Question

Consider a 9 mm diameter circular tube, calculate the length of tube that is required to transfer 100 W of
water that circulates through the tube at a rate of 0.08 kg / s.
The temperature of the water is kept constant at 50 ° C and the wall
of the tube is maintained at 45 ° C.

Answer 1

Mass flow rate of water = 0.08 kg/sec.

Dia of tube = 0.009 m

Mass flow rate = density *Area*velocity.

Velocity = Mass flow rate/( density*area) = 0.08/(1000*0.785*0.009*0.009) = 1.25 m/sec

Reynolds number = Re = velocity*Dia of pipe / Kinetic viscosity of water

Re = 1.25*0.009 / 1.003*10^-6 = 11216

Let us use dittus- Bolter equation to find convective heat transfer coefficient.

Prandtl number of water at 18c = 7.56

According to Dittus bolter equation,

Nu = 0.023*Re^0.8 * Pr^0.3.

Nu = 0.023 * (11216)^0.8* (7.56)^0.3 = 73.30

ther mal conductivity of water =0.65 W/m-k

heat transfer coefficient = h = Nu*k/D = 73.30 * 0.65/0.009 = 5293 W/m² K.

from heat balance Q= hA(T_w - T_water)

Q = 100 W

A = 3.14*D*L

Where D= dia = 0.009 m.

L =need to find=?

T_w = temp of water = 50C

T_wall = temp of wall = 45 C.

By substituting all we get

100 = 5293*3.14*0.009*L*(50-45)

Length of pipe required = L=0.133 m = 133 mm.