Consider a single pane window. The dimensions of the ¼-inch-thick glass window pane are about 0.9 m by 1.65 m. The surface temperatures of the glass will not be equal to the air temperature on the respective sides, as will be seen later in the course. For these conditions, the glass surface temperatures are approximately 1°F and -7°F. (At this time, we do not have the HT skills to calculate the surface temperatures.) Determine the heat transfer rate vector through the glass for these surface temperatures. Express your answer in vector notation. Your sketch should identify your coordinate system and your vector answer should agree with your sketch. For consistency, set your coordinate system such that the inside glass surface is at the origin and the outside surface is in the positive x direction (typically to the right!).

The heat will be conducted through the glass. We use a frame of reference with the origin on the warmer side of the glass (t1) and the positive X axis pointing perpendicular to the glass towards the colder side.

The Fourier equation for plates (one dimensional form) is:

q = -K * dT / dx

We can simplify dT/dx to ΔT/Δx if we assume the temperature changes linearly through the glass.

q = -K * ΔT/Δx

K is the thermal conductivity of the glass

ΔT = t2 - t1

ΔT = -21.7 + 17.2 = -4.5 C

Δx is the thickness of the glass

q = -K * -4.5 / 0.00635

q = 709 * k

The vector is: q = (709*K*i + 0*j + 0*k)

It has no components in Y or Z because there if no variation of temperature in those directions (the temperature of the glass is given as each face having a constant temperature throughout its area).