Journal of the Nigerian Mathematical Society最新文献

In this paper, the influence of some thermo-physical properties of fluid on heat and mass transfer flow past semi-infinite moving vertical plate is considered. The fluid considered is optically thin such that the thermal radiative heat loss on the fluid is modeled using Rosseland approximation. The governing equations representing the physical model is a system of partial differential equations which are transformed into systems of coupled non-linear partial differential equation by introducing non-dimensional variables. The resulting equations are solved using the spectral relaxation method (SRM). The result shows that an increase in Eckert number of the fluid actually increases the velocity and temperature profiles of the flow. Whereas an increase in thermal radiation parameter reduces the temperature distribution when the plate is being cooled. The computational results for velocity, temperature and the concentration profiles are displayed graphically for various flow pertinent parameters.

This article studies the motion of temperature dependent plastic dynamic viscosity and thermal conductivity of steady incompressible laminar free convective magnetohydrodynamic (MHD) Casson fluid flow over an exponentially stretching surface with suction and exponentially decaying internal heat generation. It is assumed that the natural convection is driven by buoyancy and space dependent heat generation. The viscosity and thermal conductivity of Casson fluid is assumed to vary as a linear function of temperature. By using suitable transformation, the governing partial differential equations corresponding to the momentum and energy equations are converted into non-linear coupled ordinary differential equations and solved by the Homotopy analysis method. A new kind of averaged residual error is adopted and used to find the optimal convergence control parameter. A parametric study is performed to illustrate the influence of Prandtl number, Casson parameter, temperature dependent viscosity, temperature dependent thermal conductivity, Magnetic parameter and heat source parameter on the fluid velocity and temperature profiles within the boundary layer. The flow controlling parameters are found to have a profound effect on the resulting flow profiles.

In this paper, quintic B-spline method is described for solving a class of fourth order singular singularly perturbed boundary value problems. This method is applied directly to the solution of the problems without reducing the order of the problems. The convergence analysis is also given and the method is shown to have uniform convergence of the second order. Numerical results are shown which demonstrate the efficiency of our method.

A substantial increase in efficiency is achieved by the numerical integration methods which take advantage of the second derivative terms of the differential equation to be solved. The second-derivative of high order accuracy methods are stable, convergent and hence suitable for the numerical integration of stiff systems of initial value problems in ordinary differential equations. The unique feature of the paper is the idea of using all the set of collocation points as additional interpolation points. This desirable feature of the proposed approach actually widens the applicability of the methods, to include many other types of numerical integration methods and has many advantages, including didactic advantages. Furthermore, in this formulation symmetry is retained naturally by the integration identities as equal areas under the various segments of the solution curves over the integration interval. In this way the problem of overlap of solution models usually associated with multistep finite difference methods is overcome. The applications of the second derivative multistep integration methods on a significant class of problems found in the literature produce accurate solutions with low computational cost. Comparison of the efficiency curves obtained seems to be in better agreement with the exact solutions.

The present study investigates the effect of joule heating and velocity slip on MHD peristaltic flow in a porous medium with chemical reaction. The relevant equations on the fluid flow have been developed. Analytic solution is carried out under long-wavelength and low-Reynolds number approximations. Exact solution is evaluated for the stream function, which is used to find the velocity of the fluid flow, temperature, concentration. Numerical computations have been performed for the influence of various emerging parameters on the flow characteristics velocity, temperature, concentration are shown and discussed with the help of graphs. Also, the expressions for skin friction coefficient, Nusselt number and Sherwood number at the channel wall are obtained and analyzed. It is found that a generative chemical reaction is greater than the destructive chemical reaction on the concentration. The size of the trapping bolus increases with increasing velocity slip parameter$\beta$.

The two dimensional boundary layer flow of micropolar fluid towards stagnation point formed on a horizontal linearly stretching surface is investigated. Melting heat transfer at the surface, temperature and exponentially space dependent internal heat generation within fluid domain are considered. It is assumed that dynamic viscosity and thermal conductivity are temperature dependent while micropolar vortex viscosity is constant. These assumptions are discussed. Classical temperature dependent viscosity and thermal conductivity models were modified to suit the case of melting heat transfer following all the necessary theories. Similarity transformations are used to convert the governing equations into non-linear boundary value problem and solved numerically. Effects of various parameters on the micropolar fluid flow and heat transfer are analyzed. The results reveal that one of the possible ways to increase transverse velocity of micropolar fluid flow over melting surface is to consider variable thermo-physical property of micropolar fluid at constant vortex viscosity with a decrease in melting parameter while velocity ratio increases. For correct analysis/investigation of micropolar fluid flow with variable properties over melting surface, the new thermo-physical models are to be considered. The velocity increases with the increase of velocity ratio under the new condition compare to classical condition (constant thermo-physical property) of micropolar fluid flow over melting surface.

A numerical investigation on laminar boundary layer flow, heat and mass transfer of two-phase particulate suspension induced by a linearly stretching sheet is carried out. In the mathematical formulation both the fluid and particle phases are treated as two separate interacting continua. The effects of magnetic field, diffusion-thermo, thermal-diffusion, thermal radiation and first order chemical reaction are taken into the account. The relevant governing partial differential equations corresponding to the momentum, energy and concentration are transformed into a system of non-linear ordinary differential equations with the help of appropriate similarity transformations and then solved numerically using Runge–Kutta-Fehlberg fourth fifth order method along with shooting scheme. The effects of the relevant physical parameters on the flow, heat and mass transfer characteristics of both fluid and particle phases were numerically obtained and discussed in detail. It is found that, the momentum, thermal and solute boundary layer thickness decreases with increasing the particles loading.

Present paper investigates the magnetohydrodynamic boundary layer mixed convection flow over a moving vertical plate in a non-Newtonian power-law nanofluid with variable density. The governing partial differential equations are transformed into a ordinary differential equations by suitable similarity transformations. The system of coupled non-linear ordinary differential equations are solved numerically using variational finite element method. The solutions for the flow and heat transfer characteristics are computed numerically for various values of flow controlling parameters. Investigation predict that an increase in the values of magnetic field parameter and thermophoresis parameter is to enhance the temperature and nanoparticle volume fraction profiles. Increasing power-law index reduces the velocity, temperature and nanoparticle volume fraction profiles. An increase in the Brownian motion and Lewis number is reduces the nanoparticle volume fraction profiles and temperature field is decreases with increasing Pradtl number. An increase in power-law index and thermophoresis is found to be increase in the skin friction co-efficient but decrease in the heat transfer co-efficient.

Block designs are useful in comparative experimentation for improving efficiency of treatment comparisons when working with heterogeneous experimental units. A nested balanced incomplete block design (NBIBD) is a design with two systems of blocks, the second nested within the first, such that ignoring either system leaves a balanced incomplete block design whose blocks are those of the other system. In this study, a new method of construction of nested balanced incomplete block designs for a number of parameter combinations is developed. The resulting design schemes were of the type that harmonizes both the Series-I and Series-II of Rajender et al. (2007) in which a single design scheme that can be used in the construction of both the Series-I and Series-II at the same time was produced.

This paper presents an analytical method of solution to steady two-dimensional hydromagnetic flow of a viscous incompressible, electrically conducting fluid past a semi-infinite moving permeable plate embedded in a porous medium. It is assumed that the fluid properties are constant except for the fluid viscosity which vary as an inverse linear function of temperature. The boundary layer equations are transformed in to a coupled ordinary differential equations with the help of similarity transformations. The resulting coupled ordinary differential equations were solved using the Homotopy Analysis Method (HAM). The combined effects of Dufour and Soret was investigated and presented graphically with controlling pertinent physical parameters.