EE Maths AA HL (A)

Introduction

A cooling system refers to a system designed to keep the temperature of a device below a certain limit due to needs of safety as well as efficiency1. Its applications range from machinery, such as automobiles, to electronic components, such as semiconductor chips. A cooling system usually incorporates convection through a fluid such as air or coolant as a means to transfer heat away from the system, but conduction also plays a role as a means to connect the heat source to the part of the cooling system which incorporates convection.

This extended essay focuses on the conduction which occurs between the heat source and the part of the cooling system that is in direct contact with the source. While there are many cases in which the heat source produces heat at a constant rate, this steady state problem can be solved with relative ease without the need for a time dependent partial differential equation. Thus, rather than a steady state problem, a situation in which the heat produced by the source abruptly increases will be examined. For simplicity, the conducting part of the cooling system will be modelled as a uniform rod of length through which heat is only transferred along the length of the rod, since for most cooling systems, heat transfer through the sides will be negligible compared to that in the direction of the main axis…