# Question: consider that the heat conduction equations below each represent the...

###### Question details

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)