A Mathematical Model to Pre-evaluate Thermal Efficiencies in Elongated Building Designs

Abstract

This paper exposes the basic structure and results of a mathematical model that treats in a simple way the evaluation of the energy demand for certain building typologies: those annular Courtyard types, and also long Blocks. It profits from the proven fact that the Form Factor of their three-dimensional shape is identical to the Form Factor of the mean cross section or "Perimeter to Section Area Ratio".

This model constitutes a useful application of the concepts exposed by us on a previous paper at this same forum with the title "A Simple way to Assess and Compare the Thermal Efficacy in Elongated Building Designs"[4]. Now, in continuation to it, we give here one of its more interesting practical consequences; it is the formalisation of a mathematical model that takes full advantage of the potentialities of the concepts, laws, criteria & methodology already exposed that allows to treat 3D problems just in two dimensions.

The inputs for the model are 2D geometrical and physical parameters such as width, height, thermal transmittances, etc. The outputs are 2D (& 3D) thermal efficiencies expressed as the unitary and specific flow of transmission heat through the envelope, and also some comparison percentages between different possibilities.