QUESTION $4[25$ MARKS$]$

A furnace is being used to heat a rectangular brick $(=0\mathrm{.}5).$ The furnace consists of $3$ layers;

the internal wall is fire brick $(k=1\mathrm{.}0\frac{W}{m}.K),$ intermediate wall is insulating brick

$\frac{W}{m}.K$ and the external wall is red brick $(k=0\mathrm{.}5\frac{W}{m}.K),$ with a thickness of $15cm,7\mathrm{.}5cm$

and $10cm,$ respectively. The internal wall temperature measures at $950C,$ while the

temperature between the fire brick and the insulating brick measures at $810C.$ The surface area

of the heated brick is $0\mathrm{.}2m$ by $0\mathrm{.}4m,$ placed in the centre of the furnace, and the average

surface temperature of the rectangular brick is $800C.$

$($a$)$ Calculate the heat flux through the wall and the external wall temperature of the

furnace.

$[15$ Marks$]$

$[$C$01,$ P$01,$ C$4]$

$($b$)$ For the case of dimensionless numbers of $N_{Pr}*N_{Gr}>{10}^9,$ determined the total heat flux

through radiation and convection occurring inside the furnace, through the top surface

of the brick. Please state all assumptions.

$[10$ Marks$]$

$[$C$01,$ P$01,$ C$4]$