Consider steady heat transfer between two large parallel plates at constant temperatures of T1? = 290?K and T2 = 150?K that are L = 2 cm apart. Assuming the surfaces to be black (emissivity ? = 1), determine the rate of heat transfer between the plates per unit surface area assuming the gap between the plates is (a) filled with atmospheric air, (b) evacuated, (c) filled with fiberglass insulation, and (d) filled with superinsulation having an apparent thermal conductivity of 0.00015 W/m•K.

Question

What will be an ideal response?

Answer 1

Two large plates at specified temperatures are held parallel to each other. The rate of heat transfer between the plates is to be determined for the cases of still air, evacuation, regular insulation, and super insulation between the plates.

Assumptions 1 Steady operating conditions exist since the plate temperatures remain constant. 2 Heat transfer is one-dimensional since the plates are large. 3 The surfaces are black and thus ? = 1. 4 There are no convection currents in the air space between the plates.

Properties The thermal conductivities are k = 0.00015 W/m•°C for super insulation, k = 0.01979 W/m•°C at -50°C (Table A-15) for air, and k = 0.036 W/m•°C for fiberglass insulation (Table A-6).

Analysis (a) Disregarding any natural convection currents, the rates of conduction and radiation heat transfer



(b) When the air space between the plates is evacuated, there will be radiation heat transfer only. Therefore,



(c) In this case there will be conduction heat transfer through the fiberglass insulation only,



(d) In the case of superinsulation, the rate of heat transfer will be



Discussion Note that superinsulators are very effective in reducing heat transfer between to surfaces.