Journal of the Nigerian Mathematical Society最新文献

We study the problem of a screw dislocation interacting with a double-coated cylindrical inclusion in a dissimilar matrix. Using an elastostatic image method, we determine the displacement field in each material phase and obtain the force of interaction between the inhomogeneity and the dislocation in the form of a rapidly convergent infinite series. Numerical examples are presented to illustrate the effect of double coating on the force of interaction. It is found that, for certain material combinations, the presence of a double-coated cylinder gives rise to two equilibrium positions of the dislocation. This result is significant as it indicates that multiple equilibrium positions are possible for multiply-coated inclusions interacting with a screw dislocation.

Investigation of two-dimensional steady laminar magneto-convection heat transfer of (Ag,TiO₂) water based nanofluids with variable properties inside a heat generating square enclosure having different thermal boundaries is done numerically in this paper. The governing equations are solved utilizing the finite volume method with power-law scheme and SIMPLE algorithm is used for handling the pressure-velocity coupling. The algorithm and the computer code have been also compared with numerical results in order to verify and validate the model. By using the developed fortran code, the effects of Hartmann number, heat generation (or absorption), Reyleigh number and solid volume fraction on the flow and thermal fields and heat transfer inside the enclosure are studied. Results are demonstrated in the form of streamlines, isotherms and average Nusselt number.

In this study, we analyzed the three-dimensional magnetohydrodynamic Newtonian and non-Newtonian fluid flow. Heat and mass transfer over a stretching surface in the presence of thermophoresis and Brownian motion is investigated. The transformed governing equations are solved numerically via Runge–Kutta based shooting technique. We obtained good accuracy of the present results by comparing with the exited literature. The influence of dimensionless parameters on velocity, temperature and concentration profiles along with the friction factor, local Nusselt and Sherwood numbers are discussed with the help of graphs and tables. It is found that an increase in the stretching ratio parameter enhances the heat and mass transfer rate. The heat and mass transfer rate in non-Newtonian fluid is comparatively high while compared with the heat and mass transfer rate in Newtonian fluid.

The present investigation deals with unsteady hydromagnetic chemically reacting mixed convection flow of incompressible viscous fluid past a vertically moving permeable stretching sheet in the presence of suction/injection, heat source/absorption, thermal radiation, viscous dissipation and slip effects. The governing partial differential equations are reduced into a set of non-linear ordinary differential equations by suitable transformations. Keller box method is applied to solve the system of non-linear ordinary differential equations for which the implementation is made with the help of matlab. The important parameters in this study are: Prandtl number $Pr$, Schmidt number $Sc$, buoyancy force parameter $\lambda$, radiation parameter $Nr$, magnetic parameter $M$, buoyancy forces ratio parameter $N$, the unsteady parameter $A$, suction/injection parameter $s$, Eckert number $Ec$, heat source/sink parameter $Q$, chemical reaction parameter $R$, velocity slip parameter $s_v$, temperature slip parameter $s_t$ and species concentration slip parameter $s_m$. Effects of these parameters on velocity, temperature and species concentration profile of the fluid are presented and analyzed graphically. Furthermore, numerical investigations have been made for the skin friction coefficient and surface heat and mass transfer rates for some of the parameters.

In a recent paper, we reported a generalized approximation technique for the recursive formulation of the Tau method. This paper is concerned with an extension of that discourse to non-linear ordinary differential equations. The numerical results show that the method is effective and accurate.

A theoretical investigation of the hydromagnetic three-dimensional boundary layer flow of nanofluid due to stretching sheet has been carried out in the presence of a non-linear thermal radiation, Soret and Dufour effects. Three different types of water-based nanofluids containing copper, aluminium oxide and titanium dioxide are taken into consideration. The governing boundary layer equations are transformed into a set of similarity equations using three dimensional non-linear type similarity transformations. The resultant equations are numerically solved by employing Runge–Kutta–Fehlberg fourth–fifth order method along with shooting scheme. Further, under some limiting case obtained results are compared with some previously published results and found in good agreement. The problem is governed eleven physical parameters such as magnetic parameter, radiation parameter, temperature ratio parameter, Prandtl, Schmidt, Soret, Dufour and Biot numbers, stretching ratio parameter, power index and nanoparticles volume fraction parameter. The effect of these parameters on various flow distributions is comprehensively discussed with the help of graphs and tables. It is found that, properties of the fluid can be changed by varying the concentration of nanoparticles and the nanoparticles enhance the thermal conductivity which results improvement in efficiency of heat transfer systems.

An analysis of steady MHD (magnetohydrodynamic) two dimensional free convective heat and mass transfer boundary layer flow of a viscous fluid towards an exponentially stretching inclined porous sheet in the presence of thermal radiation, Soret and Dufour effects with suction/blowing is presented. The Rossland approximation is used to describe the radiative heat transfer in the limit of optically thick fluids. Velocity slip, thermal slip and concentration slip are considered instead of no-slip condition at the boundary. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique namely homotopy analysis method (HAM). Expressions for velocity, temperature and concentration fields are developed in series form. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. A comparison of our HAM results with the available numerical results in the literature (obtained by Runge–Kutta and shooting methods) shows that our results are accurate for wide range of values of the parameters.

The study of thermal radiative heat transfer of an electrically conducting fluid over a continuously stretching sheet in the presence of a uniform inclined magnetic field with dissipation in a porous medium is investigated for power-law variation in the sheet temperature. The fluid viscosity and thermal conductivity are assumed to vary as a function of temperature. The governing partial differential equations of the model are reduced to a system of coupled non-linear ordinary differential equations by applying similarity variables and then solved numerically using shooting technique with fourth-order Runge–Kutta method. The results for Skin friction and Nusselt numbers are presented and discussed.

In this paper we investigated an unsteady free convection flow of a nanofluid bounded by a moving vertical flat plate through porous medium in a rotating system with convective and diffusive boundary conditions. We considered two types of nanofluids namely Ag-water and TiO${}_2$-water. The governing equations are solved analytically by using perturbation technique. Finally the effects of various dimensionless parameters like magneticfield parameter, chemical reaction parameter, thermal radiation parameter, volume fraction of the nano particles and shape of the nano particles on velocity, temperature and concentration profiles along with the friction factor, local Nusselt and Sherwood numbers are discussed with the help of graphs. Comparisons of the present results made with the existed studies and found an excellent agreement under some special limited cases. Moreover, we observed that the rate of heat transfer in Ag-water nanofluid is higher than that of TiO${}_2$-water nanofluid and spherical shaped nano particles effectively enhances the heat transfer rate while compared with the cylindrical shaped nano particles.

The purpose of the current study is to investigate the effect of temperature dependent thermophysical properties on thermal radiative loading characteristics of an enclosure. The results are studied the effect of heating number ($\zeta =0.05$–500), aspect ratio ($A=0.1$–1), the number of heaters ($N=1$–19), on the maximum and mean temperature of system, Nusselt number, and the maximum stream function rate have been quantitatively analyzed. The results reveal that the average heat transfer rate considering temperature-dependent viscosity are higher than considering temperature-dependent thermal conductivity and both temperature-dependent viscosity and thermal conductivity and the stream function are lower.