Answer:
The convective heat transfer coefficient of the fluid is 170.4 watts per square meter-degree Celsius.
Explanation:
The Nusselt number ([tex]Nu[/tex]) is a dimensionless factor which compares the sensitivity of a fluid due to convection with those due to conduction:
[tex]Nu = \frac{h\cdot L_{c}}{k}[/tex] (Eq. 1)
Where:
[tex]h[/tex] - Convective heat transfer coefficient, measured in watts per square meter-degree Celsius.
[tex]k[/tex] - Conductive heat transfer coefficient, measured in watts per meter-degree Celsius.
[tex]L_{c}[/tex] - Characteristic length, measured in meters.
In addition, the characteristic length of a cylinder is defined by the following formula:
[tex]L_{c} = \frac{\pi\cdot r^{3}\cdot l}{2\pi\cdot r^{2}+2\pi\cdot r \cdot l}[/tex] (Eq. 2)
Where:
[tex]r[/tex] - Radius of the cylinder, measured in meters.
[tex]l[/tex] - Length of the cylinder, measured in meters.
If we know that [tex]Nu = 14.2[/tex], [tex]k = 0.028\,\frac{W}{m\cdot ^{\circ}C}[/tex], [tex]r = 0.005\,m[/tex] and [tex]l = 0.07\,m[/tex], then the convective heat coefficient is:
From (Eq. 2):
[tex]L_{c} = \frac{\pi\cdot (0.005\,m)^{2}\cdot (0.07\,m)}{2\pi\cdot (0.005\,m)^{2}+2\pi\cdot (0.005\,m)\cdot (0.07\,m)}[/tex]
[tex]L_{c} = \frac{7}{3000}\,m[/tex]
And by (Eq. 1):
[tex]h = \frac{k\cdot Nu}{L_{c}}[/tex]
[tex]h = \frac{\left(0.028\,\frac{W}{m\cdot ^{\circ}C} \right)\cdot (14.2)}{\frac{7}{3000}\,m }[/tex]
[tex]h = 170.4\,\frac{W}{m^{2}\cdot ^{\circ}C}[/tex]
The convective heat transfer coefficient of the fluid is 170.4 watts per square meter-degree Celsius.
