Heat 1 - Heat Transfer Model

In this exercise, we will develop an algorithm for computing the temperature at a particular location on a plate being welded using the Rosenthal equation¹. We can just work in two dimensions, so assume \(z = 0\).

First, given a point \((x, y)\), calculate the radial distance \(R = \sqrt{x^2 + y^2}\).

Next, using the values of \(x\), \(R\), \(T_0\), \(V\), \(I\), \(v\), \(a\), and \(\eta\), calculate \(T\{x,R\}\) using the equation:

\[T\{x,R\} = T_0 + \frac{\eta V I}{2 \pi \lambda}\left ( \frac{1}{R} \right ) \mathrm{exp}\left \{ - \frac{v}{2 a} (R + x)\right \};\]

You will need to declare variables for each of the values above. Choose a data type you think is most appropriate for this problem. Place the code in a main function and print out the value of \(T\{x,R\}\).

Use the following initial values \(T_0 = 200.0\), \(V = 20.0\), \(I = 200.0\), \(v = 5\), \(a = 84.18\), \(\eta = 0.84\), \(\lambda = 204.2\).

Experiment with using different values of \(x\) and \(y\) and see what results you obtain.

A solution to this exercise is available here.