Numerical study of one-dimensional unsteady radiation problems with applications to the thermal structure of planetary lower atmospheres

Abstract

This document will be concerned with the study of the radiation as a mechanism of energy transfer. Several unsteady, one dimensional problems will be described, focusing in radiation atmospheric problems. The governing equations are derived taking as theoretical base the general principles of the physics of radiation. In addition, a simplified, one dimensional model of the atmosphere is described. The governing equations are written in an appropriate form in order to solve them by a numerical collocation method which is based on a finite difference discretization of the non linear algebraic integro differential unsteady radiation equations. The resulting non linear set of algebraic equations are solved using a Newton Raphson’s method which yields the temperature field within the domain at each instant of time. The method is verified by comparing the results obtained with those of the literature. Finally, implementation of the atmospheric model in the numerical method is checked and validated. The method is then used to study the evolution and steady state of different kinds of atmospheres. Lastly, to have a complete model of the energy transfer, convection is included and, again results for different atmospheres are calculated.