Mathematical Model to Calculate Heat Transfer in Cylindrical Vessels with Temperature-Dependent Materials

Abstract

In this article, a mathematical model capable of simulating the heat transfer of cylindrical vessels whose properties are dependent on temperature is proposed. As a case study, it compares, from an approach of their heat transfer and chemical migration characteristics as a function of the temperature reached, different materials commonly used for the manufacture of water bottles. More specifically, the materials studied were aluminium, polyethylene terephthalate, and polypropylene. The validation of the model consists of an experiment carried out in the laboratory with three water bottles of each of the materials under study, as well as simulations using the Network Simulation Method to recreate the heat transfer that occurs through the walls of the bottles. On the other hand, the nondimensionalization technique is also applied, which allows us to obtain the weight of each of the variables on the problem, as well as the existing relationship between them. Finally, an outside temperature of 30 °C to 50 °C is simulated, which is a common temperature range in southern Europe during the summer season, and an initial temperature of 20 °C for the water contained in the bottle to know the behaviour of the materials and what the final temperature of the water would be after one hour.

Keywords

• mathematical modelling
• heat transfer
• nonlinear material properties
• Network Simulation Method
• nondimensionalization
• coupled differential equations