Analytical solution of unsteady three-dimensional MHD boundary layer flow and heat transfer due to impulsively stretched plane surface

The unsteady magnetohydrodynamic viscous flow and heat transfer of Newtonian fluids induced by an impulsively stretched plane surface in two lateral directions are studied by using an analytic technique, namely, the homotopy method. The analytic series solution presented here is highly accurate and uniformly valid for all time in the entire region. The effects of the stretching ratio and the magnetic field on the surface shear stresses and heat transfer are studied. The surface shear stresses in x- and y-directions and the surface heat transfer are enchanced by increasing stretching ratio for a fixed value of the magnetic parameter. For a fixed stretching ratio, the surface shear stresses increase with the magnetic parameter, but the heat transfer decreases. The Nusselt number takes longer time to reach the steady state than the skin friction coefficients. There is a smooth transition from the initial unsteady state to the steady state.

Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier-Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

Relaxation system based sub-grid scale modelling for large eddy simulation of Burgers' equation

An implicit sub-grid scale model for large eddy simulation is presented by utilising the concept of a relaxation system for one dimensional Burgers' equation in a novel way. The Burgers' equation is solved for three different unsteady flow situations by varying the ratio of relaxation parameter (epsilon) to time step. The coarse mesh results obtained with a relaxation scheme are compared with the filtered DNS solution of the same problem on a fine mesh using a fourth-order CWENO discretisation in space and third-order TVD Runge-Kutta discretisation in time. The numerical solutions obtained through the relaxation system have the same order of accuracy in space and time and they closely match with the filtered DNS solutions.

Unsteady flow and heat transfer between rotating coaxial disks

A study is made on the flow and heat transfer of a viscous fluid confined between two parallel disks. The disks are allowed to rotate with different time dependent angular velocities, and the upper disk is made to approach the lower one with a constant speed. Numerical solutions of the governing parabolic partial differential equations are obtained through a fourth-order accurate compact finite difference scheme. The normal forces and torques that the fluid exerts on the rotating surfaces are obtained at different nondimensional times for different values of the rate of squeezing and disk angular velocities. The temperature distribution and heat transfer are also investigated in the present analysis.

Unsteady Compressible Boundary-Layer Flow On The Stagnation Line Of An Infinite Swept Cylinder

Numerical solutions of flow and heat transfer process on the unsteady flow of a compressible viscous fluid with variable gas properties in the vicinity of the stagnation line of an infinite swept cylinder are presented. Results are given for the case where the unsteady temperature field is produced by (i) a sudden change in the wall temperature (enthalpy) as the impulsive motion is started and (ii) a sudden change in the free-stream velocity. Solutions for the simultaneous development of the thermal and momentum boundary layers are obtained by using quasilinearization technique with an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady-state distribution. Results are presented for the skin friction and heat transfer coefficients as well as for the velocity and enthalpy profiles. The effects of wail enthalpy parameter, sweep parameter, fluid properties and transpiration cooling on the heat transfer and skin friction are considered.

Unsteady-Flow Of A Viscous-Fluid Between 2 Parallel Disks With A Time-Varying Gap Width And A Magnetic-Field

The unsteady incompressible viscous fluid flow between two parallel infinite disks which are located at a distance h(t*) at time t* has been studied. The upper disk moves towards the lower disk with velocity h'(t*). The lower disk is porous and rotates with angular velocity Omega(t*). A magnetic field B(t*) is applied perpendicular to the two disks. It has been found that the governing Navier-Stokes equations reduce to a set of ordinary differential equations if h(t*), a(t*) and B(t*) vary with time t* in a particular manner, i.e. h(t*) = H(1 - alpha t*)(1/2), Omega(t*) = Omega(0)(1 - alpha t*)(-1), B(t*) = B-0(1 - alpha t*)(-1/2). These ordinary differential equations have been solved numerically using a shooting method. For small Reynolds numbers, analytical solutions have been obtained using a regular perturbation technique. The effects of squeeze Reynolds numbers, Hartmann number and rotation of the disk on the flow pattern, normal force or load and torque have been studied in detail

Unsteady flow over a stretching surface with a magnetic field in a rotating fluid

The effect of the magnetic field on the unsteady flow over a stretching surface in a rotating fluid has been studied. The unsteadiness in the flow field is due to the time-dependent variation of the velocity of the stretching surface and the angular velocity of the rotating fluid. The Navier-Stokes equations and the energy equation governing the flow and the heat transfer admit a self-similar solution if the velocity of the stretching surface and the angular velocity of the rotating fluid vary inversely as a linear function of time. The resulting system of ordinary differential equations is solved numerically using a shooting method. The rotation parameter causes flow reversal in the component of the velocity parallel to the strerching surface and the magnetic field tends to prevent or delay the flow reversal. The surface shear stresses dong the stretching surface and in the rotating direction increase with the rotation parameter, but the surface heat transfer decreases. On the other hand, the magnetic field increases the surface shear stress along the stretching surface, but reduces the surface shear stress in the rotating direction and the surface heat transfer. The effect of the unsteady parameter is more pronounced on the velocity profiles in the rotating direction and temperature profiles.

Unsteady free convection flow in the stagnation-point region of a rotating sphere

The unsteady free convection boundary-layer flow in the forward stagnation-point region of a sphere, which is rotating with time-dependent angular velocity in an ambient fluid, has been studied. Both constant wall temperature and constant hear flux conditions have been considered. The non-linear coupled parabolic partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The skin friction and the heat transfer are enhanced by the buoyancy force. The effect of the buoyancy force is found to be more pronounced for smaller Prandtl numbers than for larger Prandtl numbers. For a given buoyancy force, the heat transfer increases with an increase in Prandtl number, but the skin friction decreases.

Unsteady free convection flow in the stagnation-point region of a three-dimensional body

The unsteady free convection flow in the stagnation-point region of a heated three-dimensional body placed in an ambient fluid is studied under boundary layer approximations. We have considered the case where there is an initial steady state that is perturbed by a step-change in the wall temperature. The non-linear coupled partial differential equations governing the free convection flow are solved numerically using a finite difference scheme. The presented results show the temporal development of the momentum and thermal boundary layer characteristics.

Influence of friction during forming processes-a study using a numerical simulation technique

Friction has an important influence in metal forming operations, as it contributes to the success or otherwise of the process. In the present investigation, the effect of friction on metal forming was studied by simulating compression tests on cylindrical Al-Mg alloy using the finite element method (FEM) technique. Three kinds of compression tests were considered wherein a constant coefficient of friction was employed at the upper die-work-piece interface. However, the coefficient of friction between the lower die-work-piece interfaces was varied in the tests. The simulation results showed that a difference in metal flow occurs near the interfaces owing to the differences in the coefficient of friction. It was concluded that the variations in the coefficient of friction between the dies and the work-piece directly affect the stress distribution and shape of the work-piece, having implications on the microstructure of the material being processed.

Reliable estimation via simulation

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Dynamic analysis and simulation of a VSC based Back-to-Back HVDC link

This paper presents the modeling and analysis of a voltage source converter (VSC) based back-to-back (BTB) HVDC link. The case study considers the response to changes in the active and reactive power and disturbance caused by single line to ground (SLG) fault. The controllers at each terminal are designed to inject a variable (magnitude and phase angle) sinusoidal, balanced set of voltages to regulate/control the active and reactive power. It is also possible to regulate the converter bus (AC) voltage by controlling the injected reactive power. The analysis is carried out using both d-q model (neglecting the harmonics in the output voltages of VSC) and three phase detailed model of VSC. While the eigenvalue analysis and controller design is based on the d-q model, the transient simulation considers both models.

Real-time simulation of electrical machines on FPGA platform

This paper presents real-time simulation models of electrical machines on FPGA platform. Implementation of the real-time numerical integration methods with digital logic elements is discussed. Several numerical integrations are presented. A real-time simulation of DC machine is carried out on this FPGA platform and important transient results are presented. These results are compared to simulation results obtained through a commercial off-line simulation software.

Unsteady Natural Convection Flow in a Square Cavity Filled with a Porous Medium Due to Impulsive Change in Wall Temperature

Unsteady natural convection flow in a two- dimensional square cavity filled with a porous material has been studied. The flow is initially steady where the left- hand vertical wall has temperature T-h and the right- hand vertical wall is maintained at temperature T-c ( T-h > T-c) and the horizontal walls are insulated. At time t > 0, the left- hand vertical wall temperature is suddenly raised to (T-h) over bar ((T-h) over bar > T-h) which introduces unsteadiness in the flow field. The partial differential equations governing the unsteady natural convection flow have been solved numerically using a finite control volume method. The computation has been carried out until the final steady state is reached. It is found that the average Nusselt number attains a minimum during the transient period and that the time required to reach the final steady state is longer for low Rayleigh number and shorter for high Rayleigh number.

Unsteady Free-Convection Flow on a Rotating flat-Plate Under Nonuniform Gravity

The free convection problem with nonuniform gravity finds applications in several fields. For example, centrifugal gravity fieldsarisein many rotating machinery applications. A gravity field is also created artificially in an orbital space station by rotation. The effect of nonuniform gravity due to the rotation of isothermal or nonisothermal plates has been studied by several authors [l-5] using various mathematical techniques.