# TRANSFORMATION OF DIMENSIONLESS HEAT DIFFUSION EQUATION FOR THE SOLUTION OF DYNAMIC DOMAIN IN PHASE CHANGE PROBLEMS

• Ashraf, Muhammad (DEPT OF MATH, COMSATS INST OF INFORMATION TECHNOLOGY) ;
• Avila, R. (THERMAL FLUID LAB, FAC OF MECH ENG, NATL AUTONOMOUS UNIV OF MEXICO (UNAM)) ;
• Raza, S. S. (GLOBAL CHANGE IMPACT STUDY CENTER)
• Accepted : 2009.02.26
• Published : 2009.03.25

#### Abstract

In the present work transformation of dimensionless heat diffusion equation for the solution of moving boundary problems have been formulated. The formulation is based on 1-D, 2-D and 3-D, unsteady heat diffusion equations. These equations are rst turned int dimensionless form by using dimensionless quantities and their transformation was formulated in liquid and solid phases. The salient feature of this work is that during the transformation of dimensionless heat diffusion equation there arises a convective term $\tilde{v}$ which is responsible for the motion of interface in liquid as well as solid phase. In the transformed heat equation, a correction factor $\beta$ also arises naturally which gives the correct transformed flux at interface.

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