- #1

Ciocolatta

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## Homework Statement

An evaporator is required to move 1000kgh-1 of water from a milk stream.

Steam is available for heating the evaporator (by condensation) at a pressure of 70.1 kPa absolute and a temperature of 90 decrees celcius.

The vapour, into which the water is evaporated from the milk, is at a pressure of 47.4kPa absolute and a temperature of 80 degrees celcius.

Number of tubes: 50

Tube inside diameter: 50mm

Tube length: 3m

tube thickness: 3mm

do one pass through calculation to

a) estimate an overall mass transfer coefficient for the evaporation

b) estimate the driving force for mass transfer

c) compare the mass transfer area required wit hthe original mass transfer area from the specification of the design variables.

## Homework Equations

antoine equation:

pressure(Pa) = 133.3 exp (18.3036 - 3816.44/(T(in celcius) + 277.02))

heat of vaporisation for water/steam = 2200 kJ/kg

properties for steam (both condensing and evaporating):

K (W/mK) = 0.023

density (kg/m3) = 0.45

Diff (m2/s) = 1.5 x 10^5

viscosity (kg/ms) = 1 x 10^-5

thermal conductivity of tube material: 45 W/mK

condensation heat transfer coefficient for steam at 90 degrees celcius: 10,000 W/m2K

overall mass transfer coefficient (m/s) from gas phase perspective:

K = 1 / [1/k(gas) + H(gas->liquid)/k(liquid)]

k(gas) = gas film mass transfer coeff

k(liquid) = liquid film mass transfer coeff

H(gas->liquid) = henry's law constant between liquid and gas (dimensionoless)

N = K * A * deltaC(LMTD)

N = mass transfer rate (kg/s)

A = mas transfer area (m2)

deltaC(LMTD) = log mean concentrarion driving force (kg/m3) = deltaC1-deltaC2/ln(deltaC1/deltaC2))

C1 and C2 are concentration driving forces at one and the other end of the mass exchanger.

## The Attempt at a Solution

this is a design question...so we're allowed to make assumptions where necessary. But the problem is...I'm not sure if I'm allowed to assume some mass transfer coefficients or if I can calculate them with the information above.

I don't really understand how to do this.

im assuming the gas MT coeff = 20, and liquid MT coeff = 200 which fall in the typical ranges

and i think henry's constant for gas --> liquid = gas mole frac/ liquid mole frac

where gas mole frac = absolute pressure of water in steam / absolute pressure of steam = 47.4/70.1

im really stuck... =/