Research Articles (Mathematics Military)

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https://scholar.sun.ac.za/handle/10019.1/104345

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MHD variable viscosity mixed convection of nanofluid in a microchannel with permeable walls
(CSIR-NIScPR, 2020) Kefene, Mesfin Zewde; Makinde, Oluwole Daniel; Enyadene, Lemi Guta
In this study, we examine the combined effects of buoyancy forces, pressure gradient, thermophoresis, Brownian motion, variable viscosity of nanofluid flow in a microchannel with suction and injection in the presence of uniform magnetic field imposed in cross-wise direction. It is assumed that the dynamic viscosity of the nanofluid is related with temperature exponentially and that the vertical parallel-plates temperature is held asymmetrically. Applying similarity transformation, the governing system of partial differential equations (PDEs) are transformed into a set of non-dimensional nonlinear partial differential equations whose solutions are obtained numerically by semi-discretization centered finite difference method along with Runge-Kutta Fehlberg integration technique scheme. Qualitative description of graphical results depicting the effect of thermophysical parameters on the dimensionless velocity, temperature, nanoparticles concentration, skin friction, Nusselt number and Sherwood number are presented.
Heat and mass transfer analysis of MHD peristaltic flow through a complaint porous channel with variable thermal conductivity
(IOP Science, 2020-02-18) Vaidya, H.; Rajashekhar, C.; Manjunatha, G.; Prasad, K. V.; Makinde, O. D.; Vajravelu, K.
The MHD peristaltic motion of Bingham fluid through a uniform channel is examined under the influence of long wavelength and small Reynolds number. The impact of variable thermal conductivity, convective heat transfer, porous boundaries, and wall properties are considered. The semi-analytical technique is utilized to solve the governing nonlinear temperature equation. The effects of different parameters on the physiological quantities of interest are captured with the assistance of MATLAB programming. The assessment reveals that an ascent in a magnetic parameter reduces the velocity field. Further, an increment in the estimation of variable thermal conductivity upgrades the temperature profiles. Besides, the trapped bolus is a function of a porous parameter, and an increase in porous parameter will have the proportional increment in the other parameter.
Impact of second order slip and non-uniform suction on non-linear stagnation point flow of alumina-water nanofluid over electromagnetic sheet
(International Information and Engineering Technology Association, 2019) Nayak, Manoj Kumar; Zeeshan, Ahmad; Pervaiz, Zeshan; Makinde, Oluwole Daniel
The purpose of the present article is to study the influence of second order slip and variable suction on non-linear stagnation point flow of Alumina-water nanofluid past an electromagnetic sheet embedded in a porous medium. A simulation model was established through hybrid Homotopy Analysis Method (HAM) and Genetic Algorithm Method (GAM). Through this it was found that favorable pressure gradient and modified Hartmann number yield accelerated fluid motion while porous matrix and first order slip result in decelerated flow over stationary/moving electromagnetic sheet. The finding of this research may serve as greater cooling agent due to more heat transfer rate from the electromagnetic sheet subject to favorable pressure gradient.
Parameter estimation and sensitivity analysis of Dysentery diarrhea epidemic model
(Hindawi, 2019) Berhe, Hailay Weldegiorgis; Makinde, Oluwole Daniel; Theuri, David Mwangi
In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease- free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for 𝑅₀ > 1. The system is formulated asa standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is 𝑅₀ = 1.1208. This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea (𝛽). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.
Impact of thermophoretic transport of Al₂O₃ nanoparticles on viscoelastic flow of oil-based nanofluid over a porous exponentially stretching surface with activation energy
(Institute of Fundamental Technological Research, 2019) Etwire, Christian John; Seini, Ibrahim Yakubu; Rabiu, Musah; Makinde, Oluwole Daniel
The influence of thermophoretic transport of Al₂O₃ nanoparticles on heat and mass trans- fer in viscoelastic flow of oil-based nanofluid past porous exponentially stretching surface with activation energy has been examined. Similarity technique was employed to transform the gov- erning partial differential equations into a coupled fourth-order ordinary differential equations which were reduced to a system of first-order ordinary differential equations and then solved numerically using the fourth-order Runge-Kutta algorithm with a shooting method. The re- sults for various controlling parameters were tabulated and graphically illustrated. It was found that the thermophoretic transport of Al₂O₃ nanoparticles did not affect the rate of flow and heat transfer at the surface but it affected the rate of mass transfer of the nanofluid which decayed the solutal boundary layer thickness. This study also revealed that activation energy retards the rate of mass transfer which causes a thickening of the solutal boundary layer.

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