Using Finite Difference Methods to Calculate Heat Transfer in Freezing the Flat Surface of Humid Materials by Cryogenic Technique

One of the methods to destroy cancer cells is freezing them to very low temperatures using cryogenic technique. To perform this technique, we need to answer these questions: how process of freezing tumor occurs, how Fast the freezing and distributing of temperature in the ice is, etc. In [1], the authors use calculus and analysis to solve the above problems. This paper presents the heat transfer when freezing the flat surface of humid materials using finite difference method, thereby, calculating the thickness of the ice sheet formed during the freezing time. This is a fundamental problem that helps scientists determine the freezing time needed to destroy cancer cells with cryogenic technique. The author has set up equations, built software in the Excel, and used VBA to solve the problem. The results are compared with the ones under analysis and other calculus methods. The calculation error between methods is less than 15