DE2701774A1 - Measurement of thermal conductivity and specific heat - uses hollow sphere enclosing radiating element, with temp. sensor on outside surface monitoring temp. variation with time - Google Patents

Abstract

The heat conductivity and specific heat measuring device consists of a heated hollow body. The hollow body is embedded in the medium to be tested and has as small as possible thermal capacity in comparison with the displaced volume. Heat is so applied to its inside by radiation, so that a constant heat flow is generated through its surface. The surface temperature, variable in time, is measured and recorded by a temperature sensor on its surface.

Description

Subject: patent application

The invention relates to a probe for the absolute determination of thermal conductivity and the specific heat.

Description With the procedures described in the literature for simultaneous ordering of the thermal conductivity and the specific heat see 1) , 2) is the closest possible observance or knowledge of the distances between the heat source and temperature measuring point required. This is the case with in situ measurements in bulk material or, for example, practically impossible to implement in the ground s.B. according to 3), in which the heating element and temperature sensor are directly connected only provide the thermal conductivity.

In the case of cylindrical probes with a finite diameter 4), which the Thermal conductivity and the specific heat it could deliver represents the heat capacity of the probes and the only imprecisely determinable heat transfer coefficient between probe and Medium is a practically ineradicable source of error, what the use of such Makes probes unsuitable for absolute measurements.

According to the invention, from the time course of the surfaces.

temperature of a probe embedded in the medium to be examined is'die thermal conductivity and the specific heat of the medium absolutely determined when the heat capacity of the probe is small compared to the heat capacity of the medium displaced by the probe. This can be achieved e.g. through a thin-walled Hollow sphere or a thin-walled hollow cylinder, who (who) from within uniformly and temporally constant from a punctiform (linear) electrical Radiant energy is used to bump the heat source to avoid the uneven convective heat transfer, the probe can be evacuated.

Under these conditions, the Surface temperature of the probe except for an additive that is almost constant over time Amount correspond to the temperature of the inner surface of the medium to be examined.

Because of this temperature jump between the medium and the probe surface the temporal course of the probe temperature can only be determined imprecisely, the the temporal variation of the probe surface temperature can be easily and precisely measured differentiated over time, the constant additive term becoming zero. From this derived measurement curve of the probe surface temperature can be the temperature diffusivity and the thermal conductivity and (if the density of the medium to be examined is known ) the specific heat can be determined absolutely.

For the surface temperature of a ball probe according to Fig. 1, under the above conditions and according to 5) - Q [1 - exp (X²) erfc (X)] / 4 ## R + Q / 4 # αR² ........ 1 with.

Purely the time derivative one gets T '(R, t) = Q X [Y exp (X²) erfc (X) - 1 / ##] / 4 ## R ............ 2 Purely the surface temperature of a cylinder probe Fig.2 applies under the above conditions and according to 6) T (R, t) = Q ([lnY + R²lnY / 2xt + R² / 2xt + ..] / 4 ## 1 + Q / 2R # α1 .....

with Y = 4xt / CR² For the time derivative we get T '(R, t) = Q [1 / t - R²lnY / 2xt² + ...] / 4 ## 1 lit the following designations in 1 to C = 1.7811 T = temperature increase [K] R = spherical or cylinder radius [m] 1 = Length of heating conductor in cylinder probe [m] # = time [h] Q = yield of the heat source [W] α = coefficient of heat transfer between probe surface and medium [# / m² / K] x = temperature guideline [m² / k] # = thermal conductivity [W / m K] From 2 as well as from leaves. through education the quotient of two successive measured values initially x and thus by insertion # determine.

Literature 1) Jaeger J.C., Australia Jl.of Physics 12 (1959) 203-217 2) Borkowetz W., Ber.Dtsch.Keram.Ges. 52 (1975) 317-319 and Kunststoffe 66 (1976) 434-435 3) Mittenbühler A, Ber.Dtsch.Keram.Ges. 39 (1962) and 41 (1964) 4) Blackwell J.H., Jl.of Applied Physics 25 (1954) 137-145 5) Kneschke A .: Diffgl.u. Randwertprobl.Bd.2, Berlin 1960, p 290 6) Carslaw & Jaeger: Conduction of Heat ... Sec.ed.Oxford 1971, p 341

Claims (3)

Claims 5 device for the absolute determination of thermal conductivity and the specific heat consisting of a heated hollow body, characterized in that the hollow body to be embedded in the medium to be examined is a compared to The mass of the displaced medium has the lowest possible heat capacity = and of inside by radiation in such a way with heat be can be added that by his Surface a temporally and spatially almost constant heat flow arises, whereby the time-varying surface temperature that is established by means of at least measured and registered by a temperature sensor attached to the surface can be. 2. Probe according to 1.) characterized in that the hollow body according to Fig. 1 consists of a thin-walled metal ball, which is used to avoid the uneven convective heat transfer can be evacuated that in its center is a in all directions radiating electrical heating coil is located that the diameter eo is large that the heat capacity of the hollow sphere including internals is smaller than the heat capacity of the mass of the displaced medium and that the temperature sensor is attached to the spherical wall 0 3. Probe according to 1.) characterized in that the Hollow body according to Fig.2 consists of a thin-walled hollow cylinder made of metal to avoid the uneven convective heat transfer can be evacuated that an electric heating wire or a heating coil along the axis of the hollow cylinder is attached, that the diameter is so large that the heat capacity of the hollow cylinder including internals is smaller than the heat capacity of the mass of the displaced medium, dab the diameter is less than 8 cm, however, that the length of the hollow cylinder is a Is a multiple of the diameter and that the temperature sensor (s) in the Is (are) attached in the middle of the lateral surface.