BACKGROUND Remember the critical insulation radius for heat

BACKGROUND Remember the critical insulation radius for heat transfer in radial systems? R_crit = k_insulation/h This was the insulated radius which maximizes the convection heat transfer from a cylinder (chapter 3). However, the derivation in chapter 3 assumed that the convection heat-transfer coefficient h was a constant, independent of temperature and the diameter of the cylinder. Now we have learned that any form of convection heat transfer from the surface of a cylinder depends on the diameter D. Furthermore, in free convection, the convection heat-transfer coefficient depends also on the temperature difference between the free surface and the fluid in a somewhat complex fashion given by the Rayleigh number. PROBLEM STATEMENT An array of horizontal steam pipes (say, at 100 degree C) will be housed in the basement of an office building, and the architect has decided to insulate the pipes so as to maximize the heat-transfer to the basement air. The insulation material has conductity k=0.55[w/m degree C], the ambient air temperature in the basement is 13 degree C, and the air is still (free convection). Complete the following table for the architect, where r_crit is the radius, including insulation, at which the heat transfer is maximized.

Solution

The answer of the following question is as follows .

The value maximum heat transfer from the given table is suited the best is 89kj/kg