The way the heat flows across some domain and some dimension has been a field of physics that has had its start in the time of Newton. Since then, with the help of partial differential equations and other techniques, it has been possible to model how heat flows by numerical means. The application of this principle is quite diverse, from how heat conducts in the heat shield of a hull of a spacecraft to how change in water temperature in one point in the ocean can affect the other portions to simply how temperature can be observed in a heat conductive rod from one end to the other.
The physics of how heat flows within a heat conductive material can be expressed as a partial differential equation.
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(2.1) |
To look more into this k value, according to CRC Handbook of Chemistry and Physics,
48th ed., Cleveland: Chemical Rubber Company, 1967, and E.S. Dana and W.E. Ford,
Textbook of Mineralogy, New York: Wiley, 1964., k value with the unit of 
, Different heat conductors possess different k numbers.
u at different induces are the values that we want to solve. There are two states with
which the heat equation is solved that we will consider;
transient and steady state. When we make reference to Transient Heat flow, the change
in state which is measured in temperatures throughout the domain over time.
Steady-state behavior is a little different in the sense that there are more of a
constraint to the rate
where q is the strength of the
source of the heat, thus making this a time-independent problem.
The main focus of this project will be to look more closely at the transient problems,
although there will be some investigation into steady state problems and how we solve
such systems.
As we will see later on, how the problem domain is broken down so that computer systems can solve them is dependent on the method we employ to solve the problem.