Application of inverse heat conduction problem on temperature measurement

Abstract

For regenerative cooling devices, such as G-M refrigerator, pulse tube cooler or thermoacoustic cooler, the gas oscillating bring about temperature fluctuations inevitably, which is harmful in many applications requiring high stable temperatures. To find out the oscillating mechanism of the cooling temperature and improve the temperature stability of cooler, the inner temperature of the cold head has to be measured. However, it is difficult to measure the inner oscillating temperature of the cold head directly because the invasive temperature detectors may disturb the oscillating flow. Fortunately, the outer surface temperature of the cold head can be measured accurately by invasive temperature measurement techniques. In this paper, a mathematical model of inverse heat conduction problem is presented to identify the inner surface oscillating temperature of cold head according to the measured temperature of the outer surface in a GM cryocooler. Inverse heat conduction problem will be solved using control volume approach. Outer surface oscillating temperature could be used as input conditions of inverse problem and the inner surface oscillating temperature of cold head can be inversely obtained. A simple uncertainty analysis of the oscillating temperature measurement also will be provided.