Question: consider that the heat conduction equations below each represent the...
Consider that the heat conduction equations below each represent the simplest form to
accurately describe conduction in a material in two different problems. For each equation, start
with the most complex form of the heat conduction equation for that geometry and show how it was simplified to obtain the form below. Answer a) through e) for each equation.
𝜕/𝜕𝑥(k(𝜕𝑇/𝜕𝑥))+𝜕/𝜕𝑦(k(𝜕𝑇/𝜕𝑦))+e,generated = 0
(1/𝛼)(𝜕𝑇/𝜕𝑡) = (1/r^2)(𝜕/𝜕𝑟)((𝑟^2)𝜕𝑇/𝜕𝑟)
a) Is the geometry rectangular, cylindrical or spherical?
b) Is heat transfer steady or transient (unsteady)?
c) Is heat transfer one-, two-, or three-dimensional?
d) Is there heat generation?
e) Is the thermal conductivity of the material constant or variable? (remember that a =
thermal diffusivity = k/(pcp)