# Heat transfer project using matlab

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Design Goal:

Car radiators are important for removing the heat produced by a car engine, thus enabling the engine’s efficient operation.   Radiatorsare an excellent example of cross-flow heat exchangers.  Hot engine coolant runs through several tubes, where heat is lost to air flowing perpendicular to the coolant flow.  In this project, you are going to design a car radiator to provide the maximum heat transfer from the coolant to surrounding air.

Design Specifications and Constraints:

In the above figure, the coolant enters an inlet plenum, where the flow is split into a number of parallel branches.  You may assume that the flowrate through each branch is the same for simplicity.  Each branch contains a tube with a diameter of 1 cm and a wall thickness of 1 mm.  Along the outside of the tubes are fins spaced 8 mm on center; thesethat may be approximated as annular fins with a thickness of 1 mm and an outer radius equal to half of the gap between two tubes as shown in the figure below:

The entire finned tube portion of the radiator contains dimensions of 0.3 m wide × 0.2 m tall. Therefore, the tubes are 0.3 m long, and the distance between the furthest points in the annular fins associated with top and bottom tubes is 0.2 m.Please note that distance between tubes is reduced as number of tubes is increased.Your job is to determine the maximum heat transfer in the radiator by varying the number of tubes in the radiator.

Other design constraints are as follows:

• The radiator is comprised solely of Aluminum Alloy 2024-T6.
• The bulk air speed is 10 m/s. You can take all properties of air at 300 K for simplicity.
• The heat transfer coefficient of the air is . (this will be covered in Chapter 7).
• The total mass flow rate of coolant is fixed at 0.01 kg/s. Coolant specific heat is J/(kg-K).
• The heat transfer coefficient of the coolant is (this will be covered in Chapter 8).
• The coolant enters at 70°C and the air enters at 20°C.

Part 1-

## Hand calculation (Base Design)

First, you will create a base case design by setting the number of tubes to 5.

1. Determine the equivalent radius of the annular fins for the specified number of tubes.
2. Determine the thermal resistance for the fin array (theexternal and internal heat transfer coefficients have been provided). You can determine the fin efficiency and resistance of annular fin from equations Table 3.5. You will need to use Table B.5 to get the values for modified Bessel functions. , , , and .
3. Determine the total thermal resistance for heat transfer from the coolant to the air.
4. Calculate the heat transfer achieved per tube. To determine the exiting coolant temperature ( ), use the modified version of the expression from the text for a tube with fixed wall temperature:

where °C and °C.

1. Calculate total heat transfer achieved by the radiator. Use the following equation:

Part 2

### Variation of Input Parameter (MATLAB)

(50 pts)& Report (20 pts)

Develop a MATLAB program to accomplish your base design ( ).You will need to use MATLAB’s built-in Bessel function capability:  in MATLAB is besselk(0,x); is besselk(1,x),  is besseli(0,x), and  is besseli(1,x).After your model is now created (and you are getting the same answer as your hand-caluclations), then vary the number of tubes to determine its effect on the total radiator heat transfer exchange.  Create a plot in MATLAB showing how the heat transfer is affected by the variation in the number of tubes from 5 to 15.What is the optimal number of tubes?  What causes this variation in total heat transfer with the number of tubes?

Also, determine the cost of manufacturing the heat exchanger.  Labor and material costs for manufacturing result in 80 cents per fin and \$3.25 per tube (disclaimer: these values are completely made up for this project!).  Determine the number of tubes in the heat exchanger that provides the least expensive heat exchanger that can dissipate at least 550 W.

#### Report

Write a concisereport in Microsoft Word describing the derivation of your equations and a description of your analysis.  Your report must include the aforementioned plot and a final design recommendation that includes important details such as the number of tubes, the exiting coolant temperature, the coolant flow rate per tube, and the total heat transfer.  Your MATLAB code must be included as an appendix to the report.  Sections of the report are as follows:

• Cover Page
• Problem Overview
• Base Case Design
• Calculations, descriptions, and discussion of the calculated values. Do they seem reasonable?
• Variation of Input Parameter
• Plot of heat transfer rate versus the number of tubes.
• Final design specifications.
• Discussion on the relationship shown on the plot. What is the physical reasoning behind the trends that are seen?
• Conclusions
• Brief summary of the project, including the determination of the base case design heat exchange value, the optimal number of tubes, and the physical reasoning behind the trends in the plot.
• Appendix: MATLAB Code
• Warning! If the code is not provided then a zero will be given for the project.
• if you are unfamiliar with MATLAB, a good tutorial can be found at