An inverse geometry problem in estimating frost growth on an evaporating tube

When humid air comes into contact with a surface whose temperature is below the dew point of water vapor in air and also below the freezing point, frost deposition takes place over the surface. The phenomena of the frost growth are very complicated and therefore it is very difficult to model mathematically the behavior of frost growth and predict it. In the present study a transient inverse geometry heat conduction problem (shape identification problem) is solved using the conjugate gradient method (CGM) and boundary element method (BEM)-based inverse algorithm to estimate the unknown irregular frost thickness and shape. Results obtained by using the CGM to estimate the frost growth are justified based on the numerical experiments. It is concluded that the accurate frost shape can be estimated by the CGM except for the initial and final time. The reason and improvement of this singularity are addressed. Finally the effects of reducing the number of sensors and increasing the measurement errors on the inverse solutions are discussed.