Transient Conduction
Consider a 2 m long metal cube has a convection heat transfer coefficient of 500 W/m^2∙K, and a thermal conductivity of 1,000 W/m∙K. Is the lumped capacitance model valid for this part?
Expand Hint
$$$Bi=\frac{hV}{kA_s}$$$
where
$$Bi$$
is the Biot Number,
$$h$$
is the convection heat transfer coefficient,
$$V$$
is the volume,
$$k$$
is the thermal conductivity, and
$$A_s$$
is the surface area.
Hint 2
The lumped capacitance model is valid if
$$Bi< 0.1$$
.
The lumped capacitance model is valid if
$$$Biot\:Number, Bi=\frac{hV}{kA_s}< 0.1$$$
where
$$h$$
is the convection heat transfer coefficient,
$$V$$
is the volume,
$$k$$
is the thermal conductivity, and
$$A_s$$
is the surface area.
$$$Bi=\frac{500W(2m)^3(m\cdot K)}{(m^2\cdot K)(1,000W)(6\cdot (2m)^2)}=\frac{4,000}{24,000}=0.167$$$
Since
$$Bi>0.1$$
, the Lumped Capacitance Model is
not valid
.
No
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