Question

On a cold night the temperatures of the two surfaces of a glass windowpane in a house are 7.8° C on the outer surface and 8.0° C on the inner surface when the air temperature is 0° C outside and 25.0° C inside. The glass is 2.73 mm thick. (The thermal conductivity for glass is 0.8 W/m-C°.)

(a) Find the rate at which heat is conducted through the glass per square meter of window area.


(b) Find the value of the convection coefficients for the heating of the inner surface of the glass and for the cooling of the outer surface.

houter	=  W/m2-C°
hinner	=  W/m2-C°

Answer 1

(a) Rate at which heat is conducted through the glass per square meter of window area = (dQ/dt)/A

= k1*dT/d

= 0.8*(8.0 - 7.8) / 0.00273

= 58.61 W/m^2

(b) From the ref, dQ/dt = k2*A*dT

=> k2 = (dQ/dt)/(A*dT)

We know (dQ/dt)/A from answer (a). To solve for k2 we simply need to divide that by dT, which is (25 - 8) = 17 deg C on the inside and (7.8-0) = 7.8 deg C on the outside.

Therefore, convection coefficient of outer environment = h (outer) = 58.61 / 7.8 = 7.514 W/m^2-C

And, convection coefficient of inner environment = h(inner) = 58.61 / 17 = 3.45 W/m^2-C