Browsing by Author "Abubakar, Jos U."
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Item Casson rheological flow model in an inclined stenosed artery with non‑Darcian porous medium and quadratic thermal convection(Journal of the Egyptian Mathematical Society, 2022) Abubakar, Jos U.; Omolesho, Q.A.; Bello, K.A.; Basambo, A.M.The current study investigates the combined response of the Darcy–Brinkman–Forchheimer and nonlinear thermal convection influence among other fluid parameters on Casson rheology (blood) flow through an inclined tapered stenosed artery with magnetic effect. Considering the remarkable importance of mathematical models to the physical behavior of fluid flow in human systems for scientific, biological, and industrial use, the present model predicts the motion and heat transfer of blood flow through tapered stenosed arteries under some underline conditions. The momentum and energy equations for the model were obtained and solved using the collocation method with the Legendre polynomial basis function. The expressions obtained for the velocity and temperature were graphed to show the effects of the Darcy–Brinkman–Forchheimer term, Casson parameters, and nonlinear thermal convection term among others. The results identified that a higher Darcy–Brinkman number slows down the blood temperature, while continuous injection of the Casson number decreases both velocity and temperature distribution.Item Confined Dirac Electron in Coulomb and Uniform Magnatic Fields: The Hill Determinant Approach(Transactions of the Nigerian Association of Mathematical Physics, 2019-01) Ibrahim, T.T.; Abubakar, Jos U.; Koffa, D.J.; Salau, M.A.; Adekanbi, I.O.The 2+1 dimensional Dirac equation is solved for electron in an oscillator potential together with external fields. Approximate eigenenergies are determined from a second order recurrence relation using the Hill determinant technique. In addition, the technique is shown to generate wave functions for the quasi-exactly solvable problem. Finite analytic closed form for the recurrence relation derived using the recursive-sum plus discrete dimensional-convolution techniques is shown to be in agreement with the analytic result from the finite Hill determinant.Item Effects of Navier slip on a steady flow of an incompressible viscous fluid confined within spirally enhanced channel(Journal of the Egyptian Mathematical Society, 2020) Gbadeyan, J.A.; Abubakar, Jos U.; Oyekunle, T.L.Investigation of the effect of slip on natural convective flow and heat transfer of a viscous incompressible fluid confined within a channel made up of a long vertical wavy wall and a parallel flat wall is carried out in this article. It is assumed that at the flat wall, there exists the slip condition. The coupled non-linear differential equations governing the fluid flow subjected to the relevant boundary conditions were perturbed and the resulting zero- and first-order set of equations were solved, using Adomian decomposition technique with the MAPLE 18 software. A comparison between the present study and an earlier one not involving a slip parameter and for which a different solution technique was used is carried out and the results are found consistent. The effects of various parameters involved in the problem viz Grashof number, slip parameter, heat source parameter, and wavelength parameter on the zero- and first-order temperature profile, velocity profile, skin friction, and Nusselt number at the walls are presented graphically and discussed quantitatively.Item Effects of radiative heat and magnetic field on blood flow in an inclined tapered stenosed porous artery(JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2020) Abubakar, Jos U.; Adeoye, A.D.A porous tapered inclined stenosed artery under the influence of magnetic field with radiation was considered. The momentum and energy equations with thin radiation governing the blood flow in the inclined artery were obtained taking the flow to be Newtonian. These equations were simplified under assumptions of mild stenosis, non-dimensionalized and solved using Differential Transform Method (DTM). The DTM were coded on Mathematica software to obtain expressions for velocity, temperature and the volumetric flow rate of the blood. The results presented graphically show that the velocity of the blood flow and the blood temperature decreases as the radiation parameter (N) increases.Item A Graph-Theoretic Method for the Basic Reproduction Number in Age-Structured HBV Model(Ilorin Journal of Science, 2018) Dotia, A.K.; Abubakar, Jos U.In this paper, we present an Age-Structured hepatitis B model. This epidemic model investigates different classes of infectious diseases that can be transmitted through an effective contact with infective individuals, who are contagious. The Graph-Theoretic Method for the Basic Reproduction Number was obtained. In addition, the numerical simulation is used to verify the model predictions. The result suggest that the endemic nature of the model is approaching equilibrium with increase immunization program and other control measures put in place.Item A Graph-Theoretic Method on HBY Epidemic Model(Bulletin of the Science Association of Nigeria, 2019) Dotia, A.K.; Zubair, O.R.; Moshood, A.R.; Ibrahim, M.O.; Abubakar, Jos U.In this paper, we present an epidemic model with non-monotonic incidence function. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out to determine the positivity of solution and the Graph-Theoretic method is used in calculating the Basic reproduction number. In addition, we obtained the numerical simulation to verify the model predictions. The results suggested that the model is approaching equilibrium with increase immunization program.Item Influence of MHD and Heat Transfer on Blood Flow in a Stenosed Porous Artery: DTM Approach(Journal of Science and Information Technology, 2021-06) Abubakar, Jos U.; Okunola, D.T.; Olotu, O.T.; Ayinde, M.A.This paper investigates the motion of blood in a stenosed porous artery subjected to heat transfer and magnetohydrodynamic impact. Atherosclerosis having attributed as one of the arterial circulation diseases risk factor, caused by the build-up of plaques resulting to stenosis and hardening in the arteries, hence the need for investigation of stenosed artery become imperative. The governing equations were modeled with assumption that the stenosis is in form of cosine-shaped. Differential Transformation Method (DTM) was implemented on the obtained momentum and energy equations, from which expressions for axial velocity and temperature were deduced. The volumetric flow rate and wall sheer stress expressions were also obtained. These expressions were used to simulate the effects of heat transfer parameter, magnetic field among other flow parameters on the wall sheer stress, volumetric flow rate, temperature and velocity fields. It was observed that an increase in the empty spaces or voids present in the artery (porosity) and the magnetic number appreciates both blood temperature and its velocity significantly. It is believed that the implementation of the present investigation will assist in preparing and forecasting for a corrective procedure.Item MHD free convective heat and mass transfer flow of dissipative Casson fluid with variable viscosity and thermal conductivity effects(Journal of Taibah University for Science, 2020-06-22) Idowu, A.S.; Akolade, M.T.; Abubakar, Jos U.; Falodun, B.O.In this paper, the Cattaneo–Christov heat flux relocation paradox on Casson fluid with MHD and dissipative effects was considered. The buoyancy and heat generation effects were believed to be responsible for the natural convection, while variable properties were perceived as temperature-dependent linear function. Under the given assumptions, the governing system of equations was formulated and transformed. Hence, the Chebyshev collocation spectral approach was therefore employed to achieve an approximate solution. However, the behaviour of temperature-dependent variability establishes the relationship between the boundary layer flow of plastic dynamic viscosity and the Casson fluid. Furthermore, it was observed that a corresponding increase in the stretching index (n) increases the skin friction and decreases the energy and mass gradient accordingly. The relocation phenomenon contributes to a decrease in the thermal process, while the temperature gradient attained maximum within (0.4 − 0.6) variation of the Casson parameter.Item Nonlinear convection flow of dissipative Casson nanofluid through an inclined annular microchannel with a porous medium(Heat Transfer, 2020) Idowu, A.S.; Akolade, M.T.; Oyekunle, T.L.; Abubakar, Jos U.The nonlinear convection study on the flow of a dissipative Casson nanofluid through a porous medium of an inclined micro‐annular channel is presented. The cylindrical surfaces were conditioned to temperature increase and velocity slip effects. A uniform magnetic field strength was applied perpendicular to the cylinder surface. The heat source and Darcy number influence are explored in the examination of the blood rheological model (Casson) through the annular cylinder. Appropriate dimensionless variables are imposed on the dimensional equations encompassing Casson nanofluid rheology through an annular microchannel. The resulting systems of equations were solved and computed numerically via Chebyshev‐based collocation approach. Thus, the solutions of flow distributions, volumetric flow rate, and other flow characteristics were obtained. The result shows that both nonlinear convection parameters decrease the nanoparticle volume fraction, whereas they increase the energy and momentum distributions. Moreover, the volumetric flow rate is upsurged significantly by a wider porous medium, annular gap, a higher Casson parameter, and nonlinear convection influence.Item Numerical Integration of Seventh Order Boundary Value Problems by Standard Collocation Method via Four Orthogonal Polynomials(Nigerian Journal of Mathematics and Applications, 2017) Bello, K.A.; Taiwo, O.A.; Abdulkareem, A.; Abubakar, Jos U.Based on standard collocation technique, four (4) different orthogonal polynomials were used as basis functions in the numerical treatment of seventh (7th) order boundary value problems in Ordinary Differential Equations. The performance of each of these polynomials as basis function in the trial solution was then compared. The results obtained from three examples showed that Chebyshev polynomial is the best in term of performance, and closely followed by Hermites polynomial, which was followed by Legendre polynomial while the least in performance is Laguerre polynomial.Item Numerical Solution of Fourth order Integro-Differential Equations by Least Square Approximation Method using Chebyshev Polynomials as Basis Function(JOURNAL OF SCIENCE TECHNOLOGY AND EDUCATION, 2023-03) Abubakar, Jos U.; Bello, K.A.; Taiwo, O.A.; Odetunde, O.S.; Azeez, G.O.In this paper, Least square approximation method is used as numerical solution of fourth order integro-differential equations using Chebyshev polynomials of the first kind as basis function. The method assumed an approximate solution using Chebyshev polynomial functions which are then substituted into the problem considered. Then the like terms of the unknown coefficients are collected and simplified. The resulting equation is minimized using the least square approximation, thus resulted into linear algebraic systems of equations which are then solved by Gaussian Elimination method, to obtain the unknown constants substituted back into the assumed approximate solution to get the required approximate solution. Numerical solutions are given to illustrate the accuracy of the methods discussed in the work. Also, absolute errors of the problem are presented in tabular forms.Item Numerical Studies for Solving Fractional Integro-Differential Equations by using Least Squares Method and Bernstein Polynomials(Fluid Mechanics: Open Access, 2016) Oyedepo, T.; Taiwo, O.A.; Abubakar, Jos U.; Ogunwobi, Z.O.In this paper, two numerical methods for solving fractional integro differential equations are proposed. The fractional derivative is considered in the Caputo sense. The proposed methods are least squares method aid of Bernstein polynomials function as the basis. The proposed method reduces this type of equation into systems to the solution of system of linear algebraic equations. To demonstrate the accuracy and applicability of the presented methods some test examples are provided. Numerical results show that this approach is easy to implement and accurate when applied to fractional integro-differential equations. We show that the method is effective and has high convergence rate.Item Optimal control approach on hepatitis B model with vaccinations(Journal of the Nigerian Association of Mathematical Physics, 2017-05) Dotia, A.K.; Ibrahim, M.O.; Abubakar, Jos U.We present a time-dependent HBV epidemic model with both prophylactic and therapeutic vaccination. This epidemic model is investigated for different classes of infectious diseases. Mathematical analyses are carried out, that determines the positivity of solution and an optimal control approach is applied in order to find the best way to fight the disease. An optimal control strategy in the form of vaccination, and to minimize or eradicate the mother to child transmission is used. The study concluded that both prophylactic and therapeutic vaccination are efficient ways to curb the epidemic.Item Radiative fluid flow over a vertical porous channel under optically thick approximation in the presence of MHD(Journal of the Nigerian Association of Mathematical Physics, 2014) Ibrahim, M.O.; Asogwa, K.K.; Uwanta, I.J.; Abubakar, Jos U.Numerous nonlinear equations that come up in real life situations defy analytical solutions; hence numerical methods are desirable to obtain the solutions of such equations. In this study, we use Newton scheme method from Taylor series to solve fourth order nonlinear problem. A mathematical software MATLAB was used to solve the system of equations to obtain the unknown constants. The velocity profiles and temperature profile are studied for different physical parameters like Magnetohydrodynamic M, porous term P, Radiation F and thermal Grashof number Ga. The results obtained after computation taking into cognizance the parameters present shows that the Magnetic and Porous parameters increase with increasing velocity, while the trend reverses with Radiation and thermal Grashof number under optically thick approximation.Item Reproduction Number of Vertical Transmission of Measles Model(A Journal of National Mathematical Centre, Abuja, 2014) Ibrahim, M.O.; Odetunde, O.; Ayoade, A.A.; Abubakar, Jos U.In this model, we study the reproduction number of measles epidemiology, the rate of vertical transmission of measles and antibodies, including the effect of maternal antibody on the spread of measles to the infant. We exempt the vaccinated class due to the finding of Viera Scheibner. We demonstrated that the disease will die out if the basic reproduction number for the disease free equilibrium R_{0}<1. This is the case of a disease free state, with no infection in the population. Otherwise, the disease may become endemic if the basic reproduction number is bigger than unity. The basic reproduction number at both the disease free state and the endemic state were obtained and the result shows stability in the effect of mother to child transmission of either disease or immunityItem Reproduction number of vertical transmission of measles model.(Journal of Mathematical Sciences, published by National Mathematical Centre, Abuja, 2015) Odetunde, Opeyemi; Ibrahim, Mohammed O.; Ayoade, A. A.; Abubakar, Jos U.In this model, we study the reproduction number of measles epidemiology, the rate of vertical transmission of measles and antibodies, including the effect of maternal antibody on the spread of measles to the infant. We exempt the vaccinated class due to the finding of Viera Scheibner [2]. We demonstrate that the disease will die out, if the basic reproductive number R0<1. This is the case of a disease-free state, with no infection in the population. Otherwise the disease may become endemic if the basic reproductive number R0 is bigger than unity. The basic reproduction number at both the disease Free State and the endemic state were obtained and the result shows stability in the effect of mother to child transmission of either disease or immunityItem Results of ω-order reversing partial contraction mapping generating a differential operator(Malaya Journal of Matematik, 2021) Akinyele, A.Y.; Abubakar, Jos U.; Bello, K.A.; Alhassan, I.K.; Aasa, M.A.In this paper, we presents some partial differential operators defined on suitably chosen function spaces such as H^{−1}(Ω), L^{p}(Ω), with p∈[1,+∞). Laplace operator on a domain Ω in R^{n} subject to the Dirichlet boundary condition was established by generating a C_0-semigroup, which is generated by an infinitesimal generator ω-order reversing partial contraction (ω-ORCP_n).Item Soret and Dufour effects on heat and mass transfer in chemically reacting MHD flow through a wavy channel(JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2018) Gbadeyan, J.A.; Oyekunle, T.L.; Fasogbon, P.F.; Abubakar, Jos U.The problem of coupled heat and mass transfer by free convection of a chemically reacting viscous incompressible and electrically conducting fluid confined in a vertical channel bounded by wavy wall and flat wall in the presence of diffusion-thermo (Dufour), thermal-diffusion (Soret) and internal heat source or sink is studied. The walls are maintained at constant but different temperatures and species concentrations. A uniform magnetic field β_0 is acting transversely to the walls which are assumed to be electrically non-conducting. The dimensionless governing equations are perturbed into mean part (zeroth-order) and perturbed part (first-order), using amplitude as a perturbation parameter. The first-order quantities are obtained by long wave approximation. The resulting set of coupled ordinary differential equations are solved numerically using the Adomian decomposition method. Some of the results indicating the influence of various parameters on the zeroth-order and first-order fluid flow, heat and mass transfer characteristics are presented graphically.Item Steady blood flow through vascular stenosis under the influence of magnetic field(Centrepoint Journal (Science Edition), 2017) Abubakar, Jos U.; Gbadeyan, J.A.; Ojo, J.B.The influence of magnetic field on a steady blood flow through vascular stenosed artery was investigated by assuming blood to be a Newtonian fluid. The Navier-Stokes equations governing the flow through the axial directions were solved using integral momentum method. The velocity profile graphs obtained show that as magnetic field increases on the stenosis area, the velocity decreases.Item THERMAL RADIATION AND CHEMICAL REACTION EFFECTS ON FREE CONVECTIVE HEAT AND MASS TRANSFER FLOW THROUGH AN IRREGULAR CHANNEL(FUW Trends in Science & Technology Journal, 2017-04) Gbadeyan, J.A.; Oyekunle, T.L.; Abubakar, Jos U.An analysis of the effects of thermal-radiation and chemical reaction on free convective heat and mass transfer flow through an irregular (wavy) vertical channel (made up of a finitely long wavy wall at one end and a parallel flat wall at the other) with constant volumetric heat absorption/generation is carried out. The Rosseland approximation is used to describe radiative heat transfer in the limit of optically thick fluids. The non-dimensional governing equations which comprises of continuity, momentum, energy and species equations were simplified using perturbation method and hence written in terms of zeroth and first order set of coupled differential equations. The solutions of these sets of coupled differential equations were obtained for velocity, temperature, concentration and pressure drop of the fluid, using Adomian decomposition method. The expressions for the fluid variables and those of some characteristics of heat and mass transfer namely Skin friction, Nusselt number and Sherwood number obtained from fluid variables are evaluated numerically and presented graphically for various parameters involved in the problem. By carrying out comparisons with the available data in the literature, our numerical results were validated and excellent agreements were obtained. It is noticed among others, that an increase in the radiation and chemical reaction parameters leads to a decrease in the fluid velocity across the entire width of the channel. The temperature decreases with an increase in the radiation parameter, while an increase in the temperature is observed with an increase in the chemical reaction parameter.