$($d$)$ Calculate the total rate of heat transfer between the plates while the gap is fully

filled with super insulation material. Draw a thermal resistance circuit and use it

to explain the difference in heat transfer when compared with case $($c$).$

$(8$ marks$)$Question $7(25$ marks$)$

Figure Q$7$ shows two large plates held parallel to each other at specified temperatures

$T_1$ and $T_2.$ Constant temperature is maintained between the two plates and steady

conditions are applied. The thermal conductivity coefficients for three different

materials are:

$.k=0\mathrm{.}00011\frac{W}{m}K$ for super insulation,

$.k=0\mathrm{.}022\frac{W}{m}*K$ at $223K$ for air,

$.k=0\mathrm{.}045\frac{W}{m}*k$ for fiberglass insulation.

The plate area involved in the heat transfer equations is $A=2m^2$ and the vacuum

radiation coefficient is $6\mathrm{.}8{10}^{-8}\frac{W}{m^2}*K^4.$

Formula: $Q_{\text{c}\text{o}\text{n}\text{d}}=kA\frac{T_1-T_2}{L},Q_{\text{r}\text{a}\text{d}}=A(T_1^4-T_2^4)$

Figure Q$7.$ Heat transfer between two plates.

$($a$)$ Assume the surfaces of the two plates are all black and the emissivity $($radiation

diffusion coefficient$)$ is $=1\mathrm{.}2.$ Calculate the total rate of heat transfer between

the plates with air. Note no convection is considered in the air between the plates.

$(9$ marks$)$

$($b$)$ Calculate the total rate of heat transfer when the gap between the two plates is

fully filled with fibreglass.

$(4$ marks$)$

$($c$)$ Calculate the total rate of heat transfer between the plates while the gap is

evacuated as a vacuum.

$(4$ marks$)$

$($d$)$ Calculate the total rate of heat transfer between the plates while the gap is fully

filled with super insulation material. Draw a thermal resistance circuit and use it

to explain the difference in heat transfer when compared with case $($c$).$

$(8$ marks$)$