Traveling wave solution of cryogenic dynamic heat transfer for a small sample

The characteristics of transient dynamic thermal conduction wave are studied when a small sample moves at high speed in a sub-cooled liquid nitrogen. From the hyperbolic model, we derived the traveling wave solutions of the temperature field in this system indicating the heat transport of small sample follows obvious wave characteristics; and we also derived the dimensionless cooling rate increases as the thermal Mach number increases, whict demonstrates that building up the speed is one effective method to increase the cooling rate. The temperature curve from the calculation agrees well with the curve from the experiments. This addresses that it is reliable to calculation the cryogenic heat of small sample from the hyperbolic model.