NUMERICAL AND ANALYTICAL STUDY FOR SOLVING HEAT EQUATION OF THE REFRIGERATION OF APPLE

Abstract

In this paper, we study the mathematical Heat and Mass transfer  model, Apple shipments from Australia to England began to decline several decades ago. Due to a disorder known as "brown heart," which developed due to insufficient cooling. When placed on deck, the apples are normally warm and must be refrigerated to keep them fresh. Storing in the cold Breathing generates heat as well. This heat was thought to be the cause. The generation successfully counteracted the apple's cooling, resulting in dark fruit. ''Brown Heart ".This was the issue that resulted in the Awberry. To investigate how heat is distributed within a room. The location where heat is produced. At first, Awberry assumed the apple was in the beginning.at a constant temperature In the suitable value, we can assume that this temperature is zero. Select a temperature scale from the drop-down menu. t = 0 is the current time. It must be concluded that the generation of heat inside the apple is not ''Brown Heart "cause. We now know that the brown core is caused by an excessive concentration of carbon dioxide and an insufficient amount of oxygen in the stockpile. It affects the metabolic activities that occur in apples and leads to a decrease in temperature separation. We have solved the heat equation for cooling apples using the method of separating variables in addition to numerical methods and clarification of the results obtained, including comparing the exact solution with the numerical solution. In terms of discovering analytical and numerical solutions, the approach is quite effective and useful.