Calculation of cryoaccumulator with heat-conducting headpiece in the form of a ribbed rod

Abstract

To equalize the temperature field in fusion cryoaccumulators, rods with developed fibbed surface or substances with capillary open pores may be used as beat-conducting headpieces. With such a design of the cryoaccurnulator, the heat removal by a solid cryogen in the process of its fusion may continue for a long time with small temperature gradients. This is particularly important for the cryostating of objects not permitting large temperature changes.The processes occurring in fusion cryoaccumulators with beat-conducting headpieces have not been sufficiently studied, and this requires therefore their physical and mathematical modeling for the purpose of subsequent calculation and optimization of such devices.Let us consider a fusion cryoaccumulator, cylindrical in shape, with a headpiece in the form of a fibbed heatconducting rod, and the method of its calculation. The heat-conducting headpiece is a rod with radius R and height H with rectangular ribs soldered to it along the axis (the number of ribs is n, the thickness of each rib is 3).To model the heat transfer in the structure under consideration (see Fig. 1), the following assumptions are made:--with z = 0 the heat Qo is removed from the cryostated object through a rod with the cross-sectional area S = ~rR2; --beat exchange in the working substance does not proceed in a circular sector but in a rectangular layer (such an assumption is possible because when the number of thin ribs is large, the layer of cryogen comes close to being rectangular); --there is no heat exchange over the height of the rib and cryogen, nor radially in the cryogen, heat removal over the height of the rod is effected solely through the r~s (this assumption simplifies the nature of the calculations with the chosen model, the calculation using it is carried out with some safety margin. In reality heat exchange proceeds with greater intensity because of the increased area of the beat-exchange surface of the ribbed rod since in modeling of the beat-transfer process heat exchange between the rod and the cryogen in the space between the ribs is not taken into account, nor is the heat removal from the end faces of the fibs); --in the middle layer of the eryoaccumulating substance (between two adjacent ribs) the temperature changes linearly from the temperature of the phase transition Tp to the running temperature of the rod over the z-axis Trd; --we neglect the temperature distribution within the rod and the fibs; --this is a steady-state problem. Such parameters of the beat-conducting headpiece of the cryoaccumulator have to be chosen (material, geometric dimensions of fibs and rod, number of ribs) so that the headpiece ensures the specified conditions of heat exchange within the eryoaccumulator, i.e., the permiss~le limit of temperature increase of the cryostated object is specified.In connection with the functional purpose of the material, viz., to equalize the temperature field within the cryoaccumulator for attaining lengthy cryostating of the heat-liberating object, the material of the...