Question

The The thermal conductivity of a sheet of rigid, extruded insulation is reported to be k=0.029 W/ m measured temperature difference across a 25-mm-thick sheet of the material is T1 - 72 = 12°C. (a) What is the heat flux through a 3 mx 3 m sheet of the insulation? (b) What is the rate of heat transfer through the sheet of insulation? (c) What is the thermal resistance of the sheet due to conduction?

Answer 1

Answer:

Heat flux = 13.92 W/m2

Rate of heat transfer throug the 3m x 3m sheet = 125.28 W

The thermal resistance of the 3x3m sheet is 0.0958 K/W

Explanation:

The rate of heat transfer through a 3m x 3m sheet of insulation can be calculated as:

$q=-k*A*\frac{\Delta T}{\Delta X}\\\\q=-0.029\frac{W}{m*K}*(3m*3m)*\frac{12K}{0.025m} =125.28W$

The heat flux can be defined as the amount of heat flow by unit of area.

Using the previous calculation, we can estimate the heat flux:

$heat \, flux=\frac{q}{A}=\frac{125.28 W}{9 m^{2} } =13.92 W/m^{2}$

It can also be calculated as:

$q/A=-k*\frac{\Delta T}{\Delta X}$

The thermal resistance can be expressed as

$\Delta T=R_t*Q\\R_t=\Delta T/Q=\frac{\Delta X}{k*A}$

For the 3m x 3m sheet, the thermal resistance is

$R_t = \frac{\Delta X}{k*A}=\frac{0.025m}{0.029W/mK*9m^{2}}=0.0958 \, K/W$