I would like to use Maple to provide an independent check on a finite element model solution (ANSYS) of a thermal transient analysis of a reinforced concrete shell. The following information is known about the shell:
- Thickness, coefficient of conductivity, diffusitivity, and density.
- Temperatures on the inside of the shell and ambient air temperature on the outside. The temperature on the inside of the shell is given as a temperature-time history loading consisting of ordered pairs.
- The in-plane dimensions can be considered as infinite and adibatic.
I have obtained a copy of "Thermal of Thermal Stresses" by Boley and Weiner which classifies this problem of heat conduction as a nonhomogeneous differential equation with variable boundary conditions. The authors suggest that the solution may be found using the technique of separation of variables or a Laplace transform. Either way, I am seeking advice on how to set up the problem in Maple to be able to calculate the thermal gradient through the wall for the applied temperature-time history. Also, the wall is initially under a linear distribution of temperature under steady state conditions at time x=0.
Any suggestions on how to set up the problem would be appreciated. Are you out there Professor Meade?
P.S. If you're wondering what the physical system is, it is the concrete containment of a nuclear reactor subject to a postulated thermal load due to accident conditions.
Thank you for your help.