On double-diffusive convection and cross diffusion effects on a horizontal wavy surface in a porous medium

An analysis of double diffusive convection induced by a uniformly heated and salted horizontal wavy surface in a porous medium is presented. The wavy surface is first transformed into a smooth surface via a suitable coordinate transformation and the transformed nonsimilar coupled nonlinear parabolic equations are solved using the Keller box method. The local and average Nusselt and Sherwood numbers are given as functions of the streamwise coordinate and the effects of various physical parameters are discussed in detail. The effects of the Lewis number, buoyancy ratio, and wavy geometry on the dynamics of the flow are studied. It was found, among other observations, that the combined effect of Dufour and Soret parameters is to reduce both heat and mass transfer

Local Convergence of an Optimal Eighth Order Method under Weak Conditions

We study the local convergence of an eighth order Newton-like method to approximate a locally-unique solution of a nonlinear equation. Earlier studies, such as Chen et al. (2015) show convergence under hypotheses on the seventh derivative or even higher, although only the first derivative and the divided difference appear in these methods. The convergence in this study is shown under hypotheses only on the first derivative. Hence, the applicability of the method is expanded. Finally, numerical examples are also provided to show that our results apply to solve equations in cases where earlier studies cannot apply

Local Convergence of an Efficient High Convergence Order Method Using Hypothesis Only on the First Derivative

We present a local convergence analysis of an eighth order three step methodin order to approximate a locally unique solution of nonlinear equation in a Banach spacesetting. In an earlier study by Sharma and Arora (2015), the order of convergence wasshown using Taylor series expansions and hypotheses up to the fourth order derivative oreven higher of the function involved which restrict the applicability of the proposed scheme. However, only first order derivative appears in the proposed scheme. In order to overcomethis problem, we proposed the hypotheses up to only the first order derivative. In this way,we not only expand the applicability of the methods but also propose convergence domain. Finally, where earlier studies cannot be applied, a variety of concrete numerical examplesare proposed to obtain the solutions of nonlinear equations. Our study does not exhibit thistype of problem/restriction

A numerical study of unsteady non-Newtonian Powell-Eyring nanofluid flow over a shrinking sheet with heat generation and thermal radiation

In this paper we investigate the unsteady boundary-layer flow of an incompressible Powell-Eyring nanofluid over a shrinking surface. The effects of heat generation and thermal radiation on the fluid flow are taken into account. Numerical solutions of the nonlinear differential equations that describe the transport processes are obtained using a multi-domain bivariate spectral quasilinearization method. This innovative technique involves coupling bivariate Lagrange interpolation with quasilinearization. The solutions of the resulting system of equations are then obtained in a piecewise manner in a sequence of multiple intervals using the Chebyshev spectral collocation method. A parametric study shows how various parameters influence the flow and heat transfer processes. The validation of the results, and the method used here, has been achieved through a comparison of the current results with previously published results for selected parameter values. In general, an excellent agreement is observed. The results from this study show that the fluid parameters ε and δ reduce the flow velocity and the momentum boundary-layer thickness. The heat generation and thermal radiation parameters are found to enhance both the temperature and thermal boundary-layer thicknesses

Entropy generation in MHD radiative viscous nanofluid flow over a porous wedge using the bivariate spectral quasi-linearization method

We study the viscous nanofluid flow over a non-isothermal wedge with thermal radiation. The entropy due to irreversible processes in the system may degrade the performance of the thermodynamic system. Studying entropy generation in the flow over a porous wedge gives insights into how the system is affected by irreversible processes, and indicate which thermo–physical parameters contribute most to entropy generation in the system. The bivariate spectral quasi-linearization method is used to find the convergent solutions of the model equations. The impact of significant parameters such as the Hartmann number, thermophoresis and Brownian motion parameter on the fluid properties is evaluated and discussed. The Nusselt number, skin friction coefficients and Sherwood number are determined. An analysis of the rate of entropy generation in the flow for various parameters is presented, and among other results, we found that the Reynolds number and thermal radiation contribute significantly to entropy generation. Keywords: Entropy generation, Wedge flows, Bivariate spectral quasi-linearization metho

A new numerical approach to MHD stagnation point flow and heat transfer towards a stretching sheet

Magnetohydrodynamic (MHD) stagnation point flow and heat transfer problem from a stretching sheet in the presence of a heat source/sink and suction/injection in porous media is studied in this paper. The governing partial differential equations are solved using the Chebyshev spectral method based perturbation approach. The method, namely the spectral perturbation method (SPM), is a series expansion technique which extends the use of the standard perturbation approach by coupling it with the Chebyshev pseudo-spectral method. Series solutions for small velocity ratio and asymptotic solutions for large velocity ratio are generated and the results are also validated against those obtained using the spectral quasi-linearisation method (SQLM). It is seen from this study that the SPM can be used as an alternative approach to find numerical solutions for complicated expansions encountered in perturbation schemes. The results are benchmarked with previously published results

DTM-Padé Numerical Simulation of Electrohydrodynamic Ion Drag Medical Pumps with Electrical Hartmann and Electrical Reynolds Number Effects

The DTM-Padé method, a combination of the differential transform method (DTM) and Padé approximants, is applied to provide highly accurate, stable and fast semi-numerical solutions for several nonlinear flow regimes of interest in electrohydrodynamic ion drag pumps, arising in chemical engineering processing. In both regimes studied, the transformed, dimensionless ordinary differential equations subject to realistic boundary conditions are solved with DTM-Padé and excellent correlation with numerical quadrature is achieved. The influence of electrical Reynolds number (ReE), electrical slip number (Esl), electrical source number (Es) and also electrical Hartmann number (Hae) are examined graphically. Applications of this study include novel ion drag pumps and astronautical micro-reactors. This study constitutes the first application of the DTM-Padé semi-computational algorithm to electrohydrodynamic biotechnology flows.Furthermore the range of solutions given significantly extends the existing computations in previous studies and provides a much more general analysis of ion drag pump electrohydrodynamics, of direct relevance to medical drug delivery systems