Problem $5$: Oil at $150C$ flows slowly through a long, thin$-$walled pipe of $35-mm$ inner diameter. The pipe is suspended in a room for which the air temperature is $25C$ and the convection coefficient at the outer tube surface is $12\frac{(W)}{m^2(K)}.$ Estimate the rate of heat loss per unit length $(\frac{W}{m})$ of tube. $($Assume the tube wall thermal resistance negligible and fully developed flow, radiation exchanges are negligible.$)$

Properties: Table A$-5,$ Unused engine oil $)=150C=(423(K)$