Answer:
The convection coefficient is ![15456.48\ W/m^{2}K](https://tex.z-dn.net/?f=15456.48%5C%20W%2Fm%5E%7B2%7DK)
Solution:
Mass flow rate, ![\dot{m} = 0.4\ kg](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%20%3D%200.4%5C%20kg)
Inner diameter of the tube, d = 0.014 m
Fluid density, ![\rho_{f} = 990\ kg/m^{3}](https://tex.z-dn.net/?f=%5Crho_%7Bf%7D%20%3D%20990%5C%20kg%2Fm%5E%7B3%7D)
Specific Heat, C = 3845 J/K
Thermal Conductivity, K = 0.74
Prandtl Number, ![P_{r} = 8.6](https://tex.z-dn.net/?f=P_%7Br%7D%20%3D%208.6)
Heat flux, ![\dot{q} = 71,297\ W/m^{2}](https://tex.z-dn.net/?f=%5Cdot%7Bq%7D%20%3D%2071%2C297%5C%20W%2Fm%5E%7B2%7D)
Viscosity, ![\mu = 0.00079\ Ns/m^{2}](https://tex.z-dn.net/?f=%5Cmu%20%3D%200.00079%5C%20Ns%2Fm%5E%7B2%7D)
Now,
To calculate the convection heat coefficient, h:
Determine the cross sectional area of the circular tube:
Determine the velocity of the fluid inside the tube by mass flow rate:
![\dot{m} = \rho_{f}A_{c}v](https://tex.z-dn.net/?f=%5Cdot%7Bm%7D%20%3D%20%5Crho_%7Bf%7DA_%7Bc%7Dv)
![0.4 = 990\times 1.54\time 10^{- 4}v](https://tex.z-dn.net/?f=0.4%20%3D%20990%5Ctimes%201.54%5Ctime%2010%5E%7B-%204%7Dv)
v = 2.624 m/s
Determine the Reynold's Number,
:
![R_{e} = \frac{\rho_{f}dv}{\mu}](https://tex.z-dn.net/?f=R_%7Be%7D%20%3D%20%5Cfrac%7B%5Crho_%7Bf%7Ddv%7D%7B%5Cmu%7D)
![R_{e} = \frac{990\times 0.014\times 2.624}{0.00079} = 46036.253](https://tex.z-dn.net/?f=R_%7Be%7D%20%3D%20%5Cfrac%7B990%5Ctimes%200.014%5Ctimes%202.624%7D%7B0.00079%7D%20%3D%2046036.253)
Thus it is clear that
> 10,000 hence flow is turbulent.
Now,
Determine the Nusselt Number:
![N_{u} = 0.023R_{e}^{0.8}P_{r}^{0.4}](https://tex.z-dn.net/?f=N_%7Bu%7D%20%3D%200.023R_%7Be%7D%5E%7B0.8%7DP_%7Br%7D%5E%7B0.4%7D)
![N_{u} = 0.023\times 46036.253^{0.8}\times 8.6^{0.4} = 292.42](https://tex.z-dn.net/?f=N_%7Bu%7D%20%3D%200.023%5Ctimes%2046036.253%5E%7B0.8%7D%5Ctimes%208.6%5E%7B0.4%7D%20%3D%20292.42)
Also,
![N_{u} = \frac{dh}{K}](https://tex.z-dn.net/?f=N_%7Bu%7D%20%3D%20%5Cfrac%7Bdh%7D%7BK%7D)
where
h = convection coefficient
Now,
![292.42 = \frac{0.014\times h}{0.74}](https://tex.z-dn.net/?f=292.42%20%3D%20%5Cfrac%7B0.014%5Ctimes%20h%7D%7B0.74%7D)
![h = 15456.48\ W/m^{2}K](https://tex.z-dn.net/?f=h%20%3D%2015456.48%5C%20W%2Fm%5E%7B2%7DK)