91Ó°ÊÓ

Heat flows from one point to another through conduction only when there is a temperature difference.The rate of heat flow by the conduction process can be obtained by examining the value of the thermal conductivity of the particular object, the area of the object, the thickness of the object, and the difference in the inner and outside temperatures.

The data given in example 14-8 is as follows:

The area of the window is\(A = 2.0\;{\rm{m}} \times {\rm{1}}{\rm{.5}}\;{\rm{m}}\).

The temperature of the inner surface is\({T_2} = 15.0{\rm{^\circ C}}\).

The thickness of the window is\(l = 3.2\;{\rm{mm}}\).

The external temperature is\({T_1} = - 5{\rm{^\circ C}}\).

From table 14-4,

The thermal conductivity of the glass is \({k_{\rm{g}}} = 0.84\;{{\rm{J}} \mathord{\left/{\vphantom {{\rm{J}} {{\rm{s}} \cdot {\rm{m}} \cdot {\rm{\circ C}}}}} \right.\\} {{\rm{s}} \cdot {\rm{m}} \cdot {\rm{\circ C}}}})\.

The rate of heat flow by conduction through the windows can be calculated by using the following expression:

\(\(frac{Q}{t} = kA\(frac{{{T_2} - {T_1}}}{l}\()

Here, k is the thermal conductivity, A is the cross-sectional area, l is the thickness of windows, and \(({T_1}\() and \(({T_2}\() are the temperatures.

Substitute the values in the above equation.

\([\(begin{array}{c}\(frac{Q}{t} = \(left( {0.84\(;{{\(rm{J}} \(mathord{\(left/{\(vphantom {{\(rm{J}} {{\(rm{s}} \(cdot {\(rm{m}} \(cdot {\(rm{\(circ C}}}}} \(right.\\} {{\(rm{s}} \(cdot {\(rm{m}} \(cdot {\(rm{\(circ C}}}}} \(right)\(left( {2.0\(;{\(rm{m}} \(times {\(rm{1}}{\(rm{.5}}\(;{\(rm{m}}} \(right)\(frac{{\(left[ {\(left( { - 15{\(rm{\(circ C}}} \(right) - \(left( { - 5{\(rm{\(circ C}}} \(right)} \(right]}}{{\(left[ {\(left( {3.2\(;{\(rm{mm}}} \(right)\(left( {\(frac{{{\(rm{1}}{{\(rm{0}}{{\(rm{ - 3}}}}\(;{\(rm{m}}}}{{{\(rm{1}}\(;{\(rm{mm}}}}} \(right)} \(right]}}\(\( = 1.6 \(times {104}\(;{\(rm{W}}\(end{array}\()

Thus, the rate of heat flow by conduction through the windows is \([1.6 \(times {104}\(;{\(rm{W}}\().