CHE2163: HEAT AND MASS TRANSFER COMBINED HEAT AND MASS TRANSFER WEEK 12
Learning Objectives, Tasks, Readings, and Learn ChemE Videos
1. Analogieslinkingheatandmass transfer coefficients
(Cengel p 882-884)
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a. Reynold’sanalogy(Pr=Sc=1)
b. ChiltonColburnanalogy(Prand
Sc not equal to 1)
c. Limitations on applying Chilton- 1
2. Problemsinvolvingsimultaneousheat AND mass transfer (Cengel p 882-884)
a. Problemsinvolvingphase change – latent heat
b. Multi-modalbalancesfor determining latent heat rates
The expected learning outcome:
Apply Chilton-Colburn analogy to
calculate MTC/HTC
• Calculate latent heat rates or
temperatures given problems involving phase change
• Special case when v = DAB = a, hence: 𝑁𝑢 = 𝑆h = 𝑅𝑒 𝑓
• Now one can solve for HTC given MTC or vice-versa
4.1 REYNOLD’S ANALOGY – RESTRICTED CASE
4.2 CHILTON-COLBURN ANALOGY – GENERAL CASE
The Chilton-Colburn analogy links the heat and mass transfer coefficients for 0.6 < Pr < 60 and 0.6 < Sc < 3000:
𝑆𝑡!"#$ 𝑆𝑐 '.)* 𝑆𝑡%#&& = +𝑃𝑟/
Clearly this is a very limited case – what about something a little more useful?
Or, if we include all of the terms:
Stanton numbers are simply another set of dimensionless numbers that can be used in place of Sh/Nu;
• How can this be useful? We can use it to solve for h given k, or the other way around. For example, if we write a mass transfer rate equation, we can substitute for unknown k:
• Note that the limitation on using Chilton-Colburn analogy is that it only applies for low mass flux conditions, where the mass transfer flux does not affect fluid velocity. Therefore it cannot be applied to situations like boiling, condensation (outside scope of this unit – but unique Nu/Sh correlations are available to calculate heat and mass transfer coefficients – e.g. Cengel Ch 10.
4.3 SIMULTANEOUS HEAT AND MASS TRANSFER
• Any problem that involves phase change will involve simultaneous heat and mass transfer
• Phase change involves the flow of mass across phase boundaries (therefore – mass transfer)
• In order for phase change to occur, there must be latent heat absorption (and possible sensible heat transfer to achieve the necessary temperature before phase change) which is likely to generate temperature differences within or between the phases (therefore – heat transfer)
• Furthermore there may be other sources/sinks of heat transfer involved, including natural convection, radiation, conduction, etc – therefore these problems can also involve multi-modal heat transfer
• The key to solving these problems involves (a) calculating heat transfer components (convective, conductive, radiative terms), and then calculating evaporation rate using Chilton- Colburn analogy to determine mass transfer rate.
• Mixture properties such as CP, molar masses etc should be calculated at the mean film composition and temperature. For air-water vapour systems at atmospheric conditions
(and under low mass flux assumption), we can simply use the properties of the gas with reasonable accuracy.
EXAMPLES: list (derive) the relevant equations which will be used for solution of the example questions.
The energy balance must be satisfied, and we can use the Chilton-Colburn analogy to link h and k. As an example
𝑞̇"+#, =𝑚̇+h-.
where hfg is the latent heat of evaporation, measured in kJ/kg or J/kg and hence the rate of heat transfer in this case is in W. To determine the evaporative rate, we need a mass transfer equation:
𝑚̇ + = 𝑘 𝐴 ( 𝜌 + , & − 𝜌 + , 0 )
Where the concentrations terms relate to the vapour at the surface or in the bulk. We also know that for the convective term:
𝑞̇ =h𝐴(𝑇 −𝑇) 123+ 0&
If these are the only heat transfer terms in the energy balance, then we know that:
Applying the Chilton-Colburn analogy:
h = 𝜌𝐶4 𝐿𝑒'.)* 𝑘
Therefore:
Hence, we can solve for the surface temperature under steady state conditions. If it is a concentration we are trying to determine we could re-arrange to suit that as well.
To determine the mass transfer rate (kg/s), in this case an evaporative rate,
If the vapour is an ideal gas (good for most systems and certainly air/water),
And if we apply Chilton-Colburn analogy,
Finally, given that we are evaluating properties at the film condition, we can substitute this into the equation,
Check if the error in earlier ed. of Cengel is still there (Table 14 – 14), p.884
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