A theory for the square guarded hot plate—a solution of the heat conduction equation for a two layer system
A theoretical treatment is given for the action of the guarded hot plate apparatus used for measuring conductivities. The flow of heat through the metal hot plate itself, and the effects of temperature unbalance between hot plate and guard plate are both taken into account. The temperature at any point in the sample or in the heater plate may be determined. The theory is comprehensive and any of the dimensions or controlling parameters may be varied in the calculation. Introduction. Although the thermal conductivity of insulating materials has been determined for many years with the guarded hot plate apparatus, it was not until recently that any attempts have been made to assess theoretically the errors associated with the use of this apparatus. Without the benefit of theoretical assessments the standards that have been specified by the ASTM [1], RILEM [2] and the British Standards Institution [3] have from necessity been drawn up relatively arbitrarily. Thus they differ to some extent one from another and in the light of recent theoretical and experimental work, do not appear to be sufficiently stringent for the 1% accuracy often demanded of the guarded hot plate apparatus. Figure 1 illustrates the layout of a typical "guarded hot plate". Essentially, two