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.

Authors:A.A. Mogbademu; S. Hans; J.A. Adepoju Pages: 243 - 248 Abstract: Publication date: Available online 1 April 2015 Source:Journal of the Nigerian Mathematical Society Author(s): A.A. Mogbademu , S. Hans , J.A. Adepoju In this paper, we put restrictions on the coefficients of a polynomial in order to improve the bounds for their zeros in a specific region. Our results extend and generalise a number of previously well known theorems including Eneström–Kakeya theorem.

Authors:Hallowed Olaoluwa; Johnson Olaleru Pages: 249 - 258 Abstract: Publication date: Available online 17 June 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Hallowed Olaoluwa , Johnson Olaleru This research work entails the study of the existence of common fixed points of some Ciric classes of contractive mappings in cone b -metric spaces. The main result obtained unifies, improves and generalizes several results in literature including those of Abbas et al. (2010) and Huang and Xu (2012). Furthermore, as a way of applications, the result is used to discuss common coupled, tripled and multipled fixed points of contractive maps defined on cone b -metric spaces, via product cone b -metric spaces.

Authors:S.A. Iyase Pages: 259 - 266 Abstract: Publication date: Available online 1 September 2015 Source:Journal of the Nigerian Mathematical Society Author(s): S.A. Iyase In this paper we present some existence results for a fourth order multipoint boundary value problem at resonance. Our main tools are based on the coincidence degree theory of Mawhin.

Authors:B.J. Gireesha; B. Mahanthesh; P.T. Manjunatha; R.S.R. Gorla Pages: 267 - 285 Abstract: Publication date: Available online 21 August 2015 Source:Journal of the Nigerian Mathematical Society Author(s): B.J. Gireesha, B. Mahanthesh, P.T. Manjunatha, R.S.R. Gorla This paper investigates the problem of MHD boundary layer flow and heat transfer of an electrically conducting dusty fluid over an unsteady stretching surface through a non-Darcy porous medium. The flow in porous medium is described by employing the Darcy–Forchheimer based model. The unsteadiness in the flow and temperature fields are because of time-dependent stretching velocity and surface temperature. The effect of thermal radiation, viscous dissipation and non-uniform heat source/sink are also taken into account. The pertinent time-dependent equations, governing the flow and heat transfer are reduced into a set of non-linear ordinary differential equations with the aid of suitable similarity transformations. The transformed equations are numerically integrated using fourth–fifth order Runge–Kutta–Fehlberg method. The effects of various physical parameters on the velocity and temperature profiles of both phases are analyzed through several plots. Obtained numerical results are compared and found to be in good agreement with previously published results as special cases of the present investigation. It is found that, by suspending fine dust particles in the clean fluid reduces the thermal boundary layer thickness. Therefore, the dusty fluids are preferable in engineering and scientific applications, involving cooling processes.

Authors:Shelly Arora; Inderpreet Kaur Pages: 286 - 302 Abstract: Publication date: Available online 1 November 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Shelly Arora, Inderpreet Kaur Technique of orthogonal collocation along with finite elements has been presented to solve the linear and non linear heat conduction problems numerically. Choice of Lagrangian interpolation polynomials as base function has been opted to discretize the trial function. Error analysis has been discussed in terms of element size for both the linear and non linear problems. Proposed technique has been applied on different types of linear and non linear heat conduction problems and the numerical values are plotted using 2D and 3D graphs.

Authors:Hari R. Kataria; Akhil S. Mittal Pages: 303 - 317 Abstract: Publication date: Available online 19 September 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Hari R. Kataria, Akhil S. Mittal Analytic expression for unsteady hydromagnetic boundary layer flow past an oscillating vertical plate in optically thick nanofluid in presence of thermal radiation and uniform transverse magnetic field is obtained. The Rosseland diffusion flux model is adopted to simulate thermal radiation effects. The momentum and energy conservation equations are made dimensionless and analytic solution is obtained using the Laplace transform. The results for velocity and temperature are obtained and plotted graphically. It is found that the velocity of the nanofluid increases with radiation parameter Nr, Grashof number Gr and time while decreases with increase in magnetic field and Prandtl number Pr. Temperature of nano-fluids increases with time while decrease with increase in Nr and Pr.

Authors:S.P. Anjali Devi; M. Prakash Pages: 318 - 330 Abstract: Publication date: Available online 14 August 2015 Source:Journal of the Nigerian Mathematical Society Author(s): S.P. Anjali Devi, M. Prakash The primary focus of this work is to numerically investigate the influence of temperature dependent viscosity and thermal conductivity on hydromagnetic flow over slendering stretching sheet. In the process held at high temperature like glass blowing, the fluid properties like viscosity and thermal conductivity may gets influenced in such temperature which motivated us to analyze those kind of problem. Considering steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness in the presence of variable magnetic field. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained and presented in tabulated form. It is noticed that, in additional to the magnetic field there are two more regulators which can manipulate to maintain the optimal heat for the glass blowing process to attain required shapes.

Authors:Temitope E. Akinbobola; Samuel S. Okoya Pages: 331 - 342 Abstract: Publication date: Available online 11 November 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Temitope E. Akinbobola, Samuel S. Okoya Steady two-dimensional non-Newtonian second grade fluid is studied under the influence of temperature dependent viscosity and thermal conductivity. The viscosity is assumed to vary inversely as linear function of temperature while the thermal conductivity varies directly as linear function of temperature. Also, effects of radiative heat, viscous dissipation and heat source/sink are considered in the energy equation. The basic governing partial differential equations for the velocity and temperature are transformed to ordinary differential equations (ODEs) using appropriate similarity variables. These coupled nonlinear ODEs have been solved approximately subject to appropriate boundary conditions by Runge–Kutta shooting technique. The quantitative effects of emerging dimensionless physical parameters on the velocity, temperature, skin friction and heat transfer rate are displayed graphically. The numerical investigation of the variable thermo-physical properties of a second grade fluid over a stretching sheet provides an extension to previous work.

Authors:A.J. Omowaye; A.I. Fagbade; A.O. Ajayi Pages: 343 - 360 Abstract: Publication date: Available online 28 August 2015 Source:Journal of the Nigerian Mathematical Society Author(s): A.J. Omowaye, A.I. Fagbade, A.O. Ajayi This paper presents the analytical solution to a 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.

Authors:A.J. Saka; B.L. Adeleke Pages: 369 - 376 Abstract: Publication date: Available online 1 September 2015 Source:Journal of the Nigerian Mathematical Society Author(s): A.J. Saka, B.L. Adeleke 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.

Authors:D. Vamshee Krishna; B. Venkateswarlu; T. RamReddy Pages: 121 - 127 Abstract: Publication date: Available online 1 April 2015 Source:Journal of the Nigerian Mathematical Society Author(s): D. Vamshee Krishna , B. Venkateswarlu , T. RamReddy The objective of this paper is to obtain an upper bound to the Third Hankel determinant denoted by H 3 ( 1 ) for certain subclass of univalent functions, using Toeplitz determinants.

Authors:D.G. Yakubu; A.M. Kwami Pages: 128 - 142 Abstract: Publication date: Available online 7 February 2015 Source:Journal of the Nigerian Mathematical Society Author(s): D.G. Yakubu , A.M. Kwami We introduce a new class of implicit two-derivative Runge–Kutta collocation methods designed for the numerical solution of systems of equations and show how they have been implemented in an efficient parallel computing environment. We also discuss the difficulty associated with large systems and how, in this case, one must take advantage of the second derivative terms in the methods. We consider two modified versions of the methods which are suitable for solving stable systems. The first modification involves the introduction of collocation at the two end points of the integration interval in addition to the Gaussian interior collocation points and the second involves the introduction of a different class of basic second derivative methods. With these modifications, fewer function evaluations per step are achieved, resulting into methods that are cheap and easy to implement. The stability properties of these methods are investigated and numerical results are given for each of the modified version to illustrate the computational efficiency of the modified methods.

Authors:O.A. Akinfenwa; B. Akinnukawe; S.B. Mudasiru Pages: 160 - 168 Abstract: Publication date: Available online 27 June 2015 Source:Journal of the Nigerian Mathematical Society Author(s): O.A. Akinfenwa , B. Akinnukawe , S.B. Mudasiru This paper presents a family of Continuous Third Derivative Block Methods (CTDBM) of order k + 3 for the solution of stiff systems of ordinary differential equations. The approach uses the collocation and interpolation technique to generate the main Continuous Third Derivative method (CTDM) which is then used to obtain the additional methods that are combined as a single block methods. Analysis of the methods show that the method is L-stable up to order eight. Numerical examples are given to illustrate the accuracy and efficiency of the proposed method.

Authors:C.S.K. Raju; N. Sandeep; C. Sulochana; V. Sugunamma; M. Jayachandra Babu Pages: 169 - 180 Abstract: Publication date: Available online 4 April 2015 Source:Journal of the Nigerian Mathematical Society Author(s): C.S.K. Raju , N. Sandeep , C. Sulochana , V. Sugunamma , M. Jayachandra Babu The steady two-dimensional flow over a vertical stretching surface in presence of aligned magnetic field, cross-diffusion and radiation effects are considered. The governing partial differential equations are transformed to nonlinear ordinary differential equation by using similarity transformation and then solved numerically by using bvp4c with MATLAB package. The effects of various non-dimensional governing parameters on velocity, temperature, concentration profiles along friction factor, Nusselt and Sherwood numbers are discussed and presented through graphs and tables’.We observed that increase in aligned angle strengthen the magnetic field and decreases the velocity profile of the flow and enhances the heat transfer rate. Comparisons with existed results are presented.

Authors:B. Ganga; S. Mohamed Yusuff Ansari; N. Vishnu Ganesh; A.K. Abdul Hakeem Pages: 181 - 194 Abstract: Publication date: Available online 3 June 2015 Source:Journal of the Nigerian Mathematical Society Author(s): B. Ganga , S. Mohamed Yusuff Ansari , N. Vishnu Ganesh , A.K. Abdul Hakeem A mathematical analysis has been carried out to investigate the effects of internal heat generation/absorption, viscous and ohmic dissipations on steady two-dimensional radiative MHD boundary-layer flow of a viscous, incompressible, electrically conducting nanofluid over a vertical plate. A system of governing nonlinear PDEs is converted into a set of nonlinear ODEs by suitable similarity transformations and then solved analytically using HAM and numerically by the fourth order Runge–Kutta integration scheme with shooting method. The effects of different controlling parameters on the dimensionless velocity, temperature and nanoparticle volume fraction profiles are discussed graphically. The reduced Nusslet number and the local Sherwood number are also discussed graphically. It is found that the presence of viscous dissipation, heat generation and magnetic field accelerates the temperature and decelerates the nanosolid volume fraction profile. Furthermore, comparisons have been made with bench mark solutions for a special case and obtained a very good agreement.

Authors:M.S. Dada; A.B. Disu Pages: 200 - 215 Abstract: Publication date: Available online 3 January 2015 Source:Journal of the Nigerian Mathematical Society Author(s): M.S. Dada , A.B. Disu This study was conducted to investigate the two dimensional heat transfer of a free convective MHD flow with radiation and temperature dependent heat source of a viscous incompressible fluid in a porous medium between two vertical wavy walls. The flow is assumed to consist of a mean part and a perturbed part. The perturbed quantities are expressed in terms of exponential series for short wave-length. The resultant differential equations are solved by Differential Transform Method (DTM). The numerical computations are presented graphically to show the salient features of the fluid flow and heat transfer characteristics. The skin friction and Nusselt number are also analyzed for variation of governing parameters.

Authors:E.O. Ifidon; E.O. Oghre Pages: 216 - 226 Abstract: Publication date: Available online 8 January 2015 Source:Journal of the Nigerian Mathematical Society Author(s): E.O. Ifidon , E.O. Oghre A nonlinear elliptic partial differential equation (pde) is obtained as a generalization of the planar Euler equation to the surface of the sphere. A general solution of the pde is found and specific choices corresponding to Stuart vortices are shown to be determined by two parameters λ and N which characterizes the solution. For λ = 1 and N = 0 or N = − 1 , the solution is globally valid everywhere on the sphere but corresponds to stream functions that are simply constants. The solution is however non-trivial for all integral values of N ≥ 1 and N ≤ − 2 . In this case, the solution is valid everywhere on the sphere except at the north and south poles where it exhibits point-vortex singularities with equal circulation. The condition for the solutions to satisfy the Gauss constraint is shown to be independent of the value of the parameter N . Finally, we apply the general methods of Wahlquist and Estabrook to this equation for the determination of (pseudo) potentials. A realization of this algebra would allow the determination of Bäcklund transformations to evolve more general vortex solutions than those presented in this paper.

Authors:R.O. Olayiwola Pages: 1 - 10 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): R.O. Olayiwola We study a model for forward propagation of a combustion front through a porous medium. The reaction involves oxygen and a solid fuel. We assume that this solid fuel depends on the space variable. We also assume that the amount of gas produced by the reaction is equal to the amount of gas consumed by it. By actual solutions, we prove the existence and uniqueness of solution of the model. We show that temperature is non-decreasing function of time. We use the similarity variable to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations and an efficient numerical technique is implemented to solve the reduced system. The results are presented graphically and discussed. It is discovered that the heat transfer and species consumption are significantly influenced by the Frank–Kamenetskii number.

Authors:Nkem Ogbonna Pages: 32 - 39 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): Nkem Ogbonna The interaction of a screw dislocation in a lamellar inclusion with multiple boundaries is investigated. An analytical solution is obtained for the force acting on the dislocation, and equilibrium positions are established for physically interesting special cases, such as a double layer bounded by free plane surfaces. A functional relationship is obtained which expresses the force on a screw dislocation on one side of an interface in terms of the force on a screw dislocation on the opposite side of the interface, thereby contributing to reduction of effort in the calculation process.

Authors:S.A. Odejide Pages: 40 - 49 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): S.A. Odejide In this paper, an incompressible viscous fluid flow and heat transfer in a collapsible tube with heat source or sink is examined. The nonlinear equation arising from the model was solved using perturbation series. An increasing or decreasing in the Prandtl number leads to increasing or decreasing in the rate of heat transfer across the wall.

Authors:A.M. Ette; W.I. Osuji Pages: 50 - 69 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): A.M. Ette , W.I. Osuji In this paper, we employ perturbation procedures in asymptotic expansions of the various variables to determine the dynamic buckling load of a lightly damped elastic quadratic model structure modulated by a dynamic periodic load. We finally relate the dynamic buckling load to its static equivalent and show that given any one of them, the other can automatically be obtained.

Authors:B.M. Yisa; R.B. Adeniyi Pages: 70 - 82 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): B.M. Yisa , R.B. Adeniyi In this paper, the generalization of the Lanczos–Ortiz’s Recursive formulation of the tau method for general non-overdetermined ordinary differential equations is presented. The generalization of the canonical polynomials and their derivatives for both overdetermined and non-overdetermined cases were reported in the earlier works of these authors, thus the emphasis here is on the error and the error estimate procedures. The accuracy of the results were established using some numerical examples and the induction principle.

Authors:Anetor Osemenkhian Pages: 83 - 93 Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): Anetor Osemenkhian In this paper we designed Rational Interpolation Method for solving Ordinary Differential Equations (ODES) and Stiff initial value problems (IVPs). This was achieved by considering the Rational Interpolation Formula. y ( x ) = U ( x ) = P 0 + P 1 x + P 2 x 2 + P 3 x 3 + p 4 x 4 + P 5 x 5 1 + q 1 x + q 2 x 2 + q 3 x 3 + q 4 x 4 + q 5 x 5 + q 6 x 6 , satisfying U ( X n + i ) = y n + i , i = 0 , 1 , 2 , 3 , 4 , 5 , 6 . We also implemented k = 6 in Aashikpelokhai (1991) class of rational integration formulas given by y n + 1 = ∑ i = 0 5 p i X n + 1 i 1 + ∑ i = 1 6 q i X n + 1 i where, P j = ∑ i = 1 j h ( j + 1 − i ) y n ( j + 1 − i ) ∑ i = 1 j ( j + 1 − i ) ! X n + 1 ( j + 1 − i ) q i − 1 + PubDate: 2015-05-04T18:23:05Z DOI: 10.1016/j.jnnms.2014.05.001 Issue No:Vol. 34, No. 1 (2015)

Authors:K.L. Krupa; Lakshmi B.J. Gireesha Rama.S.R. Gorla Mahanthesh Abstract: Publication date: Available online 27 November 2015 Source:Journal of the Nigerian Mathematical Society Author(s): K.L. Krupa Lakshmi, B.J. Gireesha, Rama.S.R. Gorla, B. Mahanthesh 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.

Authors:J.V. Ramana; Reddy Sugunamma Sandeep Sulochana Abstract: Publication date: Available online 15 September 2015 Source:Journal of the Nigerian Mathematical Society Author(s): J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, C. Sulochana 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.

Authors:Sunday Kolawole; Adegbie Kolade Isaac Lare Animasaun Abstract: Publication date: Available online 3 August 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Sunday Kolawole Adegbie, O. Kolade Kọrikọ, Isaac Lare Animasaun 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.

Authors:Nakone Bello; Jagadish Singh Abstract: Publication date: Available online 28 July 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Nakone Bello, Jagadish Singh This paper deals with the triangular points L 4 , 5 of the relativistic restricted three-body problem (R3BP) when the smaller primary is assumed triaxial. It is noticed that the locations and stability of the triangular points are affected by both relativistic and triaxiality pertubations. It can be easily seen that the range of stability region of these points is reduced by the effects of relativistic and triaxiality factors and more especially decreases with the increase of triaxiality factor.

Authors:Nkem Ogbonna Abstract: Publication date: Available online 17 July 2015 Source:Journal of the Nigerian Mathematical Society Author(s): Nkem Ogbonna 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.

Authors:I.L. Animasaun Abstract: Publication date: April 2015 Source:Journal of the Nigerian Mathematical Society, Volume 34, Issue 1 Author(s): I.L. Animasaun This present study focuses on the effects of thermophoresis, Dufour, temperature dependent thermal conductivity and viscosity of an incompressible electrically conducting Casson fluid flow along a vertical porous plate in the presence of viscous dissipation, n t h order chemical reaction and suction. It is assumed that the relationship between the flow rate and pressure drop as the fluid flows through a porous medium is non-linear. Similarity transformations are used to convert the governing equations to a system of nonlinear ordinary coupled differential equations and the numerical solutions for the velocity, temperature and concentration profiles are obtained using shooting method along with Runge-Kutta Gill and Quadratic interpolation (Muller’s scheme). The behaviour of dimensionless velocity, temperature and concentration within the boundary layer has been studied using different values of Prandtl number, Casson parameter, thermophoretic parameter, temperature dependent viscosity, temperature dependent thermal conductivity, Magnetic parameter, local Forchheimer parameter, and local Darcy parameter. The flow controlling parameters are found to have a profound effect on the resulting flow profiles except in some few cases i.e. effect of thermophoretic parameter τ over velocity and temperature profiles of fluids with constant viscosity and thermal conductivity ( ξ = ε = 0 ). The local skin friction, Nusselt number and Sherwood number for some cases are also presented.

Authors:R.A. Oderinu; Y.A.S. Aregbesola Abstract: Publication date: Available online 14 December 2014 Source:Journal of the Nigerian Mathematical Society Author(s): R.A. Oderinu , Y.A.S. Aregbesola A new, accurate and general formula for evaluating the skin friction parameter in a Magneto-Hydrodynamics (MHD) Falkner–Skan flow over a permeable wall was obtained. The formula gives the value of the skin friction of the problem in an infinite interval ( 0 , ∞ ) for all various values of the parameters involved. Shooting method via Runge–Kutta method for solving two-point boundary value problem in a truncated interval ( 0 , L ) is used to compare the results obtained. It was observed that the percentage difference between the two sets of results is very small.

Authors:E.B. Nkemnole; Abass Abstract: Publication date: Available online 13 December 2014 Source:Journal of the Nigerian Mathematical Society Author(s): E.B. Nkemnole , O. Abass Stochastic Volatility (SV) model usually assumes that the distribution of asset returns conditional on the latent volatility is normal. Previous approaches to estimation of SV model have mostly focused on Gaussian filters in practice. This paper analyzes SV model with the student-t distribution and compares the distribution with mixture-of-normal distributions of Kim and Stoffer [22]. A Sequential Monte Carlo with Expectation–Maximization (SMCEM) technique based on student-t distribution is developed to estimate the parameters for the extended volatility model. The SMC method, or particle filter based on student-t distribution, which is heavier tailed than Gaussians, provides an approximate solution to non-Gaussian estimation problem and hence more robust. Our empirical analysis indicates that extension of the SV model such as a specification of the error term with student-t distribution in the return equation dominates the normal mixture distribution. Additionally, the t-distribution based particle filter is applied to a multivariate stochastic volatility model. It is again shown that the student-t based algorithm performs quite well in explaining the joint dynamics in the volatility of a set of four exchange rates series.

Authors:C.C. Jibunoh Abstract: Publication date: Available online 4 December 2014 Source:Journal of the Nigerian Mathematical Society Author(s): C.C. Jibunoh In this paper, an explicit Exponential Method (EM), which is an off-shoot of Jibunoh’s spectral decomposition is developed for the accurate and automatic integration of nonlinear (stiff and nonstiff) ODE systems. In particular, the Vanderpol system of equations is solved. The method is also applicable to linear systems, including linear oscillatory systems or systems with complex eigenvalues. It has simplicity of implementation by automatic computation using the QBASIC Codes and produces high accuracy or the exact theoretical solutions in any nonlinear or linear systems. The EM is, therefore, superior to many traditional methods which are less accurate and which integrate nonlinear systems with cumbersome procedures.