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Heat Transport Equation (heat + transport_equation)
Selected AbstractsHeat Transport in Closed Cell Aluminum Foams: Application Notes,ADVANCED ENGINEERING MATERIALS, Issue 10 2009Jaime Lázaro Heat transport equations have been used to solve, by implementing the Finite Element Method (FEM), three different cases representative of the aluminium foams life: the production process (solidification in the molten state), post-production (water quenching heat treatments) and applications (fire barriers). [source] Modeling of a Deep-Seated Geothermal System Near Tianjin, ChinaGROUND WATER, Issue 3 2001Zhou Xun A geothermal field is located in deep-seated basement aquifers in the northeastern part of the North China Plain near Tianjin, China. Carbonate rocks of Ordovician and Middle and Upper Proterozoic age on the Cangxian Uplift are capable of yielding 960 to 4200 m3/d of 57°C to 96°C water to wells from a depth of more than 1000 m. A three-dimensional nonisothermal numerical model was used to simulate and predict the spatial and temporal evolution of pressure and temperature in the geothermal system. The density of the geothermal water, which appears in the governing equations, can be expressed as a linear function of pressure, temperature, and total dissolved solids. A term describing the exchange of heat between water and rock is incorporated in the governing heat transport equation. Conductive heat flow from surrounding formations can be considered among the boundary conditions. Recent data of geothermal water production from the system were used for a first calibration of the numerical model. The calibrated model was used to predict the future changes in pressure and temperature of the geothermal water caused by two pumping schemes. The modeling results indicate that both pressure and temperature have a tendency to decrease with time and pumping. The current withdrawal rates and a pumping period of five months followed by a shut-off period of seven months are helpful in minimizing the degradation of the geothermal resource potential in the area. [source] An economical difference scheme for heat transport equation at the microscale,NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2004Zhiyue Zhang Abstract Heat transport at the microscale is of vital importance in microtechnology applications. In this article, we proposed a new ADI difference scheme of the Crank-Nicholson type for heat transport equation at the microscale. It is shown that the scheme is second order accurate in time and in space in the H1 norm. Numerical result implies that the theoretical analysis is correct and the scheme is effective. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004 [source] A convergent three-level finite difference scheme for solving a dual-phase-lagging heat transport equation in spherical coordinatesNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004Weizhong Dai Abstract Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equation is different from the traditional heat diffusion equation since a second-order derivative of temperature with respect to time and a third-order mixed derivative of temperature with respect to space and time are introduced. In this study, we consider the heat transport equation in spherical coordinates and develop a three-level finite difference scheme for solving the heat transport equation in a microsphere. It is shown that the scheme is convergent, which implies that the scheme is unconditionally stable. Results show that the numerical solution converges to the exact solution. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 60,71, 2004. [source] An unconditionally stable three level finite difference scheme for solving parabolic two-step micro heat transport equations in a three-dimensional double-layered thin filmINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2004Weizhong Dai Abstract Heat transport at the microscale is of vital importance in microtechnology applications. The heat transport equations are parabolic two-step equations, which are different from the traditional heat diffusion equation. In this study, we develop a three-level finite difference scheme for solving the micro heat transport equations in a three-dimensional double-layered thin film. It is shown by the discrete energy method that the scheme is unconditionally stable. Numerical results for thermal analysis of a gold layer on a chromium padding layer are obtained. Copyright © 2003 John Wiley & Sons, Ltd. [source] | ||||||||||