Question 3.298E: A water-heater is covered up with insulation boards over a t...

A water-heater is covered up with insulation boards over a total surface area of 30 ft ^{2}. The inside board surface is at 175 F and the outside surface is at 70 F and the board material has a conductivity of 0.05 Btu/h ft F. How thick a board should it be to limit the heat transfer loss to 720 Btu/h ?

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Steady state conduction through a single layer board.

\dot{Q}_{\text {cond }}= k \text { A } \frac{\Delta T }{\Delta x } \Rightarrow \Delta x = k A \Delta T / \dot{ Q }

 

\Delta x=0.05 \frac{\text { Btu }}{\text { h-ft-R }} \times 30   ft ^{2}(175-70)  R / 720   Btu / h

 

= 0.219 ft = 2.6 in

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