An accurate approximation method of calculating the thermal effect of a propagating underground fire or of a moving source of heat

Author: J. Mączyński

Effects of underground fires such as mechanical damage to the strata or gasification c coal may only be modelled when temperature fields and the thermal impact on parts of th strata material are known. The paper shows a method of calculating the temperature field in an isotropic hea conducting body such as the strata surrounding a mining underground roadway. The methoi is developed around the fact that the kernel function of the linear Kelvin heat conductioi integral operator may be approximated by means of cubic splines. Such a method does no seem to have been applied elsewhere in the literature of heat conduction problems. Whe: cubic splines are applied for the approximation (these are nothing else but piecewise thin degree polynomials adjusted at a number of interpolation nodi, so that at a node, bilatera values of the function and also of its derivative coincide) analytical integration become feasible for a range of cases such as e.g. sources moving at constant speed.

A fire in a mine roadway (unless efforts to quench it are made) is a heat source movin at constant speed.

The method makes it possible to calculate the behaviour of temperatur fields as illustrated e.g. by transient temperatures at selected points.

Such temperature pulse are characteristic of the thermal impact experienced by the material and therefore may serv to feed data into further models concerning mine fires.