On 02/17/2014 05:28 PM
On blackboard photo 5 from last Friday, there is a part that says to assume u(x,t)=u0. I
interpreted this to mean that we are setting the heat distribution at time 't' to the initial
distribution. Why do we do this?
REPLY:
I'll try to add more details, until it makes sense.
The notation u0 is a constant temperature, an assumption for the created example used to
validate the integral equation formula. Let's look again at photo 5:
Validation is done by computing the total thermal energy (# BTU) from an example
with a known answer, then feed the example through the integral formula to see if the
two answers match.
The example chosen is u(x,t)=temperature=constant=u0, with a uniform rod of cross-sectional
area A, constant specific heat c and constant mass density rho per unit volume. This example
is treated in nearly every college physics textbook. The total thermal energy for this simple
case is computed from (c rho u0), the number of BTU per unit volume, then multiply by the rod
volume (cross-sectional area)(length) = AL to find total BTU = c*rho*u0*A*L.
-Doctor G.