b$)$

$(20$ marks$)$

A small electrically heated element of surface area $33\mathrm{.}2c{m}^2$ is enclosed in a large vessel. When steady state is reached, the following observations are recorded.

Voltage across heating element $-=7\mathrm{.}5V$

Current through the element $-=0\mathrm{.}68A$

Temperature of surface of element $-=90C.$

The temperature of the vessel may be taken as equal to the surrounding air temperature of $30C.$ The emissivity of the surface of the element may be taken as $0\mathrm{.}8.$

Using a representative sketch, determine;

i$)$ Heat exchange by radiation and natural convection between the element and vesse!

ii$)$ Natural convection heat transfer coefficient.

$(12$ marks$)$

$(5$ marks$)$