SETUP FOR STUDYING HEAT TRANSFER BETWEEN A DISPERSED LAYER AND A SURFACE

L. D. ALEKSEEV, V. I. OSIP

(Presented by the scientific seminar of the Department of Processes, Machines, and Apparatuses of Chemical Production)

In works (1, 2) it was shown that, when a granular layer is blown through by a sinusoidally pulsating air flow, the stage of expansion (fluidization) is preceded by its compaction. A qualitatively new state of the dispersed system is formed, characterized by small pulsations of the particles and weak mixing of them. In this state the dispersed medium is “loosened”; it retains the basic properties of fluidized systems, which makes it suitable for carrying out heterogeneous processes that do not require large flow rates of the fluidizing agent. The slight mixing of particles in the layer opens up the prospect of using it in carrying out a group of processes for which such mixing is undesirable.

The question of the possibility and expediency of using the “loosened” state in industrial practice has not yet received due dissemination because it has been insufficiently studied.

We are conducting studies to determine the influence of blowing conditions on the characteristics of the course of processes in dispersed systems, including heat transfer between a layer and a heated surface. For these purposes an experimental setup was made, including a transparent chamber with a diameter of 200 mm.

Choice of the Design of the Heating Element

In the practice of studying heat-transfer questions, both special heating elements placed inside the dispersed medium and the walls of the chamber itself are used. Our experiments were carried out in a chamber made of organic glass, which ruled out the possibility of using its walls as the heating surface because of the low heat resistance of the material; therefore it became necessary to develop an immersion-type heating element.

Two varieties of immersion-type heating elements have become widespread—electric and non-electric.

Electric heaters have become most widely used owing to the following advantages: ease of regulation of the emitted energy, independence of power from geometric dimensions, simplicity of construction, etc. They may be made in the form of spheres, tubes with coils placed inside them, in the form of thin wires, coils with external winding, etc.

Heaters with internal heating require measurement of the temperature

in several points of the surface, which complicates the experiment and the subsequent calculations.

Because of the small wire diameter, wire heaters are usually used in studies of heat exchange with finely dispersed materials.

The most universal are heaters in the form of coils. The temperature of their surface can be maintained constant by connecting the heater into a bridge circuit. They do not require special devices for measuring the surface temperature. They can be made in various shapes and sizes.

In our studies a textolite cylinder 7.5 mm in diameter and 25 mm high was used, onto which an insulated copper wire 0.18 mm in diameter and 3170 mm long was wound turn to turn. The wire cross section was \(S = 0.0254\ \text{mm}^2\). Copper has a comparatively high resistance coefficient and a linear character of its variation in the temperature interval from \(-50\) to \(+200^\circ\text{C}\) [3].

The coil parameters were calculated by the following formulas:

\[ \rho_t = \rho_0 (1+\alpha t); \tag{1} \]

\[ \rho_t = R_t \frac{S}{l} \tag{2} \]

where \(\rho_0\) and \(\rho_t\) are the specific resistance of the material at \(0^\circ\) and at temperature \(t\), \(\text{ohm}\cdot\text{mm}^2/\text{m}\);

\(t\) is the temperature of the conductor, \({}^\circ\text{C}\);

\(\alpha\) is the temperature coefficient of linear expansion, \(1/\text{degree}\);

\(R_t\) is the total resistance of the conductor at temperature \(t\), \(\text{ohm}\);

\(l\) is the wire length, m.

From the solution of these equations we obtain:

\[ t = \frac{ R_t \dfrac{S}{l} - \rho_0 }{ \rho_0 \alpha }, \tag{3} \]

\[ l = \frac{R_t \cdot S}{\rho_0(1+\alpha t)}. \tag{4} \]

For copper, \(\rho_0 = 0.017\ \text{ohm}\cdot\text{mm}^2/\text{m}\); \(\alpha = 4.267 \cdot 10^{-3}\ 1/\text{degree}\) [3]. As a result of substituting the known quantities, formula (3) takes the form:

\[ t = (110.7 \cdot R_t - 234.7)^\circ\text{C}. \tag{5} \]

The measured resistance of the coil at a temperature of \(23^\circ\text{C}\) proved to be 2.35 ohm. The calculated length was 3.2 m, which practically coincides with the adopted value. The heat-exchange surface of the heating element \(F\) was \(5.887 \cdot 10^{-4}\ \text{m}^2\).

The heater temperature was maintained constant by means of the compensating bridge circuit shown in Fig. 1.

Fig. 1. Compensating bridge circuit. \(R_{\text{h}}\) — heater; \(R_1\), \(R_2\) — fixed resistances; \(R_{\text{p}}\) — adjustable resistance; \(R_{\text{r}}\) — rheostat; galvanometer.

The bridge is in equilibrium when the equality

\[ R_{\mathrm{sh}}/R_1 = R_{\mathrm{n}}/R_2, \]

is satisfied, whence

\[ R_{\mathrm{sh}} = k \cdot R_{\mathrm{n}} \ldots \tag{6} \]

When the bridge is in equilibrium, the resistance \(R_{\mathrm{sh}}\) is uniquely determined by the resistance \(R_{\mathrm{n}}\).

A direct current is supplied to the bridge diagonal \(AB\), causing the element to heat up and increasing its resistance. The bridge equilibrium is disturbed, which is recorded by a sensitive galvanometer connected in the diagonal \(CD\).

The law of variation of resistance with temperature is expressed by the equation:

\[ R_t = R_0(1-\alpha t), \tag{7} \]

where \(R_t\) and \(R_0\) are the resistance of the conductor at temperature \(t\) and \(0^\circ\), whence

\[ t = \frac{R_t - R_0}{\alpha R_0}. \tag{8} \]

Since \(R_0\) and \(\alpha\) are constants, the conductor resistance is uniquely determined by its temperature, and vice versa.

Balancing of the circuit was carried out by means of a trimming resistance. A change in the temperature of the heater surface was compensated by a corresponding change in the current flowing through it.

The heater connection circuit is shown in Fig. 2.

Fig. 2. Schematic circuit for connecting the heater. 1—voltage stabilizer; 2—universal power supply; 3—rheostat; 4—DC bridge (type R333); 5—ammeter; 6—heating element.

By means of switches \(P_1\) and \(P_2 \ldots P_5\), it was possible to set the equilibrium resistance of the heater with an accuracy of up to \(0.001\ \Omega\), which corresponded to a change in the temperature of the coil surface by \(0.1^\circ\).

The mean heat-transfer coefficient was determined from the expression:

\[ I^2 \cdot R_t = \alpha_t \cdot F\,(t_{\mathrm{st}} - t_{\mathrm{sl}}), \tag{9} \]

where: \(I\) is the current flowing through the heater, A;
\(t_{\mathrm{st}}\) is the temperature of the wall of the heat-exchange surface, \(^\circ\mathrm{C}\);
\(t_{\mathrm{sl}}\) is the temperature of the layer, \(^\circ\mathrm{C}\).

The left-hand side of equation (9) represents the thermal energy emitted by the heater surface, and the right-hand side represents the heat absorbed by the layer.

The temperature of the heater wall in all experiments was maintained constant, equal to \(85 \pm 0.1^\circ\mathrm{C}\). The resistance of the heater coil at this temperature was \(2.9\ \Omega\).

The temperature in sections of the layer was measured by three exposed chromel-copel thermocouples and was continuously recorded by a PSR 1-18 potentiometer (class 0.5). The arithmetic mean of the readings of the three thermocouples was taken as the calculated layer temperature.

If the numerical values of the quantities entering into equation (9) are substituted into it, it takes the form:

\[ \alpha_{\mathrm{t}}=\frac{4026\cdot I^{2}}{85-t_{\mathrm{sl}}}\ \mathrm{W}/\mathrm{m}^{2}\cdot\mathrm{deg}. \tag{10} \]

The current was measured with ammeter 5.

During the experiment, \(I\) and \(t_{\mathrm{sl}}\) were determined, and the heat-transfer coefficient was calculated from formula (10).

REFERENCES

1. A. D. Alekseev. The effect of the nonstationarity of the gas flow on the behavior of a layer of granular material. Izvestiya TPI, vol. 133, 69–75, 1965.

2. A. D. Alekseev, V. M. Vityugin, Yu. A. Yanovich. Drying of granulated ammonium sulfate in a fluidized bed. Izvestiya TPI, vol. 148, 115–119, 1967.

3. M. V. Kulakov. Technological Measurements and Instruments for Chemical Production. “Mashinostroenie,” Moscow, 1966.