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The paper reports a mathematical model governing unsteady coupled moisture and heat energy transport through a green roof, e.g. the canopy (leaf cover), the soil and the structural support. The mathematical model that governs the transport phenomena in the canopy is represented by a system of nonlinear ordinary differential equations (ODEs) for the unknown temperature of the plants, and the unknown temperature and moisture content of the canopy air. A set of nonlinear partial differential equations (PDEs) describe the heat and moisture transport through the soil and structural support. Continuous field functions such as temperature and relative humidity, are considered as the driving potentials. A finite difference numerical model is used to solve the ODEs and the boundary element numerical model is used to discretize the PDEs. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the description of an unsteady heat transfer for a two-dimensional problem is presented. It is assumed that all thermophysical parameters appearing in the mathematical model of the problem analyzed are given as directed intervals. The problem discussed has been solved using the 1st scheme of the boundary element method. The interval Gauss elimination method with the decomposition procedure has been applied to solve the obtained interval system of equations. In the final part of this paper results of the numerical computations are shown. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with numerical study of the coupled fluid flow and heat transfer within a scraped surface heat exchanger “SSHEs”. The finite volume Fluent™ 6.3 code was used to solve continuity, momentum and energy equations in a real SSHE geometry using multiple rotating reference frame formulation. The mesh of a real SSHE geometry was achieved with Gambit™ 2.2.3, in order to take into account geometry singularities and their effect on the heat transfer performance within SSHE. The steady laminar non-isothermal flow of pure Glycerin, 2% CMC solution and 0.2% Carbopol solution were investigated. The cooling process without phase change within SSHE was studied. The heat correlation was established numerically and validated with the given literature heat correlations. The obtained numerical results agree well with given heat correlations in the literature. The numerical model was then used to examine in more details the heat performance of SSHE. The effect of the rotating velocity on the SSHE heat performance was investigated. For pure Glycerin, the increases on the rotating velocity significantly reduced the cooling process due to viscous heating. In the case of considered non-Newtonian fluids, increases on the rotating velocity improved the thermal efficiency of SSHE. The temperature profile a long of tip of blade, have shown an important influence of blade fixation on the heat performance within SHHE. Viscous heating was investigated and occurred for Newtonian viscous fluids. The numerical results have shown, in the case of Glycerin when the rotating velocity was ω =9revs−1, that the total energy can reach 25% more than without viscous heating. Finally, the study of the mixing time have shown a best heat performance when mixing time was equal to t mix =6.72s. [Copyright &y& Elsevier]