MECH5320 Convective Heat and Mass Transfer
Take home test 3
1. It is known that flow boiling heat transfer coefficient hfb for saturated flow in
vertical tubes depends on the convective heat transfer coefficient (without boiling)
hlo, the diameter of the tube D, the mass flow rate m (kg/s), the dimensionless
quality of the steam x , the latent heat hfg, the tube wall heat flux qw and the
densities of the vapor and liquid g and l, i.e.,
h fb  Fn( x, hlo , D, m, h fg , qw ,  g ,  l )
Please carry out a dimensional analysis on this problem.
2. (a) Suppose that you have pits of roughly 0.002 mm diameter in a metallic heater
surface. At what temperature might you expect the water to boil on that surface if
the ambient pressure is 20 atm. (b) Measurements have shown that water at
atmospheric pressure can be superheated about 200 C above its normal boiling
point. Roughly how large an embryonic bubble can trigger a nucleation boiling in
water in such a state. (Please refer to thermodynamics books for the properties of
water and vapor)
3. In a natural convection on a hot vertical surface, if the
velocity and temperature profiles are of the following
forms (boundary layer thickness  and thermal boundary
layer thickness T are known)
u
y
y
y
 ( )  a ( ) 2  b( )3
V ( x) 


T  T
y
y
 d  e( )  f ( ) 2
Ts  T
T
T
(a) Write down the governing equations and boundary
conditions for this natural convection problem
(thermal expansion coefficient is  , and the density
of the fluid is 
(b) Determine the values of a, b, c, d,e
(c) Determine the expression of V(x) in terms of 
(d) Determine the location y where u achieves its maximum and the corresponding
maximum u value.
4. What are the Taylor instability and Helmholtz instability in a pool boiling? How
can these two instabilities affect the qmax? Will the relationship keep the same for the
boiling in a micro channel?