(a) The working principle setup of the four ball support (FBS). (b) Aligned section view of the FBS. The nomenclature of dimensions, acting forces, temperatures, and heat flows is displayed. Here Q = 3·Q K.
(a) Model of a thermal circular contact. Here, a is the radius of the contact area at temperature T 1, whereas temperature T 2 is in infinity. 6 (b) Model of a contact of two solids with unknown contact temperature T x (generally not constant over the contact area) and temperatures T 1, T 2 in infinity.
Experimental setup of the measurement of the heat flow Q between a glass ball and an aluminum plate loaded by a force F.
Dependence of the heat flow Q between the aluminum plate at temperatures of 100 K and 200 K and the glass ball at 5 K on the loading force F. Average values obtained in three runs of the measurement are displayed. Error bars represent the maximum spread of the heat flows Q measured at individual forces within corresponding temperature series (±13% at T 2 = 100 K and ±10% at T 2 = 200 K).
(a) Model used for calculation of the heat flow Q through the complete FBS drawn in Fig. 1 . It includes two spot thermal contacts: the first one between the loading plate and the upper ball (thermal resistance R), while the second one represents one of the three contacts between the balls (thermal resistance R k). Thermal resistance of the contact between the lower ball and the seat is neglected. (b) Lumped element model of the FBS thermal resistance.
Dependence of the heat flow Q through the FBS on the loading force F. The temperature drop on the FBS was 100 K to 5 K and 200 K to 5 K, respectively. Average values obtained in three runs of the measurement are displayed. Error bars represent the maximum spread of the heat flows Q measured at individual forces within corresponding temperature series (±4% at T 2 = 100 K and ±15% at T 2 = 200 K).
Practical construction of the FBS, where the upper ball is placed in a conical seat. All balls are protected against the heat radiation inleakage from the surroundings.
Experimental setup of the dummy sample holder attached to a base plate via three FBSs. The glass balls are shielded by small aluminum tubes against thermal radiation and are not visible. Also the temperature sensor and electric heater placed on the top of the holder are shielded by a copper cover. A phosphor bronze plate spring preloads the dummy holder from which is thermally insulated with the fourth FBS (not visible).
Mechanical and thermal properties of used materials.
Calculated and measured heat flows through the supports. The sample holder is at 44 K.
Heat flows for different types of support compared with the heat flow through three FBSs. All the values are calculated for a temperature drop from 300 K to 20 K.
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