Lab experiment A

Estimation of the overall heat transfer coefficient

This lab experiment was adapted from the Climbing Film Evaporator Instruction Manual UOP1b.

This text was prepared as a guide for using a specific equipment. In this case: Climbing Film Evaporator from Armfield. However, the instructions are so general, that these can be used with other equipments.

Please, follow safety instructions for the start-up and operation the evaporator and boiler.

 CONTENTS

 1 The object of the experiment

 2 Procedure

 2.1 Steps to follow

 2.2 Experimental to be recorded

 2.3 Theoretical background for calculations

 2.4 How to perform the calculations

 3 Your results

1 Object of the experiment

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Measured the rate of evaporation $L$ and from it, estimate the overall heat transfer coefficient.

2 Procedure

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The stream $L$ is to be measured from the operation of the evaporator. Therefore, a set of spreadsheets are to be needed. Be aware of the related variables of interest.

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2.1 Steps to follow

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Please, follow the next steps in order to achieve the goal of this task,

1. make sure there is water in the feeding tank L1,
2. start-up the boiler so that steam at $1.5\, bar\, man$ is available,
3. start-up the evaporator following the instructions for it and make sure a feed $F=10\,L/hr$ is set in the flow meter F2 (see this post on how to use a rotameter). Flow rate $F$ can be adjusted with valve C8 (ball valve V8 should be completely open),
4. once steam stream $W$ and $F$ are ready, open the steam valve C10 to throttle so that the steam chamber gets pressurized. Remember that $p_W$ is to be $1.5\, bar\, man$,
5. check for steam pressure in Bourdon manometer P2 and evaporated water stream $L$ temperature in probe T7. At the beginning pressure and temperature will vary. Wait some minutes until the process in the evaporator stabilizes so that pressure and temperature remain constant (steady conditions),
6. once the system achieves its steady conditions, record: steam $W$ pressure and vapor $L$ temperature,
7. measure the $L$ flow rate in condensate tank L3,
8. repeat from step 4 for suitable pressure steps so that noticeable pressure and temperature changes can be read in the instruments P2 and T7.

You will see labels for each component in the equipment.

2.2 Experimental data to be recorded

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For short, only the steam pressure $p_W$, the evaporated water temperature $T_L$ and the volumetric flow rate $L$ are to be measured. However, other data are required. For example,

• the heating area $A$,
• the steam temperature $T_W$ and
• the latent heat $\lambda_L$

so that these has to be looked for in tables and in the equipment data sheet. For the purpose of systematic measurements, spreadsheets need to be prepared not only to collect data but to homgenize units and to perform operations between columns.

2.3 Theoretical background for calculations

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Since in this experiment water is being used in $F$, estimation or indirect measurement of the overall heat transfer coefficient starts with the familiar equation,

$q=UA\left( T_W-T_L \right)$        Eq. (01)

where the heat flow $q$ is defined as,

$q=L\, \lambda_L$        Eq. (02)

And from the combination of Eqs. (01-02) and expression for $U$ is obtained,

$U=\dfrac{L\, \lambda_L}{A\left( T_W-T_L \right)}$        Eq. (03)

Equation (03) basically tells us that $U$ will depend directly on the temperatures $T_W$ and $T_L$ so that this is a parameter that will change with the conditions of operation. $U$ is not a constant per se. Also, Eq. (03) states a proportionality between $U$ and the temperature gradient,

$U \propto K_1 \left(T_W-T_L\right)^{-n}$        Eq. (04)

where $K_1$ is a constant. In Eq. (04) $K_1$ and $n$ are two free parameters to be determined from fitting of the experimental data to the power law Eq. (04).

As you may have observed $K_1$ is not constant but there are conditions at which it is, so that $n$ is also a constant.

2.4 How to perform the calculations

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Equation (04) is the key to estimate $U$ from experimental data. However, the experimental data may have a non linear behavior. In fact, it is to be determined yet. This is the reason for $K_1$ and $n$.

These free parameters in a power law Eq. (04) need to be estimated by a fitting process to the experimental data. 

For the process of fitting the experimental data, the reader is referred to: Fitting data to a power law equation.

With $K_1$ and $n$ known, Eq. (04) becomes a master equation for evaporators design. This equation could also be known as a correlation.

3 Your results

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Key results of these experiments are,

• a plot of $U$ versus $\left(T_W-T_L\right)$,
• a log-log plot of $U$ versus $\left(T_W-T_L\right)$,
• a plot of $L$ versus $\left(T_W-T_L\right)$,
• a log-log plot of $L$ versus $\left(T_W-T_L\right)$, and of course
• the values of $K_1$ and $n$.

This is the end of the post. I hope you find it useful.

Any question? Write in the comments and I shall try to help.

Other stuff of interest

• LE01 - AC and DC voltage measurement and continuity test
• LE 02 - Start and stop push button installation 24V DC
• LE 03 - Turn on/off an 24V DC pilot light with a push button
• LE 04 - Latch contact with encapsulated relay for turning on/off an AC bulb light
• LE 05 - Emergency stop button installation
• About PID controllers
• Ways to control a process
• About pilot lights
• Solving the Colebrook equation
• Example #01: single stage chemical evaporator
• Example #02: single stage process plant evaporator
• Example #03: single stage chemical evaporator
• Example #04: triple effect chemical evaporator

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Ildebrando.