### Overview

Source: Michael G. Benton and Kerry M. Dooley, Department of Chemical Engineering, Louisiana State University, Baton Rouge, LA

Heat exchangers transfer heat from one fluid to another fluid. Multiple classes of heat exchangers exist to fill different needs. Some of the most common types are shell and tube exchangers and plate exchangers^{1}. Shell and tube heat exchangers use a system of tubes through which fluid flows^{1}. One set of tubes contains the liquid to be cooled or heated, while the second set contains the liquid that will either absorb heat or transmit it^{1}. Plate heat exchangers use a similar concept, in which plates are closely joined together with a small gap between each for liquid to flow^{1}. The fluid flowing between the plates alternates between hot and cold so that heat will move into or out of the necessary streams^{1}. These exchangers have large surface areas, so they are usually more efficient^{1}.

The goal for this experiment is to test the heat transfer efficiency of a finned-tube heat exchanger (Figure 1) and compare it to the theoretical efficiency of a heat exchanger without fins. The experimental data will be measured for three different flow rates of monoethylene glycol (MEG). Two different water flow rates for each MEG flow rate will be used. Using the Wilson plot method the heat transfer coefficients will be determined from the experimental data. Additionally, the Reynold's number and the amount of heat transferred will be compared for flow with and without the fins to evaluate heat transfer efficiency.

**Figure 1: Finned-tube Heat Exchanger.** 1) MEG outlet temperature 2) water inlet temperature 3) MEG inlet temperature 4) water outlet temperature 5) water meter 6) MEG accumulation sight glass/cylinder.

### Principles

Heat exchangers transfer heat between two or more fluids. The exchangers use fluid species which flow in a separate space from an opposing stream that is providing heat. Fins can be added to the flow area to facilitate more heat transfer, as they increase the surface area available for transference. The added fins decrease the area through which the species flows and provide more surfaces on which boundary layers can form, resulting in flow that is less turbulent. The less turbulent a flow, the larger boundary layer it will have. A boundary layer inhibits heat transfer, so with less turbulent flow less heat is transferred. When the boundary layer is laminar, there is very little mixing.

The relationship between the area through which heat can flow and the heat transfer coefficient is used in calculating the total heat transferred. This relationship is calculated through Equation 1:

(1)

where *Q* is heat transferred (Btu/hr), *U* is overall heat transfer coefficient, *A* is area through which heat is transferred (ft^{2}), ΔT_{LM}* *is the logarithmic mean temperature difference.

The overall heat transfer coefficient equation is:

(2)

where A_{b} is the surface area of bare inner pipe, A_{f} is the surface area of the fins, A_{LM} is the logarithmic mean area difference, A is the surface area of the pipe (o = outside, i = inside), Δx thickness of the pipe, k is thermal conductivity of the pipe, h = Individual heat transfer coefficient. (o=outside, i=inside)

The Wilson plot method uses experimental data to find U_{o}A_{o} from typical energy balance on the MEG flow and plot its reciprocal to 1/Re^{0.8} of the inside pipe. By fitting a straight line and finding the y-intercept, which is related to the heat transfer coefficient and is described in the first two terms on the right of the equation above. A typical longitudinal rectangular profile fin efficiency equation is used as the second equation to solve for the heat transfer coefficient and fin efficiency by minimizing the sum of squares of an objective function. This method is applied to MEG flow conditions with varying water flow rates.

To calculate the heat transfer coefficient, the Reynolds Number is used, which is given by the following equation:

(3)

where G is the mass velocity of fluid flow, D is the diameter of pipe where the fluid flows (D_{eq}, the equivalent diameter will replace D for calculations with fins), and µ is the fluid's viscosity. Fin efficiency equation for a longitudinal rectangular profile fin is:

(4)

where m is √(2h/kt), h is the heat transfer coefficient, k is thermal conductivity of the pipe, t is thickness of fin, and b is the height of fin.

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### Procedure

1. Start and Flow Rate Determination

- Open the charge valve located below the steam generator.
- Start the unit, and allow 15 min for steam to begin forming.
- Calculate the flow rate of water
- Start a stopwatch and monitor the gauge displaying the volume of water.
- Stop the watch after 30 s and record the total volume of water displayed on the gauge.
- Divide the volume of water by the time to determine the volumetric flow rate.

- Record the MEG flow rate from the flow meter.
- Observe the temperature from the thermocouples, and record the values.

2. Varying the flow rate and shut down

- To collect data for 6 different runs, set the flow rate of water to either a high or low flow rate and run it with a high, medium, or low flow rate of MEG.
- For reference, the previous flow rates have been used: 0.0439, 0.0881, and 0.1323 gal/sec for the low, medium, and high flow rates of MEG, respectively.

- As previous, record the volumetric flow rates and temperature difference on the thermocouple for each run.
- When finished, shut down the instrument.
- Close the valves to stop the flow of steam, monoethylene glycol and water.
- Turn off the main switch.

3. Calculations

- Use Equation 1 to calculate the total heat transferred, Q, with the temperature difference read from the thermocouples (devices used to measure temperature) and the known physical dimensions of the heat exchanger (found in the user manual for the unit being operated). The temperature differences can be taken from the temperature readings of each run.
- Calculate the heat transferred for each unique trial run, and use the Wilson plot method to find the heat transfer coefficients for the three MEG flow rates.
- Compare the calculated heat transferred and Reynolds number to theoretical values of the heat exchanger without fins.

Heat exchangers transfer heat between two species and are used for a wide variety of applications from car radiators to large-scale chemical plants. There are many heat exchanger designs including shell and tube exchangers and finned tube exchangers. For these an array of tubes and fins is used to transfer heat from the hot fluid to the cold fluid. An understanding of the heat transfer efficiency is important for heat exchanger design optimization and their integration into larger systems. This video will illustrate the principles of heat exchangers, demonstrate how to calculate the heat transfer coefficient and efficiency for a finned tube heat exchanger and discuss related applications.

Now, let's look at how heat exchangers work and examine the principles governing their efficiency. The heat transfer in a heat exchanger is generated by fluid species in close contact that are separated by a physical barrier. They can flow either parallel or counter currently to each other. Heat exchange is driven by local temperature differences between the fluids. The hotter of the two fluids entering the heat exchanger will exit with a reduced temperature whereas the colder will exit with an increased temperature. The heat transfer efficiency can be increased by the addition of fins to the flow area which increases the surface area available for heat transference. However, the added fins also decrease the region through which the fluid flows, providing more surfaces for boundary layers to form. A boundary layer is the thin layer of fluid in contact with the surface that is affected by shearing forces. When the boundary layer is laminar, there is very little mixing and heat transfer is inhibited. At higher flow rates, or longer distances, the laminar flow breaks down and transitions to a turbulent flow where the bulk fluid mixes more effectively. During steady state operation, the total heat transferred, Q, can be calculated using the overall heat transfer coefficient U, the area through which the heat flows, A and delta TLM, the logarithmic mean temperature difference between the bulk fluid flow and the heat surface. UA is the overall conductance and is a measure of the heat transfer capacity of a heat exchanger. The overall heat transfer coefficient is determined by this equation which takes into account the surface areas of the pipe and fins, the heat transfer coefficients and the thermal conductivity and thickness of the pipe. The heat transfer coefficient is estimated from experimental data using graphical methods such as the Wilson plot which plots the reciprocal of the overall conductance versus one over the Reynolds raised to the eight tenths power. Linear regression is used to solve for the heat transfer coefficients. The dimensionless Reynold's number is the ration of inertial forces to viscous forces and it used to describe flow pattern. Where D is the equivalent diameter of the pipe, G is the mass velocity of the fluid and Mu is the viscosity of the fluid. A higher Reynold's number indicates a more turbulent flow, greater fluid mixing and increased heat transfer. Now that you understand how to calculate the heat transfer coefficients and Reynold's numbers, let's evaluate the heat transfer efficiency of a finned tube heat exchanger by varying the flow rates of water and monoetilenglicol.

Before your start, familiarize yourself with the finned tube heat exchanger apparatus. Open the charge valve, start the unit and wait for steam to begin forming. Using a stopwatch and the gauge, determine the water flow rate. Start your stopwatch and monitor the gauge displaying the volume of water. Stop the stopwatch after 30 seconds. Record the total volume of water on the gauge and divide the volume by the measured time. Next, read the MEG flow rate on the display. When the 30 seconds for flow rate calculation have passed, record the temperature from the thermocouples.

Now, vary the flow rates to obtain data for six unique runs. Each run consists of a set water and MEG flow rate. Set the water flow rate to either high or low and run it with a high, medium or low flow rate of MEG for a total of six runs. Repeat the same procedure above for each flow rate to record the volumetric flow rates of water and MEG and the temperature difference from the thermocouple. When finished, shut down the instrument. Close the valves for the steam, glycol and water flow. Then turn off the main switch.

To calculate the total heat transferred, Q, for each run, use the obtained temperature differences from each experiment and the physical parameters of monoetilenglicol. Then determine the Reynold's number for each unique run using the dimensions of the pipe and the mass velocity and viscosity of water.

Now let's compare the results to the theoretical values of the heat exchanger without fins. A Wilson plot was used to determine the heat transfer coefficients by plotting one over UA, versus one over the Reynold's number raised to the eight tenths power and relating the linear fit to the equation for the overall heat transfer coefficient. The blue, red and green lines indicate the high, middle and low monoetilenglicol flow rates in the experiment. When compared to a non-finned tube, the finned tube did not reach turbulent flow. The fins provide additional surfaces for boundary layers to form and maintain the monoethylene glycol in a more laminar flow regime. However, when comparing the heat transferred between the exchanger with and without fins at different MEG flow rates, it is clear that a finned tube transferred more heat than a tube without fins at the same operating settings. Heat transfer is more effective with a greater surface area, despite the fact that the finned tubes induce laminar flow, their heat efficiency was much higher than for the non-finned tube.

Heat exchangers are used in a variety of settings to transfer heat from one species to another. In all buildings, heat exchangers are part of the heating and air conditioning systems to regulate temperature. They are also used to control core patient temperature in critical care settings, such as after cardiac arrest, neurogenic fever or surgery. Heat exchangers are also used on the small scale in the denature and heat precipitation of proteins from plant extracts. This technique was used in the extraction of a malarial vaccine candidate from transgenic tobacco plants to reduce the concentration of host cell proteins.

You've just watched JoVE's introduction to finned tube heat exchangers. You should now understand the principles of heat transfer, be able to evaluate heat efficiency and know several applications of heat exchangers in various processes. Thanks for watching.

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### Results

The finned tube heat exchanger did not reach turbulent flow (**Figure 2**). The fins provide additional surfaces on which boundary layers form, as known through laminar and turbulent flow theory. If the fluid is not at a sufficient velocity, the fluid will not reach turbulence. The boundary layers between the fins overlap in the laminar region, so the fluid will remain laminar.

**Figure 2****: Reynolds numbers for each setting.**

The amount of heat transferred, Q, in the tubes with and without fins at different flow rates of MEG was compared (**Figure 3**). The results show that a finned-tube transfers more heat than a tube without fins at the same operating conditions. In this experiment, the fins clearly improved heat transfer. This is because heat transfer is more effective when there is a greater surface area available. The finned-tube heat exchanger transferred more heat (**Figure 3**), despite the lower Reynolds number (**Figure 2**).

**Figure 3****: Heat transferred between exchangers with and without fins at each flow rate.**

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### Applications and Summary

Heat exchangers are used in a variety of industries, including agriculture, chemical production, and HVAC. The goal for this experiment was to test the heat transfer efficiency of a finned-tube heat exchanger and compare it to the theoretical efficiency of a heat exchanger without fins. Experimental data was measured for three different flow rates of monoethylene glycol (MEG) and two unique water flow rates for each MEG flow rate used. The Reynold's number was determined for flow with and without the fins and was used to calculate the heat transfer coefficient, surface area, and fin efficiency for each unique trial run. This data was used to evaluate if turbulent flow is possible without the fins and under which set of trial conditions the most heat transfer occurs. The finned tubes did not reach turbulent flow. The results showed that a fin tube will transfer more heat than a tube without fins at the same operating conditions because the flow of MEG through the heat exchanger will not reach turbulence.

In the agriculture industry, heat exchangers are used in the processing of sugar and ethanol^{2}. Both of these products are processed into a juice, which must be heated to be further processed^{2}. Heat exchangers are used in heating the juices for clarification^{2}. Once the juices have been processed into even syrups, further heating with exchangers is necessary to continue processing and form molasses^{2}. Molasses is cooled using heat exchangers, after which it can be stored for later processing^{2}.

Heating, ventilation, and air conditioning systems, together known as HVAC, all make use of heat exchangers^{3}. Household air conditioning and heating units make use of heat exchangers^{3}. In larger settings, chemical plants, hospitals, and transportation centers all make use of similar heat exchanger HVAC, on a much larger scale^{3}. In the chemical industry, heat exchangers are used for heating and cooling a large variety of processes^{4}. Fermentation, distillation, and fragmentation all make use of heat exchangers^{4}. Even more processes like rectification and purification require heat exchangers^{4}.

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### References

- Types of Heat Exchangers."
*Types of Heat Exchangers*. N.p., n.d. Web. 19 Jan. 2017. - Heat exchangers for sugar factories and distilleries."
*Heat exchanger for sugar and ethanol industry*. N.p., n.d. Web. 19 Jan. 2017. - Biotechnology and green chemistry heat exchangers."
*Heat exchanger for green chemical industry*. N.p., n.d. Web. 19 Jan. 2017. - Heat exchangers for heating and cooling."
*Heat exchangers for district heating, cooling and HVAC*. N.p., n.d. Web. 19 Jan. 2017.