Question

Its winter time, and you areinsulating your windows with plastic shrink wrap(although it’s a little late). You need to calculatethe optimal spacing between the window pane and the shrink wrap to minimize the overall heat loss fromthe house. Using your knowledge of free convection in enclosures, calculate the optimal gap width.Assume that the average temperature outside is 0°C, and the inside temperature is 20°C. You can assume the window pane is the same temp as the outside air and the plastic wrap is the same temp as the inside of the house. State any assumptions you make in your analysis.

Answer 1

Suppose window's cross section area is A m²

So, wrap cross section area will also be A m² and let suppose that wrap width or thickness be 'x' metres

Inside room temperature = 20⁰C

Outside room temperature = 0⁰C

Let convective heat transfer coefficient of air inside and outside the house = h (W/m²K)

Let thermal conductivity of wrap material = 'K' (W/mK)

Therefore , overall heat transfer 'Q' is given by

For minimum heat loss, we are differentiation Q with 'x'

For minima , equating above equation to 0,

Hence ,for minima heat loss all values of 'x' will be able to insulate the window from outside