# Thermodynamics of the greenhouse

## Intro

There are many techniques that can be used to model the heat flow of a Martian greenhouse. The following models will assume a half cylindrilrical greenhouse cut along the axis and with the axis parallel to the ground.

## Model 1 All Heat Transfer Though the Walls

In this model the outside wall of the Martian greenhouse is the temperature of the martian air, the inside wall is the temperature of the inside of the greenhouse. All heat is transferred through thermal conductivity. Either the wall thickness is given and the heat loss is computed or the heat loss is given and the wall thickness is given. This model will be valid if the walls of the greenhouse are highly reflective to infra red light and thick enough so that the temperature of the walls is the same temperature as the Martian air.

This model is similar to that used to estimate insulation thickness for houses, and can give an estimate for the necessary overall thermal resistance needed to maintain the greenhouse's internal temperature with a given heat input.

## Model 2 Flow Heat Exchange

In this model, the greenhouse is modeled as a heat exchanger in which heat transfer is conducted by flowing fluids - Martian air outside the greenhouse and greenhouse air inside the greenhouse.

## Model 3 Transmission of infra red radiation through the walls

In this model either the heat dissipation from the outside of the wall is assumed to be black body, condition or a mix of black body and conduction. The heat passing though the walls however will be mix of electromagnetic (e.g. infra red) radiation and thermal conductivity. The thermal conductivity as before depends on the temperature difference on the inside and the outside of the wall. The electromagnetic radiation can be taken as the difference between the blackbody radiation from the air at the surface of the outside of the greenhouse coming into the greenhouse plus the blackbody radiation from the air near the inside wall of the greenhouse moving towards the outer wall. The black body radiation will be significant if the conductivity of the walls is low and the walls transmit infra red radiation easily.

## Model 4 Cooling by wind

Mars is windy. There will be air at the same temperature as the surface of the greenhouse relatively close to the greenhouse. Consider the wind blowing across a greenhouse that is in the shape of a cylinder which is cut in half along the axis and has the axis parallel to the ground. Using a laminar flow approximation the pressure and wind speed of the wind can be approximated.

The air that is infinitesimally close to the greenhouse immediately touching the greenhouse does not flow because of viscous friction. The air pressure at the surface on the wind side of the approaching wind can be determined using Baronolies Equation. The air pressure on the other side can be taken as marten ambient pressure, the viscous force across the cylinder can be treated as constant and then the air velocity close to the cylinder can be obtained by using the relationship between viscous force and the change in velocity.

The inside walls again can be taken as the temperature of the air inside the greenhouse. The temperature on the surface of the outside walls of the greenhouse will be colder on the side of the approaching wind then on the other side. The temperature on each point of the outside wall of the greenhouse can be numerically approximated by a partial differential equation. It will be also important to consider the heat transported by the wind the convection perpendicular and to the air flow.