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Heat Transfer Flow

Title: To analyse two different heat exchangers and to understand the factors and parameters affecting the rates of heat transfer.

Abstract

The behaviour of a parallel flow and cross flow heat exchangers, subjected to variations in temperature was investigated in this report. The parallel flow heat exchanger was subjected to increasing flow rates ranging from 400mL/min to 1600mL/min for water and 40% to 70% of the max capacity for the air heater. The inlet and outlet temperatures for air and water were noted. Through experimental and correlation calculations an analysis of the heat exchanger was completed.

For the cross flow heat exchanger a cylindrical copper tube was heated and then subjected to different air speeds in a staggered tube array. The results of these experiments were investigated and graphed.

Nomenclature

Symbol Description Units

A Area m^2

Cp Specific heat capacity at constant pressure J Kg⁻¹ K⁻¹

D Diameter m

I Current amps

L Length m

Nu Nusselt Number

Pr Prandtl's

Q Heat Transfer W

Re Reynolds number

T Temperature C

T_1, T₂ Hot Air and water Inlet Temp C

U Overall Heat Transfer Coefficient W/(m^2)

V Voltage volts

g Gravitational acceleration m/s

h heat transfer coefficient W/(m^2)

k Thermal conductivity W/mC

m Mass Kg

Mass flow rate Kg/s

t₁, t₂ Cold Air and water Inlet Temp C

u Velocity m/s

v Flow rate m^3.s

ρ Density Kg/m^3

μ Dynamic Viscosity Kg/m.s

∆T Change in temperature C

Log mean temperature difference C

Subscripts:

i Inside

o Outside

w Wall

Contents

Section No. Section Title Page No.

1. Introduction

Heat exchangers transfer heat between two or more different fluids at different temperatures. This Heat transfer between flowing fluids is one of the most important processes in engineering. Heat exchangers are found in numerous applications from power plants to automotive cooling systems.

Because of the diversity of applications, heat exchangers are constructed with a wide variety of flow arrangements and physical configurations. In heat exchanger systems, the exchange of thermal energy is achieved using various combinations of conductive, convective and radiative heat transfer. The scope of this report deals with two types of heat exchangers: parallel flow (where both fluids travel in same direction. See Fig 1) and cross flow (fluids flow perpendicular to each other. See Fig 2). Conduction and convection are assumed to be the primary modes of heat transfer for these two heat exchangers.

This experiment was conducted to evaluate the performance of two actual heat exchangers. The principle figure of merit for the parallel heat exchanger is its overall heat transfer coefficient time's surface area, UA which was determined using the air-water heat parallel flow. With regards to the performance of the cross flow the variations in air velocity and position within a staggered tube array.

The goal of the analysis was to determine four things, U, the overall heat transfer coefficient, Nu, the Nusselt number, Re, the Reynolds number and Pr, Prandtl's number.

There are three main factors that govern the overall heat transfer rate between the two pipes. Those being the convective factor of the cold water, the transfer through the pipes walls, and the flow rate of the streams.

The heat exchangers performance can also be hugely influenced by small changes to the boundary conditions. For example increasing the length or adding fins to the cross flow would increase the surface area and may channel fluid flow or induce turbulence. (Massey 2005). The parallel flow heat exchangers performance can also be altered for example increasing the temperature of the cold water entering the concentric tube in this experiment would of lead to an increased overall thermal heat transfer coefficient.

Experimentation was done using a system in which the flow could be controlled and measured and therefore the temperatures could be measured accurately. For the parallel flow the heat transfer coefficient and Reynolds's number could be calculated. As with the parallel flow, the cross flow used the Reynolds number to calculate the Nusselt number which was used to compare different velocities. The formulas that were used to do this are included in the theory portion of the report. Overall this report showed how a system responded the way it did when the flow rates were adjusted.

Objectives

Parallel:

To carry out an experiment which will record the inlet and outlet temperatures for air and water for a parallel flow heat exchanger at different air and water flow rates.

To calculate the Reynolds number and the overall heat transfer coefficient from the experimental and correlations and to plot the results.

To compare and discuss the experimental results from the laboratory session with the correlations derived previously.

Cross Flow:

To subject a cylindrical tube to a cross flow of air and to investigate the presence of a wake.

To investigate the variation in Nusselt number with varying air cooling speeds.

To investigate the variation in Nusselt number for the copper cylinder at different positions in a staggered tube array.

2. Theoretical Analysis

Experimental Equations Parallel Flow:

Experimental:

The type of heat exchanger used in this experiment was a concentric tube, single-pass heat exchanger. This means that the fluid was running through the heat exchanger once and at a constant rate. To calculate the rate of the heat exchanged, the first step was to create an energy balance for the system. The equation for enthalpy for each system was:

(1) (Holman)

The V (voltage) and I (current) were both obtained from the air blower. The unit for Q was Watts.

The log mean temperature difference must be used because the temperature changed with the length of the pipe. See Fig. The LMTD was calculated using equation (2).

(2) (Holman)

=

Where:

T₁ = Hot Air Inlet Temp.

T₂ = Hot Water Outlet Temp.

t₁ = Cold Air Inlet Temp.

t₂ = Cold Water Outlet Temp.

The area of the tube was calculated using equation (3), the mean surface area

(3)

Where D is the diameter, L is the length and where л is 3.14

After all the equations were combined, the total energy transfer between the two fluids can be described as the following:

(4) (Holman)

U is the overall heat transfer coefficient, W/m k.

Correlations:

The overall heat transfer coefficient, U, is the inverse of the total thermal resistance. In the case of the parallel flow heat exchanger:

(5) (Eastop & McConkey)

Where: is the convective resistance between the cold fluid and the wall.

is the conductive resistance between the hot fluid and the wall.

is the convective resistance between the hot fluid and the wall.

Fig 5 shows a schematic of these resistances in an axial section of a heat exchanger.

Fig 4. Thermal resistance in an axial section of a tube heat exchanger

(6) (Kearney)

The value of h for water and air was found using the equation 7.

(7) (Holman)

When the Reynolds number was laminar the Nusselt number was calculated using:

(8) (Holman)

And when the Reynolds number was Turbulent equation (9) was used:

(9) (Holman)

The diameter for the air was the diameter of the inner tube but the diameter for the water was the outer diameter minus the inner diameter. See Fig 3.

(10)

Prandtls number was also needed when calculating Nusselt values for the different flow rates:

(11) (Eastop & McConkey)

Fig 3. Diameter

And the Reynolds number was calculated using equation.

(12) (Eastop & McConkey)

Where is the dynamic viscosity, u is the velocity and is the density.

The mass flow rate of air could then be calculated from equation (13).

(13) (Holman)

The flow rate for water was given during the experiment in mL/min. This was converted to m/s. Then equation (14) could be used to calculate the velocity.

(14) (Holman)

From this the mass flow of the water was calculated using equation (15).

= (15) (Holman)

Finally the area of any tube was calculated using equation 16.

(16)

Theoretical Analysis Cross Flow:

Experimental

Equation (7) was used to find the Nusselt number

(7)

Where the h is the unknown value and is the convection coefficient of heat transfer,

D is the diameter of the pipe and k is the thermal resistivity of the copper.

To find h, the lumped capacity method was used. The Biot number must be less than 0.1. The lumped capacity method is based on the fact that the rate of change of internal energy for a body being cooled in a cross flow equals the surface heat transfer (Kearney 2007). Therefore the formula

(17) (Kearney)

Through integrating and manipulation an equation for h was formulated.

(18) (Kearney)

Where m is the mass of the copper cylinder, Cp is the specific heat capacity, t is the time it takes for the copper cylinder to reach 20C after been heated up to 80 C and A is the area which was calculated using equation.

(19)

Where L is the length of the copper cylinder and D is the diameter.

The velocity of the air must also be calculated using equation (20).

(20)

Where g is 9.81m/s and h is the height of the manometer in terms of air.

To find use equation 20.

(21) (Eastop & McConkey)

Where ρ is the density of air and water respectively and the is height taken from the manometer in meters.

3. Experimental Work

The analysis of the two heat exchangers was carried out in two different laboratory sessions. During the first session, the inlet and outlet temperatures for water and air were recorded on the parallel flow heat exchanger for three different water and air flow rates.

During the second laboratory session, the analysis on the cross flow heat exchanger again was divided into three sections. The first involved using a manometer and pitot tube to verify the presence of a wake. The second section involved heating a hollowed copper cylinder to 80C and recording the time and temperature for three different fan speeds.

The third experiment involved using just one fan speed and heating the copper cylinder to 80C and placing the tube in four different positions in the staggered array tube and to record data using the computer program Lab View.

3.1. Experimental Procedure

Parallel flow heat exchange

To analyse the parallel flow heat exchanger (see Fig 4) the water flow rate was kept constant for three different air speeds. The voltage and current were kept constant throughout the entire experiment. This experiment was carried out three times where the water flow rate was changed from small (400-500mL/min), to medium (900-1000mL/min) and finally to high (1500-1600mL/min). At these different water flow rates the temperatures were taken at:

T₁ = Hot Air Inlet Temp.

T₂ = Hot Water Outlet Temp.

t₁ = Cold Air Inlet Temp.

t₂ = Cold Water Outlet Temp.

2. Set the water flow rate to between 400-500mL/min.

3. Set the air flow rate to 40% capacity.

4. Allow apparatus and temperatures to stabilize for 10minutes.

5. Note the temperatures T1, T2, T3 and T4.

6. Adjust the air flow rate to 55% capacity.

7. Note the temperatures T1, T2, t₁ and t_2.

8. Adjust air speed to 70% capacity.

9. Note the temperatures T1, T2, t₁ and t_2.

10. Repeat above procedure for medium water flow rate and high water flow rate.

Cross Flow Rate

Part 1: To verify presence of a wake.

1. Place the copper cylinder in the staggered tube array.

2. Set a voltage output for the air speed. Keep this constant.

3. Using the calliper place a datum point above the cylinder.

4. Note the value on the manometer.

5. Using the calliper to move down in 1mm increments until below the cylinder record the manometer reading.

6. Plot a graph using the results.

Part 2: To investigate the variation in Nu with varying air cooling speeds.

1. Remove the callipers.

2. Heat the copper cylinder to 80C. Ensure not to heat above 90C.

3. Place heated copper cylinder in the chamber.

4. Set the fan speed.

5. Let the cylinder cool down.

5. Wait for the computer program Lab View to gather the cooling values automatically.

6. Repeat for two other fan speeds.

Part 3: To investigate the influence of the staggered tube array.

1. Heat the copper cylinder to 80C.

2. Place copper cylinder at different positions in the chamber. Ensure all others are blocked by Perspex cylinders.

3. Wait for the computer program Lab View to gather the cooling values automatically.

4. Repeat for four different positions in the staggered tube array.

4. Results

Parallel Flow

The data obtained from the experimental procedure was used to calculate the relationship between the overall heat transfer coefficient and the Reynolds number. For each flow rate configuration, an overall heat transfer coefficient was calculated using equation (4) and equation (6). The coefficient ranged from 71.82W/mK to 107.089W/mK for the correlations, and from 93.5 W/mK to 133.5 W/mK from the experimental calculations and the complete table can be found in Fig in the appendices.

The general trend of the heat transfer coefficient U was to increase with an increase in the flow rate of the water or the air. This can be observed in the graph of U and the Reynolds number in Fig 5. The experimental values are consistently higher than the correlations by about 18%.

Sample Calculation Parallel Correlation: Water @ 440ml/min and air @ 40%

Given that:

Diameter = 0.00455m Change in Temp = 15.5C

Radius = 0.002275m Specific heat capacity = 4190 KJ/kg K

Density = 1000Kg/m^3 Dynamic viscosity =1.00E-03 Kg/ms

Thermal Conductivity = 0.585 kW/mK Flow Rate = 7.33E-6 m^3/s

Area Tube = 1.69920E-04 m^2

Descriptions Equation Solution

Heat Transfer 750W

Velocity 4.50992E-01m/s

Mass Flow Rate 4.31556E-02 m/s

Reynolds Number 2.05E+03

Prandtl Number 7.1623932

Nusselt Number 3.79E+00

Convection

Coefficient of Heat Transfer 487.42 W/ (m)

Overall Heat Transfer

Coefficient 71.821250 W/ (m)

Sample Calculation Parallel Experimental: Water @ 440ml/min and air @ 40%

Given that:

Temp Air in = 132C Radius = 0.01075m

Temp Air out = 51 C Area = 0.124956848m^2

Temp Water in = 11 C

Temp Water out = 26.5 C

Descriptions Equation Solution

Heat Transfer 750W

Mean log temp difference 60.42136 C

Overall Heat Transfer

Coefficient 99.3367 W/(m)

Cross Flow

Fig 6 confirms the presence of a wake around the copper cylinder. These wakes would have had an influence on other tubes in the array if they were present. They graph also demonstrates how the cooling of the copper cylinder would take place. This reinforces the idea that surface area plays a large role in cross flow heat exchangers.

These graphs were used to find the time constants which in conjuction with the slope of the graph where used to find the various Nusselt numbers.

Fig 8 and Fig 9 shows the how the Nusselt number varies with different air speeds and also in different positions within the staggered array tubes. The results in both experiments had a difference of about 18%. The experimental values where constantly higher than the correlations.

Fig 8 Variation in Nusselt no with cooling air speeds

Fig 9 Variations in Nusselt in staggered array tube

Sample solutions for Cross flow Experimental: Presence of a wake

Given that:

Density Air = 1000 Kg/m

Density water = 1.2 Kg/m

Gravitational Accelerarion = 9.81 m/s

= 0.001m

Description Theory Section Number Solution

14.14967m

Velocity 16.6618m/s

Sample solutions for Cross flow Experimental: Nusselt no. Vs cooling speeds: 60V

Given that:

Density Air = 1000 Kg/m

Density water = 1.2 Kg/m

Gravitational Accelerarion = 9.81 m/s

= 0.016m

Mass copper cylinder = 0.0780 Kg

Description Formula Solution

Time constant 0.368421s

13.137m

Velocity 16.164m/s

h 72.238 W/(m)

Nusselt number 67.7814

5. Discussion

Parallel Flow

Since the fluid characteristic remained constant, the Reynolds number has a direct relationship to flow velocity, and consequently the flow rate. This relationship between the overall heat transfer coefficient and the flow rate can be explained because U depends on the convective effects of the hot fluid, and the heat transfer coefficient of the heat exchanger material (Massey). As the flow rate of the cold fluid was increased, the convective factor increased, the convective factor increased, and increased the observed overall heat coefficient.

From the results it was obvious that a larger flow rate will increase the heat transfer coefficient between the hot fluid and the wall. Increasing the flow rate of the cold fluid would also increase the heat transfer coefficient because the convectiver fact would be increased

The effect of inlet variation was also noted during this experiment. The increase in temperature of the hot air raises the log mean temperature difference and increases the overall heat transfer rate for both fluids.

The only sources of error in this experiment could have come from the heat exchanger system not coming to thermal equilibrium or the water tube containing bubbles, scale or dirt along the tube wall

Cross Flow

The results from the cross flow were exactly what was expected. In relation to the four different positions in the staggered tube array the Nusselt was expected to increase as the air flow rate at this point was more concentrated. See Fig 9.

As for the increasing air speeds results these were slightly lower than what was expected. But as was well the maximum Nusselt number occurs at the front stagnation point where the boundary layer and resistance to heat transfer is minimum.

6. Conclusions

The heat transfer of the system was calculated at multiple flow rates for both parallel and cross flow heat exchangers. From the results it was clear that the overall heat transfer coefficient was hugely affected by the flow rates of the cold water and the hot air.

When the water flow rate was increased the heat transfer of the liquid also increased. This was due to the fact that there was more water flowing through the pipe, creating a greater temperature difference. Since there was less heat absorption per unit of cold water the water had more potential to absorb the heat from the warm water. The cold water was not only open to heat transfer from the warm air inside the inner tube but also from the surrounding air. This small error could have been minimized by wrapping insulation around the pipes.

The correlation equations for the overall heat transfer coefficient of a parallel flow heat exchanger were proved true in this experiment. The equations for the cross flow were also confirmed in this experiment.

By in large, both experiments illustrated accurately the behaviour of heat transfer in both heat exchangers and it showed the apparent connection between the values obtained experimentally and theoretically through correlations.

7. References

Eastop T.D., McConkey A., (1996) Applied Thermodynamics Prentice Hall 5^nd Ed.

Holman. (1997) Heat Transfer Pergamon 3^rd Ed.

Massey B., Mechanics of Fluids, (2001) Taylor & Francis 8^th Ed.

Mr. Daniel Kearney (2008) Heat Transfer Project Notes

http://www.rpi.edu/dept/chem-eng/Biotech-Environ/SeniorLab/heatx/heatx.htm (12/04/07)

http://www.me.wustl.edu/ME/labs/thermal/me372b5.htm (12/04/07)

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