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 21.8° C inside. The glass is 3.36 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.

h outer = ? W/m2-C°

h inner = ? W/m2-C°

Explanation / Answer

here,

outside temprature , Ti = 7.8 degree C

inside temprature , To = 8 degree C

outside temprature of air , Toa = 0 degree C

inside temprature of air , Tia = 21.8 degree C

the thermal conductivty for the glass , k = 0.8 W/m-C

A.

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

R = k1 * dT/d

R= 0.8* 0.2/0.00336

R = 47.62 W/m^2

the rate at which heat is conducted through the glass per square meter of window area is 47.62 W/m^2

B.

dQ/dt = k2*A*dT

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

We know (dQ/dt)/A from answer A.

To solve for h2 we simply need to divide that by dT,

which is 21.8 C - 8 C on the inside and

7.8 C - 0 C on the outside

Inside:

h2 = 47.62 /13.8

h2 = 3.45 W/m^2-C

Outside:

h2 = 47.62/7.8

h2 = 6.11 W/m^2-C

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