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• A boiling fluid consists of a two-phase mixture of vapor and liquid. When

such a fluid flows through a tube, a number of distinct flow regimes can

occur depending on the flow rate and the relative amounts of vapor and

liquid present. Two-phase flow is thus more complex than single-phase

flow, and special methods are needed to calculate the pressure drop in

equipment handling boiling fluids.

• Condensation is the reverse of boiling, and the condensing curve is the

same as the boiling curve. Thus, many of the computational difficulties

encountered in the analysis of reboilers are present in condensers as well.

For wide-boiling mixtures, in particular, the nonlinearity of the condensing

curve and the variation of liquid and vapor properties over the condensing

range mean that a zone or incremental analysis is required for rigorous

calculations.

• In reboilers and vaporizers, boiling usually takes place either on the

exterior surface of submerged tubes or on the interior surface as the fluid

flows through the tubes. In the former case the tubes are oriented

horizontally, while in the latter they may be either horizontal or vertical

Boiling / Condensation Heat Transfer

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Condensation on Vertical Tubes

• The average heat-transfer coefficient, h, for the condensate

film can now be obtained by integrating the local coefficient

over the length, L, of the wall:

• For tube diameters of practical interest, the effect of wall

curvature on the condensate film thickness is negligible.

Hence, above Equation can be used for condensation on either

the internal or external surfaces of vertical heat-exchanger

tubes. The alternate form, below Equation is also applicable

with the appropriate modification in equivalent diameter.

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Determine laminar/turbulant conditions

For a bank of nt tubes, the wetted perimeter is ntπD, where D is either the inner

or outer tube diameter, depending on whether condensation occurs inside or

outside the tubes.

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For vertical tubes, A / P = L , whereas, for horizontal tubes A/P = 3.14 D

Condensation on Horizontal Tubes

• The Nusselt analysis for condensation on the external surface

of a horizontal tube is similar to that for a vertical surface. The

result corresponding to:

The alternate form is:

Where:

Above equations apply to a single tube or a single row of tubes.

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Turbulent/Laminar !!

In trying to calculate Re we found it is dependent on the mass flow

of the condensate but this depends on the heat transfer coefficient,

which is depending on Re. To solve the problem we assume either

laminar or turbulent flow. Then calculate the heat transfer

coefficient and check the Re number to confirm whether the

assumption was correct

Let us assume laminar film condensation.

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Example: Condensation on tube bank

One hundred tubes of 0.5 in (1.27 cm) diameter are

arranged in a square array and exposed to atm steam.

Calculate the mass of steam condensed per unit length of

tubes for a tube wall temperature of 98C

Solution

The condensate properties are obtained from the previous

example, and replacing d by nd,

Where n =10

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1)

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Heat-Transfer Coefficients for Pure Component Nucleate Boiling for a Single

Tube

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Heat-Transfer Coefficients for Pure Component Nucleate

Boiling in tube bundles

• Heat-transfer coefficients for boiling on tube bundles are generally higher

than for boiling on single tubes under the same conditions. Palen [4]

presented an approximate method for calculating convective effects. The

average boiling heat transfer coefficient, hb, is expressed as follows:

where hnc is a heat-transfer coefficient for liquid-phase natural convection and Fb can be

calcualted using:

The coefficient, hnc, can be estimated using equation:

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1.1)

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1.2)

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1.3)

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( )

2)

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Bubbly flow: At low vapor fractions, vapor bubbles are

dispersed in a continuous liquid phase.

Slug flow: At moderate vapor fractions and relatively low

flow rates, large bullet-shaped vapor bubbles flow through

the tube separated by slugs of liquid in which smaller

bubbles may be dispersed. A percolating coffee pot

exemplifies this type of flow.

Churn flow: At higher flow rates, the large vapor bubbles

present in slug flow become unstable and break apart,

resulting in an oscillatory, or churning, motion of the liquid

upward and downward in the tube.

Annular flow: At high vapor fractions and high flow rates,

the liquid flows as a film along the tube wall while the vapor

flows at a higher velocity in the central region of the tube.

This condition, which is characteristic of flows with a high

mass flux, is referred to as wispy annular

flow.

Mist Flow: At very high vapor fractions, the liquid phase

exists entirely as droplets entrained in a continuous vapor

phase.

Two phase flow regimes

where ΔTx is the temperature difference between the surface and

saturated liquid in Celsius and p is the pressure in Mega pascals. The

heat-transfer coefficient has the unit of watts per square meter per

Celsius. This equation is valid for a pressure range of 5-170 atm

Convective Boiling heat transfer Coefficient

(Vertical Tubes)

Forced-convection inside vertical tubes can be found using the

following two methods

First Method

ℎ = 2.54(∆𝑇𝑥)3𝑒𝑝/1.551

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Convective Boiling heat transfer Coefficient

(Vertical Tubes)

• Chen Correlation

and

Note that the Reynolds number in this equation is calculated using the

flow rate of the liquid phase alone.

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A reboiler is a heat exchanger that is used to generate the vapor

supplied to the bottom tray of a distillation column. The liquid from

the bottom of the column is partially vaporized in the exchanger,

which is usually of the shell-and-tube type. The heating medium is

most often condensing steam, but commercial heat-transfer fluids and

other process streams are also used. Boiling takes place either in the

tubes or in the shell, depending on the type of reboiler. Exchangers that

supply vapor for other unit operations are referred to

as vaporizers, but are similar in most respects to reboilers.

Thermal and hydraulic analyses of reboilers are generally more complex than

for single-phase exchangers. Some of the complicating factors are the following:

• Distillation bottom liquids are often mixtures having substantial boiling

ranges. Hence, the physical properties of the liquid and vapor fractions can

exhibit large variations throughout the reboiler. Thermodynamic

calculations are required to determine the phase compositions and other

properties within the reboiler.

• A zone or incremental analysis is generally required for rigorous

calculations.

• Two-phase flow occurs in the boiling section of the reboiler and, in the case

of thermosyphon units, in the return line to the distillation column.

• For recirculating thermosyphon reboilers, the circulation rate is determined

by the hydraulics in both the reboiler and the piping connecting the

distillation column and reboiler. Hence, the reboiler and connecting piping

must be considered as a unit. The hydraulic circuit adds another iterative

loop to the design procedure.

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