ME 323 Sample Problem 4B
Microwave ovens are said to cook from the inside out. What does this mean?
Solution
Consider a slab with uniform properties subjected to microwave
heating, e.g. a thick steak. The microwaves excite water molecules
within the meat, causing them to vibrate and generate thermal
energy. As a first approximation, the microwave heating can be
assumed to be absorbed uniformly, or =
v
q
&constant. At steady
state for surface temperature Ts, the temperature distribution within
the slab is predicted by integration of the energy equation
S
Lx
x
vTT
dx
dT
q
dx
Td
k===+=
=
;0;0
0
2
2
&
Integrating twice and employing the boundary conditions:
1
Cx
k
q
dx
dT v+−=&
21
2
2
CxC
x
k
q
Tv++−=&
with the boundary condition of 0=
dk
dT at x=0,
0;)0(011 =+−=CC
k
qv
&
and the boundary condition at =L
2
;
2
2
22
2L
k
q
TCC
L
k
q
Tv
S
v
S
&& +=+−=
yields
(
)
22
2xL
k
q
TT v
S−+=&
This solution is quadratic with the maximum temperature occurring at x = 0. Since the
hottest part of the slab is in the center, then the description of a microwave oven "…
cooking from the inside out" is accurate. Note, however, that we have examined only the
steady state temperature at this stage, and have not looked at the transient process to
achieve this steady state temperature distribution.
TS
X
L
T(x)
