A pipe is insulated such that the outer radius of the insulation is less than the critical radius. Now the insulation is taken off. Will the rate of heat transfer from the pipe increase or decrease for the same pipe surface temperature?

Note that the critical radius of insulation depends on the thermal conductivity of the insulation k and the external convection heat transfer coefficient h .

[tex]r_{cr} =\frac{k}{h}[/tex]

The rate of heat transfer from the cylinder increases with the addition of insulation for outer radius less than critical radius (r₂< [tex]r_{cr}[/tex]) 0, and reaches a maximum when r₂ = [tex]r_{cr}[/tex], and starts to decrease for r₂< [tex]r_{cr}[/tex]. Thus, insulating the pipe may actually increase the rate of heat transfer from the pipe instead of decreasing it when r₂< [tex]r_{cr}[/tex] .

AFOKE88 AFOKE88 · Answer 2 · 2021-11-26T11:44:37+01:00

When the insulation is taken off, the rate of heat transfer at the same pipe surface temperature will; decrease.

The formula for critical radius of insulation is;

r_cr = k/h

Where;

k is thermal conductivity

h is external convection heat transfer coefficient

Now, the more the insulation the outer radius gets less than the critical radius, the more will be the rate of heat transfer.
In contrast, the more the insulation of the outer radius gets more than the critical radius, the less will be the heat transfer.

Thus, if the insulation is taken off, it means that the heat transfer would be reduced.

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