The Theoretical Analysis of Mass and Energy Flow Through Solar Collector – Chimney System

Abstract

The goal of the paper was to simplify the designing process for mass and energy flow through solar collector - chimney system. Theoretical analysis allowed to get involved system of three nonlinear analytical equations in dimensionless forms that have been saved. Dimensionless numbers for the problem are well known in the literature on fluid mechanics and thermodynamics: Reynolds, Grashof, Galileo, Biot and Prandtl. In the analyzed equations are also dimensionless geometric parameters expressing the ratios of basic geometrical dimensions of the collector system-chimney: the radius disc collector to the thickness gap, the height and radius of the chimney. In the system of equations, the Reynolds number is treated as the determined number, which is a novelty of the method used.

Analytical and Experimental Investigation of the Solar Chimney System

“…By using the original transformations of the equations describing the air flow in the solar chimney, combined with several additional assumptions, a system of equations was obtained, which allowed one to solve the problem analytically. This article is a continuation of the previous work [15]. Some of the theoretical considerations have been repeated and refined.…”

“…The incompressible flow of air (with a constant viscosity) inside the collector (see Figure 1), the stationary Navier-Stokes equation and principle of the conversation of mass flux crossing cylindrical surfaces have the forms [15]:…”

“…The solutions to Equations (1) and (2) (in dimensionless form) in the collector can be expressed as the dimensionless pressure drop and dimensionless distribution of temperature, respectively [15]:…”

“…An increase in the chimney height causes an increase in air velocity and a decrease in air temperature. The increase in heat flux density increases both the temperature and air velocity in the chimney (see [15]). Figure 5 shows the dependence of the energy efficiency of the solar chimney to the chimney height.…”

“…Kasaeian et al [5] presented a comprehensive review of solar chimney systems. Depending on the research directions, solar chimneys may serve various goals [6][7][8][9], such as natural ventilation in the buildings [2,5,[10][11][12][13], small-scale power plants, generation in full-scale energy generation systems, and some applications in smart islands [14][15][16][17][18].…”