Application of Finite Difference Method for determining lunar regolith diurnal temperature distribution

¹ Department of Building Engineering, Rzeszow University of Technology, 2 Poznanska st. 35-959 Rzeszow, Poland
² Centre for Astronomy, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, 5 Grudziadzka st., 87-100 Torun, Poland
³ Department of Structural Mechanics, Rzeszow University of Technology, 2 Poznanska st., 35-959 Rzeszow, Poland

^* Corresponding author: kaczmar@prz.edu.pl

Abstract

This study was performed in order to verify viability of using finite difference method and proposed simple astrometrical model for modelling heat transfer in lunar regolith. The concept was examined by developing FD model of heat flow for upper 0,9 m of lunar regolith, and comparing obtained results with in situ measurements provided by Apollo 15 and 17 heat flow experiments. The model was based on FDM approximation of Fourier’s law for one dimensional transient heat flow. Both constant and temperature-dependent thermophysical properties of lunar regolith were obtained from in situ measurements. Thermal boundary conditions were assumed on in situ measurements and on remote sensing based analytical model. In order to approximate Sun's position at lunar sky, simple analytical astrometric model of lunar rotation was developed. Matlab 2012a was used to conduct the calculations. Stable solutions were obtained for latitudes between 0 and 80°. Satisfactory agreement between Apollo 15 and 17 in situ measurements and FDM modelling was observed. A conclusion was reached, that both FDM and proposed astrometrical model are to be successfully applied for modelling heat transfer in lunar regolith.