Time to cool a cryogenic object by a gaseous cryogenic agent

Dependences to compute the cooling time of a single-channel object are obtained theoretically and confirmed experimentally.Notation D mass of helium in the channel - M mass of metal of the channel wall - G mass flow rate of the cryogenic agent - G_equ equivalent mass flow rate - c_p, c_m mean integrated specific heat of the cryogenic agent and the channel wall material - U perimeter - cooling time - ₁ time of the first cooling period - T₂ time of the second cooling period - channel wall temperature - T flow temperature - T_o initial flow temperature - T_in flow temperature at the channel input - W flow velocity - L channel length - L_in, L_out lengths of the delivery and removal pipelines - F, F_in, F_out cross-sectional areas of the channel being cooled, and of the delivery and removal pipelines - F_s total heat-transfer surface - d channel inner diameter - d_in, d_out inner delivery and removal pipeline diameters - P flow pressure - P flow pressure at the input to the element - P_out flow pressure at the output from the element - G_o, G₁ initial and final flow rates of the cryogenic agent - z a coordinate - ¯z=z/L a dimensionless coordinate - dimensionless channel length - dimensionless cooling time - V₁ dimensionless temperature - k_G,a, k_u, f, m, , g parameters - A, B constants - Re Reynolds number - R gas constant - coefficient of dynamic viscosity - hydraulic drag coefficient - coefficient of heat eliminationTranslated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 4, pp. 629–635, October, 1980.