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Chapter 4
Transient Heat Conduction
443
A rib is roasted in an oven. The heat transfer coefficient at the surface of the rib, the temperature of
the outer surface of the rib and the amount of heat transfer when it is rare done are to be determined. The
time it will take to roast this rib to medium level is also to be determined.
Assumptions
1
The rib is a homogeneous spherical object.
2
Heat conduction in the rib is onedimensional
because of symmetry about the midpoint.
3
The thermal properties of the rib are constant.
4
The heat
transfer coefficient is constant and uniform over the entire surface.
5
The Fourier number is
τ
> 0.2 so that
the oneterm approximate solutions (or the transient temperature charts) are applicable (this assumption
will be verified).
Properties
The properties of the rib are given to be
k
= 0.45 W/m.
°
C,
ρ
= 1200 kg/m
3
,
C
p
= 4.1 kJ/kg.
°
C,
and
α
= 0.91
×
10
7
m
2
/s.
Analysis
(
a
) The radius of the roast is determined to be
Oven
163
°
C
Rib,
4.5
°
C
m
08603
.
0
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 Fall '10
 Dr.DanielArenas
 Thermodynamics, Mass, Heat

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