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A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic for Newtonian fluid whereas it is flatter for a shear-thinning fluid and sharper for a shear-thickening fluid. For a Bingham fluid, the velocity reaches a constant value known as the plug velocity in the central plug flow region, and it decreases gradually to zero at the pipe wall. [ABSTRACT FROM AUTHOR]

We consider mathematical modeling of blood glucose-insulin regulatory system with the additional effect of the secreted insulin by the pancreatic beta cells and in the presence of an external energy input to such system. Such modeling system is investigated to determine the time-dependent nonlinear dynamics that take place by the quantities, which represent the glucose and insulin concentrations in the blood, insulin action as well as in the absence or presence of secreted insulin due to the pancreatic beta cells. Using both analytical and numerical procedures, we determine such quantities versus time for both diabetes patients and normal human and for different values of the parameters. We find that the nonlinear effect of the dynamics of the investigated regulatory system increases the values of the insulin action and the glucose and insulin concentrations. In the absence of the beta cells effects, which can correspond to the case of severe type 1 diabetes, the plasma glucose is higher and the insulin action and the insulin concentration are less active than the corresponding ones for the case in the presence of beta cells, which is relevant for type 2 diabetes or moderate type 1 diabetes patients. For the present system, smaller values of the parameters of the model, which represent kinetics of the glucose and insulin action, insulin sensitivity, insulin secretion enhancement and the plasma insulin decay rate, can lead to notably lower values of the glucose concentration. In the presence of the secreted insulin by the pancreatic beta cells the insulin action and the insulin concentration are more effective to reduce the blood glucose, which can help to improve the diabetes patient's health. [ABSTRACT FROM AUTHOR]

Here we investigate the effect of the vertical rate of change in thermal diffusivity due to a hydrothermal convective flow in a horizontal porous medium. The continuity equation, the heat equation and the momentum-Darcy equation constitute the governing system for the flow in a porous medium. Assuming a vertically varying basic state, we derive the linear system and from this linear system, we compute the critical Rayleigh and wave numbers. Using fourth-order Runge-Kutta and shooting methods, we obtain the marginal stability curves and linear solutions to analyze the solution pattern for different diffusivity parameters. [ABSTRACT FROM AUTHOR]

Here we investigate the use of cubic B-spline functions in solving boundary value problems. First, we derive the linear, quadratic, and cubic B-spline functions. Then we use the cubic B-spline functions to solve second order linear boundary value problems. We consider constant coefficient and variable coefficient cases with non-homogeneous boundary conditions for ordinary differential equations. We also use this numerical method for the space variable to obtain solutions for second order linear partial differential equations. Numerical results for various cases are presented and compared with exact solutions. [ABSTRACT FROM AUTHOR]

We investigate the effect of hydro-thermal convection in an aquifer system. It is assumed that the aquifer is bounded below and above by impermeable boundaries and it is heated from below. The solution of the governing system is expressed in terms of the basic steady state solution and perturbed solution. We obtain the critical Rayleigh number and critical wavenumber using Runge-Kutta method in combination of shooting method and present the marginal stability curve. The amplitude equation is derived by introducing the adjoint system. After amplitude is obtained, we compute the linear solutions for super-critical and sub-critical cases. Numerical results for various spatial and time values are presented in graphical forms. [ABSTRACT FROM AUTHOR]