HEAT TRANSFER IN FALLING FILMS

Before die start of die lab lesson you should be able to explain / answer

die following points or questions regarding heat transfer in falling films:

1. What simplified assumptions have been made (in the theory for falling

films on a vertical plate) with regard to the temperature?

2. What is here meant with r?

3. Defme Reynolds number for falling films. When (at what Re-number) does

the change between laminar and turbulent flow take place?

4. Defme the Nusselt number. Express also Graetz number in other

non-dimensional numbers.

5. What thermal property affects the heat transfer most with varying

temperature?

REA T TRANSFER LAB LESSON NO.5-

1

HEAT TRANSFER IN FALLING FILMS

INTRODUCTION:

Heat transfer in falling films takes place between a thin liquid film and a

surface that emits or absorbs heat: The liquid flows or falls over this

surface because of gravity.

With falling films one can obtain comparatively very high coefficient of heat

transfer and this method is often used at cooling and heating processes in

such industries as breweries, dairy factories, chemical industries, etc. These

traditional applications nonnally operates with low Reynolds number and

laminar flow.

Falling films have lately found a new area of application as evaporators in

large heat pumps using water as heat source. A high mass flow rate is normally

used giving turbulent flow that in falling films usually is obtained when

Reynolds number is > 1600, while Re < 1600 usually gives laminar flow.

OBJECT:

The purpose of the lab lesson is to determine the coefficient of heat transfer

and Reynolds number as well as the Nusselt number as a function of the mass

flow rate at a vertical falling film and turbulent flow. Water is flowing on

the outside of a vertical tube that is heated by a water circuit in the tube.

The coefficient of heat transfer shall be determined for a number of measuring

points where the mass flow rate of the falling film varies. The results of the

experiment are then compared with an empiric equation by McAdams for falling

films with turbulent flow.

LAB LESSON NO.5REA T TRANSFER

2

THEORY:

"Heat transfer in falling fIlms" is summarized in the 1996 edition of "HeatTransfer - Collection of formulas and Tables of Thermal Properties" by Eric

Granryd.

Simplifying assumptions made in the theory of falling films:

The flow velocity of the falling fIlm along

assumed to be constant. This would mean that no

there is balance between liquid friction and the

effect of the curving of the liquid fllm on the tube

The heat transfer in the direction of the liquid flow is small in comparison

can thereby be regarded as constant.

- The curves of temperature.

The whole tube wall surface is

assumed to have the same

temperature, tv, while the

temperature of the falling

medium at the inlet is to and

its mean temperature at the

outlet is tmH. In the picture

the falling medium is heated

by the tube wall, but it can

be either heated or cooled.

the vertical tube wall is

acceleration takes place as

weight of the liquid. Any

wall is disregarded.

t

1mH

1:~ Temperature profile where falling

f11m is heated by the tube wall

3

For falling films on vertical walls and with the above given temperature

conditions we can arrive at an equation for the coefficient of heat transfer

related to the logaritrnic mean temperature difference, hln, for a wall with

the height, H. The heat flux divided by the breadth of the wall, q', can with

symbols according to the Table of symbols (p.9) be expressed as:

q' = r.Cp.(~o-~H) = hb1.H.(~o-~H)/(ln(~o/~H)

This equation can be changed to the following form:

hJn.HJk = r'(cp/k).ln(~o/~)

When the non-dimensional Nusselt and Graetz numbers (see p.9) are introduced

the equation can be written in the following non-dimensional form:

Nuln = Gz.ln( ~o/~)

Experimental correlations for heat transfer at turbulent flow.

Heat transfer in falling films with turbulent flow has experimentally been

examined among others by McAdams, Drew and Bays. At these experiments water

was heated by flowing inside vertical tubes while water steam of 1 bar was

condensing on me outside of me tubes. Wim support from experimental data

McAdams states generally that the following non-dimensional equation can be

used to determine the coefficient of heat transfer at turbulent flow and a

vertical falling fIlm:

hln/(k3.p2.g/~11/3 = O.Ol.(~.cP/k)I/3.(4.r/~)I/3 (4)

By introducing non-dimensional numbers the equation can be written as:

3 2 1/3 1/3 1/3NUIn = O.O159'(g'H Iv) .(r'cp/k) = O.Ol59.(G.Gz) (5)

All the property constants in this equation shall be related to the so calledfilm temperature, tf = (tv+tb)/2.

4

EXPERIMENTAL APPARATUS:

The experimental apparatus is built as a simple heat exchanger.circuit heats up a vertical brass tube (H = 1.00 m; dy = 0.065

from a water pipe is flowing outside the tube. At the bottom

water runs to the bottom container and is then led out through

Figure 2).

1. Flow meter for falling water r11m

Control and cut-off valve

Falling film distributor

Brass tube for falling film

Circulation pump, inner circuit

Electric water heater, - " -

Electric kWh-meter, - " -

Temperature recorder (thermo

couples are marked as arrows)

2.

3.

4.

5.

6.

7.

8.

Figure 2: Outline diagram of experi-

mental apparatus

The inner heat emitting water circuit is heated up by an electric heater.

Water is pumped through the circuit with high speed with the aid of a

circulation pump. The high water velocity contributes to an almost constant

tube wall temperature as the temperature difference between the incoming and

outgoing water outside the tube wall is small. This gives a rather good agree-

ment with the theory where constant tube wall temperature is assumed.

Falling film distributor

The .water that is to flow outside the tube is taken fro~ a water pipe andenters at the lower edge of the upper receptacle (See Figure 3). In thereceptacle the water level raises until it reaches the upper end of the middletube. The water then flows into this tube and passes two centering plates withmany holes. These plates even the falling film flow and prevent whirls.

An inner water

rn). Cold water

of the tube the

the drain. (See

5

In the bottom of the receptacle there are a number of plates by which the

width of the gap can be regulated in a number of steps. When the water has

passed these plates it falls as an even film down the outside of the vertical

brass tube over which the heat transfer takes place.

1. Glass gauge showing apparent

pressure level

2. Glass g~uge showing actual

pressure level

3. Inlet, falling water film

4. Middle tube

5. Thermo couple for measuring

tube wall temperature

6. Thermo couple pocket

7. Blind pipe

8. Brass tube for falling film

9. Plates for plate regulating

=> Path of falling water

> Path of inner medium

Figure 3: Falling film distributor

Measuring devices

Thermo couple threads of copper - konstantan connected to a temperature

registrator are used for temperature measurements. Some threads are solderedto the measuring objects and some are inserted into thermo couple pockets.

A volume flow meter is used to measure the incoming cold water volume flow.

Incoming electric power to the pump and heater for the inner circuit is

measured with a normal kWh-meter. (Measure the time for several revolutions.)

This measurement is made as a control of the energy balance.

TEST PROCEDURE:

Start of lab lesson

A control should first be made that there is water in the inner circuit. This

is done by observing the glass gauge at the top of the expansion vessel. Water

has to be added if no water level is visible.

To start the water flow on the outside of the brass tube you fIrst have to

fully open the water tap at the wall (green pipe) and thereafter fully open

the red tap situated after the volume flow meter. This red tap is also used to

regulate the water flow for the five measuring points.

Your laboratory assistant will show you the switch used to start the pump and

electric heater for the inner circuit.

Measuring and guiding values

Wait for steady conditions, reasonable thermal balance, which can be observed

on the registrator, for each of the measuring points. Measurements are then

made of temperatures, volume (mass) flow and electric power. The five

measuring points should be made at decreasing and evenly spread water flowsbetween max flow (appr 0.5 1/s) and =:: 0.1 1/s (kg/s). (The left small red

indicator at the flow meter makes one revolution/liter. Measure the time for a

suitable number of revolutions.) Enter the measured values in Table 1.

The values listed under Calculated values in Table 1 are easily calculatedwith the help of the Table of symbols (p.9) and Appendix (p.14) with propertyconstants for water. These property constants should be taken at the so calledfilm-temperature, tf = (tv + tb)/2.

7

The mass flow rate divided by the breadth of the plate, r, is calculated fromr = fn/(n.dy) where m is mass flow of the falling water film.

The transferred heat flow is calculated from q = ffi'cp.J1.t, where J1.t = tmH - to.

The coefficient of heat transfer hln, related to the logaritmic mean

temperature difference is calculated from the equation:

q = hIn.Ar'(~~H)/ln(&/~) (6)

where At = n.dy. H (m2) is the outside area of the brass tube. Corresponding

Nusselt number is calculated from NUIn = hln. H/k. Reynolds number is hereeasiest calculated fron Re = 4. r/J!.

The heat losses can be estimated from qr = qel - q. All the calculated values

are entered into Table 1.

Mark in DIAGRAM 1 measured temperatures (tin, tout, tvo, tvH, to, tmH) at the

top or bottom of the brass tube. Connect appropriately with (straight) lines.

Mark in DIAGRAM 2 calculated hbl-values as a function of r1f3. Draw also lines

for ~~ (McAdams equation) in the same diagram for tf = 10, 20 and 30 °C.

First you can trim ~~ to the form hbl = O.01.( )I/3.rl/3 outlined in

~ 1: and then calculate hbl for the given r1/3-values.

Mark in DIAGRAM 3 calculated Nuln-values as a function of Reynolds number.Draw also lines for ~~ in the same diagram for tf = 10 and 30 °C. These

lines can also be obtained by trimming ~~, but now to calculate NUIn =1/3 1/3 .

0.01.( ) .Re and then calculate Nuln for the given Re-values.

How do the marked values from the measuring points in Diagrams 2 and 3 comparewith the lines based on McAdams equation? - Can we give any explanation

for possible deviations from these lines?

8

TABLE OF SYMBOLS:

A (m1 cross section area of water fIlm

At (m1 outside area of brass tube (= n.dy.H)

de (m) hydraulic diameter of water fIlm

dy (m) outer diameter of brass tube wall

H (m) height of brass tube wall

g (m/s1 acceleration due to gravity (:== 9.81)

qel (W) electric power to inner circuit

m ~:W/m) mass flow of falling medium

r (kg/m,s) mass flow rate divided by breadth of plate wall (= in/n.dy)

q (W) heat flow

q' (W 1m) heat flow per length of plate wallqr (W) heat losses (= qel - q)

to (oC) temperature of flowing medium at inlet

tmH (oC) temperature of flowing medium at outlet

tvO (oC) temperature of tube ~all at inlet

tvH (°C) temperature of tube ~all at outlet

tin (oC) temperature of inner circuit at illiet

toot (oC) temperature of inner circuit at Q!!!let

tb (oC) mean temperature of flowing medium (= (to+tmH)/2)

tv (°C) mean temperature of tube ~all (= (tvo+tVH)/2)tr (°C) [1lm temperature (= (tv+tb)/2)

L\t (K) temperature difference of flowing medium (= tmH-to)

~O (K) temperature difference at inlet of tube (= tvO-to)

~ (K) temperature difference at outlet of tube (= tvH-tmH)

cp (J/kg,K) specific heat (at tr)

k (W Im,K) thermal conductivity (at tr)

J.l (Ns/m1 dynamic viscosity (at tr)V (m2/s) kinematic viscosity (at tr)

p (kg/m3) density (at tr)hJn (W/m2,K) coefficient of heat transfer (see defmition at equation 6)

Nuln (-) corresponding Nusselt number (= hJn.HJk)G ( - ) gravity number (= g. H3/V1Gz ( - ) Graetz number (= r.Cp/k)Pr ( - ) Prandtl number (= J.l'Cp/k)Re ( - ) Reynolds number (= wm.de/v = ffi.de/(A.J.l) = 4.r/J.l)

<)

TABLE 1: MEASURED AND CALCULATED VALUES

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TABLE 2: CALCULATIONS FOR McADAMS EQUATION

11

DIAGRAM 1 and DIAGRAM ~

~

1:...t+..-o

C

0.--0c

c2=t/j=

~.c

NI

I"

Q)

se .8Co,a

~ t<U >08. e

5 ~E-o <U.:.:, ;a

Iu

°u

s0+J+J0

.J:I

0("'I

0N

(:>-

12

DIAGRAM .;1: f(Re)function of Reynolds number (NUInnumber as aNusselts

~

0000..-

000Ln

000(f')

0011'1

13

APPENDIX: PROPERTY CONSTANTS FOR WATER

p density (kg/m3)specific heat (J/kg,K)thermal conductivity (W /m,K)

dynamic viscosity (Ns/m1

Cp

k

J.1

1000 4225

995 4200

990 4175

0

1,0-10-30.60

-)0.55 0.5.10

500C4020

14