Error Analysis of Measuring Thermal Conductivity by Circular and One Side Heat Flow Type Guarded Hot Plate Apparatus

This paper deals with the theoretical analysis on total errors which occur upon measuring the thermal conductivity of a circular specimen using a one side heat flow type guarded hot plate.

Introducing three input parameters, that is, (a) temperature of ambient air, (b) that of guard ring, and (c) that of guard plate, which are normalized by letting the temperature of a hot plate be a unit and that of the cooling plate be zero, the theoretical solution of the total errors was derived. The errors were classified into the ones caused by the three parameters, and they were also classified according to the heat flow paths.

Heat exchange at the edges of the specimen and insulation between hot plate and guard plate was treated as the surface heat transfer including edge insulation.

The total errors were expressed with the following seven normalized parameters, that is, (a) ratio of the radius of the hot plate to that of the guard ring, (b) ratio of the thickness of the specimen to the radius of the guard ring, (c) ratio of the thickness of the insulation between the hot plate and the guard plate to the radius of the guard ring, (d) ratio of the thermal conductivity of the insulation to that of the specimen, (e) ratio of the equivalent edge insulation thickness to the radius of the guard ring, (f) ratio of the direct heat flow across the gap to the heat flow out of the hot plate into the specimen which is obtained assuming one-directional heat flow, and (g) ratio of the direct heat flow through the thermal bridges between the hot plate and the guard plate to the heat flow out of the hot plate into the insulation which is obtained assuming one-directional heat flow.

In this paper, each of (f) and (g) is considered to be determined by the analytical solution using experimental data.