Authors:I.L. Animasaun; E.A. Adebile; A.I. Fagbade Pages: 1 - 17 Abstract: Publication date: April 2016 Source:Journal of the Nigerian Mathematical Society, Volume 35, Issue 1 Author(s): I.L. Animasaun, E.A. Adebile, A.I. Fagbade 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.

Authors:K. Issa; R.B. Adeniyi Pages: 18 - 24 Abstract: Publication date: April 2016 Source:Journal of the Nigerian Mathematical Society, Volume 35, Issue 1 Author(s): K. Issa, R.B. Adeniyi 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.

Authors:P. Umadevi; N. Nithyadevi Pages: 82 - 92 Abstract: Publication date: Available online 3 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): P. Umadevi, N. Nithyadevi 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.

Authors:S.O. Salawu; M.S. Dada Pages: 93 - 106 Abstract: Publication date: Available online 27 February 2016 Source:Journal of the Nigerian Mathematical Society Author(s): S.O. Salawu, M.S. Dada 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.

Authors:D.G. Yakubu; S. Markus Pages: 107 - 127 Abstract: Publication date: Available online 23 February 2016 Source:Journal of the Nigerian Mathematical Society Author(s): D.G. Yakubu, S. Markus 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.

Authors:C. Sulochana; G.P. Ashwinkumar; N. Sandeep Pages: 128 - 141 Abstract: Publication date: Available online 23 February 2016 Source:Journal of the Nigerian Mathematical Society Author(s): C. Sulochana, G.P. Ashwinkumar, N. Sandeep 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.

Authors:F.I. Alao; A.I. Fagbade; B.O. Falodun Pages: 142 - 158 Abstract: Publication date: Available online 3 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): F.I. Alao, A.I. Fagbade, B.O. Falodun 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.

Authors:M.Y. Abdollahzadeh Jamalabadi Pages: 159 - 177 Abstract: Publication date: Available online 23 February 2016 Source:Journal of the Nigerian Mathematical Society Author(s): M.Y. Abdollahzadeh Jamalabadi 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 ( ζ = 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.

Authors:B. Mahanthesh; B.J. Gireesha; Rama Subba Reddy Gorla Pages: 178 - 198 Abstract: Publication date: Available online 24 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): B. Mahanthesh, B.J. Gireesha, Rama Subba Reddy Gorla 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.

Authors:Macha Madhu; Naikoti Kishan Pages: 199 - 207 Abstract: Publication date: Available online 24 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): Macha Madhu, Naikoti Kishan 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.

Authors:C.S. Sravanthi Pages: 208 - 226 Abstract: Publication date: Available online 24 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): C.S. Sravanthi 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.

Authors:Gnaneswara Reddy Machireddy; Venugopal Reddy Kattamreddy Pages: 227 - 244 Abstract: Publication date: Available online 21 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): Gnaneswara Reddy Machireddy, Venugopal Reddy Kattamreddy 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 β .

Authors:Mitiku Daba; Ponnaian Devaraj Pages: 245 - 256 Abstract: Publication date: Available online 24 March 2016 Source:Journal of the Nigerian Mathematical Society Author(s): Mitiku Daba, P. Devaraj 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 P r , Schmidt number S c , buoyancy force parameter λ , radiation parameter N r , magnetic parameter M , buoyancy forces ratio parameter N , the unsteady parameter A , suction/injection parameter s , Eckert number E c , 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.

Authors:Ram Kishun Lodhi; Hradyesh Kumar Mishra Pages: 257 - 265 Abstract: Publication date: Available online 25 April 2016 Source:Journal of the Nigerian Mathematical Society Author(s): Ram Kishun Lodhi, Hradyesh Kumar Mishra 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.