Natural convection: air flows upward in a vertical heated cylindrical pipe. the fluid loses heat to the pipe walls as it flows upward. the incoming fluid temperature is th ('h' = "hot"), the pipe wall temperature is tc ('c' ="cold"). in the first case, the pipe radius is large enough that the boundary layers can be approximated as those for a vertical flat plate (sections 9.1 -9.4). find the nusselt number for the flow and then calculate the average convective heat transfer coefficient h and ý for pipe length h. in the second case, the pipe is thin enough that the entire pipe flow is fully developed (i. e., ignore the development length). the inflow is u(r) = umax [1 – (r/r.)2] with um = lap! /(84) with 14p! ~ p9b (th – tc). calculate the average convective heat transfer coefficient h and ġ for pipe length h. evaluate į versus d for both cases. now assume that as in the class example there is an array of tubes. there are now nx m tubes of diameter d in an l x w cross sectional area so nd x md = l x w or nxm= 6 ). to calculate the total heat transfer, multiply each ģ by the total number of tubes, n xm. then make an engineering estimate for the optimum value, if one exists. h . h iii)