7.2 Consider fully developed laminar flow of a fluicd inside a wide rectangular

Question

7.2 Consider fully developed laminar flow of a fluicd inside a wide rectangular duct with both the upper and lower surface at uniform surface temperature, as schematically shown in the figure below. The effect of the two sides of the duct is neglected (W H), and at a location far from the entrance the velocity distribution is assumed to be uniform, 7.5 n(x) = Cu whereas the temperature distribution has a parabolic profile given by From the given velocity and temperature distribu- tions, calculate the Nusselt number, which is given by its definition as h H where Tb is the average bulk temperature of the flow- ing fluid at the specified location, and k is the thermal conductivity of the fluid. 7.6 Uniform surface temperature, T Oil flow en Problem 7.2 7.7 N

Explanation / Answer

A/C to 7.2 Nuh=hcH/k=q'(H/k)/(Ts-Tb) q'=-kdT/dx T=Ts+CT[1-(2x/H)2] dT/dx=-8CTx/H2

hcH/k=(8CTx/H)/(Ts-Tb) hc=8CTkx/(Ts-Tb) H A/C TO 7.3 mcpdT=hc(Ts-T)pdx m = mass flowrate

cp=heat capacity of water incase of 7.3 H=diameter p= perimeter Tb=bulk temperature =(ti+tf)/2

.5*3600*4180*(dT/(Ts-T))=[8CTkx/H(80-40)]pdx on integrating 7524000ln[(Ts-ti)/(Ts-tf)]=[3.14CTkd/5d](x2/2) L to 0

L=5130.76/(CTk).5

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