Exercise 4: Dimensionless constant, r

Compute the constant “r” for stainless steel. What value do you obtain? If it is greater than 0.5, you will need to adjust your discretization of the position and/or the time to decrease the values of r.

Exercise 5: 2D array and initial temperature

Generate a 2D array that will be used to store temperature as a function of both position and time, Tij.

The temperature of the frying pan handle will begin at a room temperature of Ti0=72 F. Store this initial (j=0) value in the 2D array for all slices of the rod (for all i).

Exercise 6: Temperature of the pan

You will need to generate an array of temperatures for the frying pan (at the left edge of the handle) as a function of time, T0(t). The frying pan will start out at room temperature at time t=0. A typical frying pan will then heat up quicky for the first minute or two after a stove is turned on, and then it will reach a constant temperature of around 350 to 400 F. This behavior can be reproduced using the equation

(24)T0(t)=Troom+ΔTstove×tanh(tτ)

with Troom=72 F, ΔTstove=300 F, and τ=60 seconds. “tanh” is the “hyperbolic tangent” function, which is one of the standard built-in functions for any computer math library.

Use this equation to compute an array of T0(t) values, and then plot T0 versus t to verify that the temperature of you frying pan agrees with the following plot:

Once you have verified that T0(t) is correct, use the 1D array of T0(t) values to set the temperature of the left (i=0) edge of the handle in the 2D array, T0j, for all values of time (for all j).