5 water passes through a long tube in diameter at a mean vel

5) water passes through a long tube in. diameter at a mean velocity of 6 ft/s. The water enters the tube at leaves at F. inner surface of the tube is held at a constant temperature of 90 Determine the heat transfer from the tube over the length of the tube. all your work. 20 Points)

Solution

GIVEN:- Diameter of tube D = 1in = 0.0254m, Mean velocity V = 6ft/s, Tin = 60F = 288.70K, Ttube = 190F = 360.93K

TO FIND:- Heat transfer per unit length Q = ?

SOLUTION:-

Reynold\'s number for Water Re = 25.8 and Pr = 7.46 (By standard formula),

Thermal conductivity of water k = 0.6 W/mK

Using use the Churchill-Bernstein correlation,we find Nud as follows-----

Nud = 0.3 + [ (0.62 x Re^0.5 x Pr^0.333) / (1 + (0.4 / Pr^0.666)^0.25 ] x [ 1 + (Re/282000)^0.625]^0.8

So, Nud = 6.24

Now Nud = h x D / k, so h = Nud x k / D, i.e. h = 6.24 x 0.6 / 0.0254 = 147.40 W/m2 K

Now heat transfer Q = h x 3.142 x D (Ttube - Tin) = 147.40 x 3.142 x 0.0254 (360.93 - 288.70) = 849.68 W/m

i.e. Heat transfer per unit length Q = 849.68 W/m (ANSWER)