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### Semi Analytic Investigation of Heat and Mass Transfer Modelling in Solidification

#### Affiliations

• Department of Mathematics, Jain University, Bengaluru - 560069, Karnataka, India
• Department of Mathematics, Dayananda Sagar College of Engineering, ShavigeMalleswara Hills,Kumaraswamy Layout, Bengaluru -560078, Karnataka, India
• Department of Mechanical Engineering, K.S. Institute of Technology, Bengaluru - 560062,Karnataka, India

#### Abstract

Objectives: The objective of this study is to develop a mathematical model to describe the heat and mass transfer of the solidification process with surface ice sublimation, in a square section, considering conduction and convection mode of heat transfer in the medium. Methods/Statistical analysis: The basic equations that describe the process are non-linear PDE. With semi analytical techniques the model turns in to a system of ODE and these equations are solved using finite difference method, and numerical simulations are carried out using MATLAB software. Findings: Temperature distributions in the active regions are discovered along with the sublimation front temperature. Also position of the advancing moving fronts at any time t is traced out. The results of numerical calculations are used to find the effect of mass transfer coefficient, frozen mass, and sublimated mass on the dehydrated front, sublimation front, and also on the sublimation and frozen temperature are investigated. Mass transfer coefficient shows significant influence on the sublimation front evolution and on the dehydrated front temperature. Whereas the increase of frozen mass volume increases the dehydrated front evolution and decreases the freezing front evolution. Many phase change problems deal with only active frozen region for consideration. In this paper along with the frozen part, sublimation region is also considered, with which the effect of frozen mass volume on the movement of sublimation front is studied. Application/Improvements: Freezing with surface ice sublimation is an important phenomenon to study the characteristics of the frozen tissues, final quality of the food. Diffusion of water vapor through the sublimation plays an important role in the freezing process of moving boundary problems. These models can be used to optimize the productivity, minimize the solidification time in food processing techniques.

#### Keywords

Dehydrated Region, Frozen Region, Ice Sublimation, Heat and Mass Transfer Coefficients, Moving Boundary Problems.

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#### References

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