Shellandtube heat exchangers with hundreds of tubes housed i

Shell-and-tube heat exchangers with hundreds of tubes housed in a shell are commonly used in practice for heat transfer between two fluids. Such a heat exchanger used in an active solar hot-water system transfers heat from a water-antifreeze solution flowing through the shell and the solar collector to fresh water flowing through the tubes at an average temperature of 60 degree C at a rate of 15 Us. The heat exchanger contains 80 brass tubes 1 cm in inner diameter and 1.5 m in length. The roughness of brass tubing is epsilon = 1.5 times 10^-6 m. Determine the pressure drop across a single tube. Calculate the pumping power required by the tube-side fluid of the heat exchanger. After operating for a long time, 1-mm-thick scale builds up on the inner surfaces with an equivalent roughness of 0.4 mm. For the same pumping power input, determine the percent reduction in the flow rate of water through the tubes.

Solution

Let f(x) =y

Sin(y-5)=2x-1

{Sin(y-5) +1}/2=x

Replace x by f inverse and y by x

Hence inverse of f is

{Sin(x-5)+1}/2