Exercise 4: Dimensionless constant, r
Compute the constant “” 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 .
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, .
The temperature of the frying pan handle will begin at a room temperature of F. Store this initial ( ) value in the 2D array for all slices of the rod (for all ).
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, . The frying pan will start out at room temperature at time . 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 F. This behavior can be reproduced using the equation
with F, F, and 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 values, and then plot versus to verify that the temperature of you frying pan agrees with the following plot:
Once you have verified that is correct, use the 1D array of values to set the temperature of the left ( ) edge of the handle in the 2D array, , for all values of time (for all ).