Abstract: This study presents the numerical simulation of
optimum pin-fin heat sink with air impinging cooling by using
Taguchi method. 9 L ( 4 3 ) orthogonal array is selected as a plan for
the four design-parameters with three levels. The governing
equations are discretized by using the
control-volume-based-finite-difference method with a power-law
scheme on the non-uniform staggered grid. We solved the coupling of
the velocity and the pressure terms of momentum equations using
SIMPLEC algorithm. We employ the k −ε two-equations
turbulence model to describe the turbulent behavior. The parameters
studied include fin height H (35mm-45mm), inter-fin spacing a , b ,
and c (2 mm-6.4 mm), and Reynolds number ( Re = 10000- 25000).
The objective of this study is to examine the effects of the fin
spacings and fin height on the thermal resistance and to find the
optimum group by using the Taguchi method. We found that the fin
spacings from the center to the edge of the heat sink gradually
extended, and the longer the fin’s height the better the results. The
optimum group is 3 1 2 3 H a b c . In addition, the effects of parameters are
ranked by importance as a , H , c , and b .
Abstract: This paper describes a one-dimensional numerical model for natural gas production from the dissociation of methane hydrate in hydrate-capped gas reservoir under depressurization and thermal stimulation. Some of the hydrate reservoirs discovered are overlying a free-gas layer, known as hydrate-capped gas reservoirs. These reservoirs are thought to be easiest and probably the first type of hydrate reservoirs to be produced. The mathematical equations that can be described this type of reservoir include mass balance, heat balance and kinetics of hydrate decomposition. These non-linear partial differential equations are solved using finite-difference fully implicit scheme. In the model, the effect of convection and conduction heat transfer, variation change of formation porosity, the effect of using different equations of state such as PR and ER and steam or hot water injection are considered. In addition distributions of pressure, temperature, saturation of gas, hydrate and water in the reservoir are evaluated. It is shown that the gas production rate is a sensitive function of well pressure.
Abstract: In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.
Abstract: In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.