Dimensionless temperatures at the wall of an infinitely long, variable-rate, cylindrical heat source

In geothermal applications the thermal conductivity of rocks is needed, for example, to determine terrestrial heat flow, to evaluate heat losses to the surrounding formations in wells and to design borehole heat exchangers. Cylindrical probes (heaters) with a constant heat flow rate are used in boreholes or in the laboratory to obtain the thermal conductivity of formations and of cementing systems in geothermal wells. A new technique to calculate the temperature at the wall of an infinitely long, cylindrical, time-dependent heat source is presented.