Question

A fluid is flowing through a circulat tube at 0.4 kg/s. Tube inner surface is smooth with a diameter 0.014 m. Fluid density is 990 kg/m^3, specific heat is 3,845 J/(kg-K), viscosity is 0.00079 Ns/m^2, thermal conductivity is 0.74, and Prandtl number is 8.6. A uniform heat flux of 71,297 W/m^2 is supplied to the flow from the surface. If the flow is fully developed, what is the convection coefficient in W/(m^2-K)

Answer 1

Answer:

The convection coefficient is $15456.48\ W/m^{2}K$

Solution:

Mass flow rate, $\dot{m} = 0.4\ kg$

Inner diameter of the tube, d = 0.014 m

Fluid density, $\rho_{f} = 990\ kg/m^{3}$

Specific Heat, C = 3845 J/K

Thermal Conductivity, K = 0.74

Prandtl Number, $P_{r} = 8.6$

Heat flux, $\dot{q} = 71,297\ W/m^{2}$

Viscosity, $\mu = 0.00079\ Ns/m^{2}$

Now,

To calculate the convection heat coefficient, h:

Determine the cross sectional area of the circular tube:

$A_{c} = \frac{\pi}{4}d^{2} = \frac{\pi}{4}\times (0.014)^{2} = 1.54\time 10^{- 4}\ m^{2}$

Determine the velocity of the fluid inside the tube by mass flow rate:

$\dot{m} = \rho_{f}A_{c}v$

$0.4 = 990\times 1.54\time 10^{- 4}v$

v = 2.624 m/s

Determine the Reynold's Number, $R_{e}$:

$R_{e} = \frac{\rho_{f}dv}{\mu}$

$R_{e} = \frac{990\times 0.014\times 2.624}{0.00079} = 46036.253$

Thus it is clear that $R_{e}$ > 10,000 hence flow is turbulent.

Now,

Determine the Nusselt Number:

$N_{u} = 0.023R_{e}^{0.8}P_{r}^{0.4}$

$N_{u} = 0.023\times 46036.253^{0.8}\times 8.6^{0.4} = 292.42$

Also,

$N_{u} = \frac{dh}{K}$

where

h = convection coefficient

Now,

$292.42 = \frac{0.014\times h}{0.74}$

$h = 15456.48\ W/m^{2}K$