A mathematical model of a solar air thermosyphon integrated with building envelope

Abstract

A mathematical model comprising of analytical and two dimensional network procedures is proposed for predicting steady heat flow and heat transport in a solar heated thermosyphon integrated with building envelope. The detail mathematical solution method is presented for solving partial differential heat flow and transport equations by performing two dimensional energy balances at surface and air nodes through conjugate heat exchange and heat transport analysis of a solar thermosyphon. The mathematical solution procedure is devised for conduction and radiation heat exchange between surface nodes to improve the accuracy of traditional analytical solution for predicting buoyancy-induced mass flow rate of air flowing through a solar thermosyphon. The matrix inversion solution of mathematical model is unconditionally stable, with accuracy dependent on magnitude of conductance terms and number of nodes in the grid. Only Δy is chosen as aspect ratios (Δx = L, L/H and W/H) are defined by the geometry of the thermosyphon. The conduction and convection conductance terms are based on discretisation height Δy, thermal capacity conductance (mcp) is based on air-gap length Δx, whilst integrated radiation conductance terms are based on both height Δy and width Δx of the grid. The proposed model has compared the results obtained from analytical method, two dimensional network method for a single set of environmental condition with given geometry of thermosyphon. The proposed model is validated with experimental results obtained from outdoor experimental setup comprising of thermosyphon based photovoltaic solar wall system.