Question

Problem 2 (10, pts) A 30-cm O.D. horizontal steam pipe has an outer surface temperature of 600K and is located in still air at 300K. Calculate the average heat transfer coefficient and the convective heat transfer per unit length of pipe.

Answer 1

Answer:

7.26 W/m^2 K ( average heat transfer coefficient )

2052.72 W  ( convective heat transfer per unit length of pipe )

Explanation:

Data given for this problem

Outer diameter ( O.D )  D = 30 CM = 0.3 m

outer surface temperature  Ts = 600K = 327⁰c

atmospheric temperature ( air temp ) Ta= 300k = 27⁰c

assuming ; steady state conditions and  atmospheric pressure = 1 atm

properties of air at film temperature which is = 177⁰c  = ( (Ts +Ta)/2)

thermal conductivity k  = 0.03625 W/m K

Kinematic viscosity , v = 3.17645 * 10^-5 m^2/s

Prandtl number, Pr = 0.6995

β = 1/450 = 2.22 * 10^-3

Rayleigh number (Rad) = $\frac{gB(Ts-Ta)D^3}{v^2} * Pr$

substituting the given values

Rayleigh number = 122.29 * 10^6

 Nu = $[0.6 + \frac{0.387Rad^\frac{1}{16} }{[1+(0.559/Pr)^\frac{9}{16}]^\frac{8}{27} } ]^2$

substituting all the given values

Nu = 60.05

A) calculate the average heat transfer coefficient

H avg = $\frac{K}{D} * Nu$

         =  (0.03625 / 0.3 ) * 60.05

         = 7.26 W/m^2 K

B)  calculate convective heat transfer per unit length of pipe

Q = H avg * ( $\pi$Dl )(Ts - Ta)

assuming l = 1 m

Q = 7.26 * ( $\pi$ * 0.3 * 1 )(327 -27 ) =  2052.72 W