International Journal of Engineering Research in Africa Vol. 55

Abstract: In this paper, based on Parker-Sochacki method for solving a system of differential equations,a multistage technique is developed for solving the nonlinear boundary layer equations of powerlawfluid on infinite domain. The problem domain is split into subintervals over which the boundaryvalue problem is replaced with a sequence of subproblems. In a shooting-like approach, the boundarycondition at infinity is converted to an equivalent initial condition. By recasting the problem as apolynomial system of first-order autonomous equations, the sub-problems are solved with Parker-Sochacki method with very high accuracy. The interval of convergence of the solution is deriveda-priorly in terms of the parameters of the polynomial system, which guides optimal choice of thediscretization parameter. The technique yielded a convergent piecewise continuous solution over theproblem domain. The results obtained, demonstrated graphically and in tables, compared well withexisting ones in the literature.

Abstract: This article investigates the flow of Casson nanofluid induced by a stretching Riga plate in the presence of a porous medium. The implication of the Riga plate is to generate electromagnetohydrodynamic force which influences the fluid speed, and as well applicable in delaying boundary layer separation. The complexity of the equations governing the problem is reduced using similarity transformation. The resulting coupled nonlinear ordinary differential equations are solved by employing Chebyshev collocation scheme (CCS) and validated with Galerkin weighted residual method (GWRM). The influence of parameters, such as modified Hartmann number and melting parameter, on the nanofluid flow, heat, and mass transfer is considered. Some of the major findings include that modified Hartmann number tends to increase nanofluid flow. Also, increasing the value of melting parameter is in favor of both velocity and nanoparticle volume fraction profiles but diminishes temperature profile. The application of this work can be found in polymer synthesis, metallic processing, and electromagnetic crucible systems.

Abstract: This article aims to computationally study entropy generation in a magnetohydrodynamic (MHD) third grade fluid flow in a horizontal channel with impermeable walls. The fluids viscosity and thermal conductivity are assumed to be dependent on temperature. The flow is driven by an applied uniform axial pressure gradient between infinite parallel plates and is considered to be incompressible, steady and fully developed. Adomian decomposition method (ADM) is used to obtain series solutions of the nonlinear governing equations. Thermodynamic analysis is done by computing the entropy generation rate and the irreversibility ratio (Bejan number). The effects of the various pertinent embedded parameters on the velocity field, temperature field, entropy generation rate and Bejan number are analysed through vivid graphical manipulations. The analysis shows that an appropriate combination of thermophysical parameters efficiently achieves entropy generation minimization in the thermomechanical system. The analysis shows that entropy generation minimization is achieved by increasing the magnetic field and the third grade material parameters, and therefore designs and processes incorporating MHD third grade fluid flow systems are far more likely to give optimum and efficient performance.

Abstract: IIn this paper, two finite difference methods are used to solve the one-dimensional second order wave equation with constant coefficients subject to specified initial and boundary conditions. Two numerical experiments are considered. The two methods are Central in Time and Central in Space scheme with second order accuracy in both time and space, abbreviated as CTCS (2,2) and Central in Time and Central in Space scheme with second order accuracy in time and fourth order accuracy in space, abbreviated as CTCS (2,4). Properties such as consistency and stability are studied. We also perform spectral analysis of dispersive and dissipative properties of the two methods. Two numerical experiments are considered, and the numerical results are displayed.

Abstract: The paper is devoted to the problem of obtaining weighting functions for the Greeks of an option price written on a stock whose dynamics are of pure jump type. The problem is motivated by the work of Fourni\'e et al. [8, 9], who considered the price sensitivities of a frictionless market and proved that Greeks can be computed as the expectation of the product of the discounted payoff $\Phi$ and a suitable weighted function, i.e.Greek = E[Φ(X_T)weight]. Since the weighting functions are random variables that need to be explicitly computed on each specific case, we establish necessary and sufficient conditions to be satisfied. The method used relied on the Malliavin calculus for Levy processes.

Abstract: Inverse problem of the Lorenz system parametric identification is considered in the case of incomplete information about solutions of the system. In the present paper, it is assumed that only two solutions of the system from three are known in different combinations. The problem of the parameter identification of the system is solved by means of elimination of unknown functions from the original system. The obtained system of equations has the same order as the original one, but contains the unknown original parameters in new combinations. Sometimes, the number of new unknown parameters is higher than number of the original unknowns. In this case, the method of the constrained least squares minimization is used in the special formulation, developed by the authors. This novel formulation exploits linearity of the system with respect to the new unknown parameters, by means of which the number of nonlinear equations becomes equal to the number of the constraints between the new parameters. Two methods of the constraint minimization are considered: the classical method of Lagrange’s multipliers and a novel method of the auxiliary parameters. Numerical simulations demonstrate effectiveness of the algorithms.

Abstract: In the present paper, which is the continuation of the previous one, the problem of parameter identification of the Lorenz system is solved in assumption that only one of three functions is known at discrete time instants on finite time initial time interval. Two other functions are assumed to be unknown. The regular methods of guess values determination of the unknown parameters are developed. They are based on the Lagrange multiplier and auxiliary parameters approaches. A novel method of initial value problem solution is proposed in which the abovementioned guess values are used for more accurate estimation of the system parameters. It is demonstrated that the proposed IVP method simultaneously solves three different tasks: the problem of function interpolation from its discrete values on the initial time interval; the problem of unknown functions reconstruction on the same time interval, and the problem of extrapolation of all functions on limited time interval. It is also shown that the proposed method reconstructs the Lorenz attractor from limited data volume and data including random components.

Abstract: Smart Grid (SG) systems involves large Information Communication Technology (ICT) infrastructure integrated with the power grid system to allow bidirectional flows of information, for effectiveness and to provide economic and sustainable processes that facilitates constant electricity supplies. As a result of open IoT used in smart grid infrastructure, electricity generation and distribution information are getting more vulnerable to online threats. The need to find effective and mitigating measures to the vulnerability and threats in the systems. As broadband network moves from 4G to 5G networks with its attendant advantages, smart grid interoperability will require a well-structured security strategy to avert cyber-attacks and ensure grid security. Cyber-attack issues are critical factors that need to be understood and mitigating techniques developed to ensure the smooth running of smart grid systems. Research has shown that severe vulnerabilities in the implementation of the smart meter pose a threat to grid infrastructure, as such, it is only when these issues are resolved that we can have a sustainable and realistic smart grid technology. This study addressed these concerns by developing a conceptual model for the mitigation of security vulnerabilities in IoT-based smart grid electric energy distribution systems.

Abstract: This work examine the potential of ZrB₂ in the presence of Ni-P-Zn sulphate rich bath coating on mild steel under change in time from 10-25 min. The coating pH of 5, current density of 1 A/cm², and stirring rate of 250 rpm was considered in the fabrication process. The microstructure evolution and properties of the deposited coating was analysed using a scanning electron microscope enhanced with energy dispersive spectroscopy (SEM/EDS). All deposited composite coating was investigated in 0.5 M H₂SO₄ and 3.5% NaCl with the help of linear polarization and open circuit potential. From the result, a solid crystal formation containing zirconium boride was seen from the SEM study. At 25 min a remarkable dispersed and even thin film was noticeable at the interface. From all indication, coating produced with Ni-P-Zn-10ZrB₂ at 25 min provides a passive response against corrosion damage. Keywords: Electrodeposition, interface, nanocrystalline, structure, coating

Abstract: The conventional method of producing titanium components introduces defects into the matrix of the materials, thus resulting in poor microstructure, tribological properties and performance of the materials in service. To overcome these challenges, a Ti-Ni-TiCN nanocomposite was developed using the novel spark plasma sintering (SPS) technique. The morphology and the phases present in the initial powders and the sintered specimen were investigated using the scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD) techniques. The dry sliding wear behaviour of the sintered samples was studied at ambient temperature by ball-on-disc tests, under an applied normal load of 25 N. The presence of unreacted TiCN, in-situ formed TiN and Ti₂Ni intermetallic phases were revealed by the SEM/EDS analysis and confirmed by the XRD results. The developed titanium matrix nanocomposite displayed a much lower coefficient of friction and wear resistance than the CP-Ti. The strong interface between the matrix and the reinforcements prevents the reinforcements from pulling out of the matrix. Ti-Ni-TiCN nanocomposite showed the predominance of abrasive wear while mixed wear mode was observed, in the CP-Ti. The developed material has the capacity to replace CP-Ti and perform admirably in a tribo-system.