Numerical Simulation of the Thermal Behavior of a Traditional Greenhouse by Using the Theory of the Green's Functions

Abstract

In this article, we present a precise modeling translating the influence of the ground inertia in the thermal behavior of a greenhouse without vegetation. This work takes into account all the real mechanisms of exchanges (solar conduction, convection, radiations, thermal inertia) between the various elements of the system (cover, interior air, ground), but does not take into account the mass transfers (diffusions of moisture in the ground, evapotranspiration). We sought here to define a model constituting a core of procedure on which new extensions will be based. We show via the Green functions theory that the differential equations of the model are reduced to a system of integral equations on the ground surface. These equations implicitly take into account the heat propagation in the ground. This model carefully describes in detail the exchanges between the ground and the interior of the greenhouse. It also aims at defining the evolution of the greenhouse internal air temperature as well as that of the superficial temperature of its ground according to the following external data (power, exterior temperature). The mathematical study is completed by a digital simulation on an isolated greenhouse.