A proposed method to reduce heat losses from a horizontal, isothermal cylinder placed within a large room is to encase it within a larger cylinder, as shown in the schematic, with all surfaces painted with a low emissivity coating.

Air at atmospheric pressure exists within the annular region. For a concentrically located inner cylinder of surface temperature T_i = 70°C and radius r_i = 20 mm, and for an ambient temperature of T_∞ = 30°C, determine the optimal radius of the outer cylinder r_o that will minimize the convection heat loss. Compare the convection heat loss from the inner cylinder with the optimally sized outer cylinder in place to the heat loss without the outer cylinder. Is the approach effective?

Transcribed Image Text:

Quiescent air, T Air- Flow pattern T;> To -Inner cylinder, r,, T₁ -Outer cylinder, Tor To