Heat Transfer with Melting or Freezing : 1st Report, An Approximate Solution of Phase Front by Heat Conduction, when Cooling-Surface Temperature Is a Function of Time

Abstract

In this report, the following analyses, numerical calculations and experimental results are reported, concerning a one-dimensional transient heat conduction problem with melting or freezing.(1) For a substance, the thermal diffusicity of which in solid state is sufficiently larger than that in liquid state, simple approximate equations of the temperature gradient in solid and the temperature distribution in liquid are proposed when the cooling-surface temperature varies slowly and arbitrarily.(2) Using the above equations, an approximate solution for the position of the solid front is proposed as a simple explicit equation.(3) The applicable range of the above equation is discussed through both analysis and numerical calculations, and the limit of application is shown using a non-dimensional parameter.(4) Expermental results for distilled water agree with the above approximate equation within an error of 10% in cases of various cooling-surface temperature changes.