ON THE PROBLEM OF FREE-CONVECTIVE HEAT TRANSFER IN AN ENCLOSED VOLUME WITH DISPLACEMENT OF THE HEAT SOURCE

A. S. Lyashkov, Yu. A. Zagromov

(Presented by Prof. Dr. G. I. Fuks)

Extensive experimental material has been accumulated in the domestic and foreign literature on heat transfer through symmetric liquid and gas horizontal cylindrical layers under natural convection (survey in [1]). Meanwhile, in practice there are cases of heat transfer through asymmetric layers.

As is known [2], if a heat source is placed in an enclosed volume of liquid or gas, its level is the plane of separation of two temperature fields, of which the field located above the heater is determined by convective, and the field located below the heater by conductive, heat transfer. When the heater is displaced in the vertical plane, one may naturally expect a change in the regions of convection and conduction and, consequently, in the temperature regime of the heater at one and the same power. In particular, an upward displacement leads to a decrease in the convection region and an increase in the conduction region, as a result of which the transfer of one and the same power must occur at an elevated temperature of the heat-releasing surface (with the ambient temperature being the same, $t_f = idem$). A downward displacement, on the other hand, should cause an expansion of the convection region and a decrease in the temperature of the heater.

There is no information in the literature whatsoever not only on the quantitative but also on the qualitative aspect of heat transfer with an asymmetric arrangement of the heat-emitting element.

The present communication gives the results of experiments carried out in order to check the proposed assumptions concerning the dependence of the overheating of the surface of the heat-emitting element on its location in an enclosed volume.

From Fig. 1 one may become acquainted with the experimental setup on which the experiments were carried out.

Its main part is a glass cylindrical burette 1, sealed at one end, with heater 2 inserted into it. The heater consists of a brass tube with a nichrome coil mounted inside it.

Four copper-constantan thermocouples, arranged as shown in Fig. 1, served to measure the temperature of the heater, while the temperature on the surface of the glass burette was measured by eight copper-constantan thermocouples fastened around the perimeter in its middle part.

Fig. 1. Diagram of the experimental setup: 1—glass burette, 2—heater, 3—thermocouples, 4—flange, 5—rubber gasket, 6—thermal insulation, 7—switch, 8—cold-junction thermostat, 9—potentiometer P-300, 10—null galvanometer, 11—class II standard cell, 12—M80 ammeter, 13—M106 voltmeter.

Fig. 2. Change in the overheating of the surface at the middle of the heater, \(\vartheta_h\), as a function of eccentricity \(e\). Curve 1—from experiments with water; curve 2—from experiments with air.

The experiments were carried out with water and air.

In the experiments with water, the heater was supplied with alternating stabilized current (\(P = 40\ \text{W}\)), and in the experiments with air—with rectified stabilized current (\(P = 10\ \text{W}\)). In addition, in the experiments with air, in order to check tightness, the burette volume was connected to a water manometer, whereas in the experiments with water a drain fitting was made in cover 6.

All experiments were carried out under steady thermal conditions, as evidenced by the stability of the readings and by the identical mean integral overheating over the surface of the burette,

\[ \vartheta_{b} = t_{w} - t_{f} \qquad \left(\vartheta_{b}^{\mathrm{H_2O}} = 40.1^\circ\text{C}; \quad \vartheta_{b}^{\mathrm{air}} = 15.4^\circ\text{C}\right). \]

The study was carried out for seven vertical displacements of the heater. The dependence of the overheating \(\vartheta_{h} = t_{h} - t_{f}\) on the eccentricity \(e\) is given in Fig. 2.

It is evident from Fig. 2 that, as the heater is displaced upward relative to the center of the burette, the overheating of its surface increases to a certain value and then, for small gaps between the burette and the heating surface, begins to decrease again. Displacement of the heater downward leads to a decrease in the overheating \(\vartheta_{h}\).

The deviations of the overheating of the heat-emitting surface from the overheating in its central position amounted, in the experiments with water, to 13–18.5%, and in the experiments with air, to 10.5–14%. This provides grounds for conducting a broader investigation of heat transfer with an asymmetric arrangement of the heat-emitting element in an enclosed volume, with the aim of obtaining a detailed qualitative picture and quantitative design correlations.

REFERENCES

1. D. I. Boyarinov. Heat transfer through liquid and gas interlayers. ZhTF, vol. 20, No. 9, 1950.

2. E. M. Lvova. Candidate’s dissertation, 1948.