## Lumped Capacitance

Consider a 2 m long metal cube has a convection heat transfer coefficient of 750 W/m^2∙K, and a thermal conductivity of 500 W/m∙K. Is the lumped capacitance model valid for this part?

##
__
__**Hint**

**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**

**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.

$$$Bi=\frac{750W(2m)^3(m\cdot K)}{(m^2\cdot K)(500W)(6\cdot (2m)^2)}=\frac{6,000}{12,000}=0.5$$$

Since
$$Bi>0.1$$
, the Lumped Capacitance Model

**is not valid**.
No