Question

Water flowing at a rate of 0.03 kg/s is heated from 20 to 40°C in a horizontal pipe (inside diameter = 3 cm). The inside pipe surface temperature is 70°C. Estimate the convective heat transfer coefficient if the pipe is 1 m long. Assume forced convection conditions.  Ts is not held constant!

Properties of Water

	20°C	30°C	40°C
ρ (kg/m3)	998.2	995.7	992.2
k (W/mK)	0.597	0.615	0.633
μ (Pa s)	993.414 x 10-6	792.377 x 10-6	658.026 x 10-6
Cp (KJ/Kg K)	4.182	4.176	4.175
α (m2/s)	0.143 x 10-6	0.149 x 10-6	0.151 x 10-6
NPr	7.0	5.4	4.3

	A.	442.6 W/m2°C
	B.	262.6 W/m2°C
	C.	82.6 W/m2°C
	D.	662.6 W/m2°C

Answer 1

Water flowing at mass rate m = 0.03 kg/s is heated from 20 C to 40 C.

Inside surface pipe temperature Ts = 70 C

Diameter of pipe d = 0.03 m

Length of pipe L = 1m

Calculations : for this calculation we take data for water at mean bulk temperature Tm = (20 + 40)/2 = 30 C

at 30 C,

Prandtl number Pr = 5.6

Viscosity mub = 792.37*10^-6 Pa.s

Density rho = 995.7 kg/m3

Thermal conductivity k = 0.615 W/m.k

By table, At 70 C, viscosity of water at surface mus = 0.4024*10^-3 Pa.s

Reynolds number :

mass flow rate m = rho*A*v

A = π/4 *d^2

Re = rho*v*d/mub = rho*A*v*d/A*mub = 4m/π*d*mub

Re = 4*0.03/(3.14*0.03*792.37*10^-6) = 1607.6

Here Re< 2100 it means flow is laminar then

For heat transfer correlation for laminar flow,

Nu = 1.86*(Re*Pr*d/L)^(1/3) * (mub/mus)^0.14

Nu = 1.86*(1607.6*5.4*0.03/1)^(1/3) * (0.7923*10^-3/0.4024*10^-3)^(0.14)

Nu = 13.05

hd/k = 13.05

h = 13.05*0.615/0.03 = 267.5 W/m2.k

heat transfer coefficient in pipe h = 267.5 W/m2.k

it means right ans is B) 262.6 W/m2.C