variable-viscosity-on-vortex-instability-of-mixed-3rbgrhdks8.pdf

Effect of Variable Viscosity on Vortex Instability of Mixed Convection Boundary Layer Flow Adjacent to a Non-isothermal Horizontal Surface in a Porous Medium

In this paper, we derive a class of extended one-step methods of order m for solving delay-differential equations. This class includes methods of fourth and fifth order of accuracy. Also, the class of these methods depends on two free parameters. A convergence theorem and convergence factor of these methods are given. Stability regions for such methods are determined in terms of the time-lag τ. Some numerical examples are given to illustrate the effectiveness of the numerical schemes.

/pdf/a-class-of-extended-one-step-methods-for-solving-delay-493wloqp55.pdf

A Class of Extended One-Step Methods for Solving Delay Differential Equations

We discuss extended one-step methods of order three for the numerical solution of delay-differential equations. A convergence theorem and the numerical studies regarding the convergence factor of these methods are given. Also, we investigate the stability properties of these methods. The results of the theoretical studie s are illustrated by numerical examples.

/pdf/extended-one-step-methods-for-solving-delay-differential-29gsa2ortp.pdf

Extended one-step methods for solving delay-differential equations

Stability Analysis of Extended One-Step Schemes for Stiff and Non-Stiff Delay Differential Equations

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Papers

Effect of Variable Viscosity on Vortex Instability of Mixed Convection Boundary Layer Flow Adjacent to a Non-isothermal Horizontal Surface in a Porous Medium

A Class of Extended One-Step Methods for Solving Delay Differential Equations

Extended one-step methods for solving delay-differential equations

Stability Analysis of Extended One-Step Schemes for Stiff and Non-Stiff Delay Differential Equations