Fig. 6

Comparison of the planar solution \(T^{{{\text{plane}}}}\) and the solution \(T^{{{\text{source}}}}\). The ratio between \(\left( {T^{{{\text{plane}}}} \left( {x, t} \right) - T_{0} } \right)\) and \(\left( {T^{{{\text{source}}}} \left( {x, t} \right) - T_{0} } \right)\) and its deviation from unity are plotted against the nondimensional parameter \(t_{{\text{s}}} /t\) when a, b \(x/2\sqrt {\alpha t} = 0\), and c, d \(x/2\sqrt {\alpha t} = 5\), respectively. The solutions were calculated with Eqs. (23) and (29). The other nondimensional parameters were set to \(c_{3} t = \left( {10^{5} , 10^{11} } \right)\) and \(c_{5} /c_{4} = \left( {0, 10} \right)\)