In this paper, we constructed a control operator, G, which enables an Extended Conjugate Gradient Method (ECGM) to be employed in solving for the optimal control and trajectories of continuous time linear regulator problems. Similar operators constructed in the past by various authors have limited application. This call for the construction of the control operator that is aimed at taking care of any of the Mayer’s, Lagrange’s and Bolza’s cost form of linear regulator problems. The authors of this paper desire that, with the construction of the operator, one will circumvent the difficulties undergone using the classical methods and its application will further improve the result of the Extended Conjugate Gradient Method in solving this class of optimal control problem. The constructed Linear Control Operator is applied in ECGM algorithm to solve Continuous-Time Linear Regulator Problems with the convergence profile showing the efficiency of the operator.

The numerical studies are performed to examine the mass transfer flow through porous medium with an inclined plate. The governing partial differential equations are transformed to a system of dimensionless coupled partial differential equation. Finite difference technique is used as a tool for the numerical approach. The corresponding momentum, concentration and continuity equation are derived by employing the usual transformation, and finite difference method has been used to solve the above equations. The effects on the velocity and concentration distribution of various parameters entering into the problem separately are discussed with the help of graphs and tables.

Well Stimulation and machinery extraction are two main methods which the engineer of oil production and related industry used to increase production .The purpose is to enhance the oil field final recovery ratio though speeds up the production rate of the petroleum fluid, especially for old oil field development. A set of methods which be suitable for the high water content maturing field about predicting output of well stimulation used in Xiaermen oilfield and providing the foundation of the oil field natural decline regular pattern. Then, a decline-analysis model is derived based on reservoir characteristic parameters and used to analyze natural decline rates for the Xiaermen oilfield developed by waterflooding. Formation factor and remaining oil saturation are included in this model, which reveals non-linear relationships between natural decline rates and the production time. We applied the model to the oil-production data from different blocks in the Xiaermen oilfield and found non-linear relationships between natural decline rates and production time as foreseen by the model, especially at the high water cut period. The results showed that the analytical model could match the natural decline rate data satisfactorily. It was also found there are non-linear relationships between oil incrementals for water flooding step stimulation and step time which different laws with permeability, net pay, and remaining oil saturation and structure place of reservoir in limit period. Decline analysis can be used to predict different oil wells production nature decline rule. Furthermore, we made computer programming in Matlab-m language to calculate the natural decline rate with any time, which made it much easier and practical to predict the future decline rate. Finally, the analytical model was compared with conventional models.

We study existence of solution in the presence of upper and lower solutions of some second-order nonlinear coupled ordinary differential system (ODS for short) depending on first order derivatives with nonlinear coupled boundary conditions (CBCs for short). Our method for nonlinear coupled system with nonlinear CBCs is new and it unifies the treatment of many different second order problems. Nagumo condition is used to define bound for the derivative of the solution. Coupled lower and upper solutions, Arzela-Ascoli theorem and Schauder's fixed point theorem play an important role in establishing the arguments.

This paper investigates the effect of thermal radiation on magneto hydrodynamic (MHD) flow over a vertical plate with convective boundary conditions. The governing partial differential equations were transformed into coupled nonlinear differential equations which were solved numerically using the fourth order Runge-Kutta algorithm with a shooting method. Numerical results for the skin friction coefficient, the rate of heat transfer represented by the local Nusselt number and the plate surface temperature were presented whilst the velocity and temperature profiles illustrated graphically and analyzed. The effects of the Biot number, Grashof number, magnetic field parameter, Eckert number, Prandtl number and radiation parameter on the flow field were discussed.

This study is conducted to investigate the thermal stability of a reactive Hydromagnetic Poiseuille fluid flow through a channel. It is assumed that the reaction is exothermic under different chemical kinetics: Sensitized, Arrhenius and Bimolecular neglecting the concentration of the material. The analytical solutions of the nonlinear dimensionless equations governing the fluid flow are obtained using Adomian Decomposition Method (ADM) together with Pade Approximation technique to determine the thermal stability of the fluid flow and important properties of temperature fields including bi-furcations and thermal criticality conditions are discussed.

In this paper we consider the combined effects of viscous dissipation and heat generation on MHD natural convection flow along a vertical wavy surface are studied. The governing Navier-Stokes equations with associated boundary conditions are transformed into non-dimensional boundary layer equations using appropriate variables. Implicit finite difference method based on Keller-box scheme is used to solve these governing equations. The numerical results in terms of the skin friction coefficient, the rate of heat transfer in terms of local Nusselt number, the streamlines as well as the isotherms are discussed and shown graphically for different values of viscous dissipation parameter N, heat generation parameter Q and magnetic parameter M.