On a cold night the temperatures of the two surfaces of a glass windowpane in a

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 24.0° C inside. The glass is 3.24 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.

Explanation / Answer

glass windowpane in a house are 7.8° C

outer surface and 8.0° C

air temperature is 0° C

outside and 24.0° C

glass is 3.24 mm thick

thermal conductivity for glass is 0.8 W/m-C°

  A). (dQ/dt)/A = k1*dT/d = 0.8*0.2/0.00324 = 49.382 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 24.8-8 C on the

inside and 7.8-0 C on the outside.

Inside: k2 = 49.382/16.8 = 2.9394 W/m^2-C

Outside: k2 = 49.382/7.8 =6.3310 W/m^2-C

Note that k2 is a property of the air, not the glass.

Typical values for air are quoted in the ref as 10 to 100,

so these answers are below the "typical" range.

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