A Numerical Study on Different Types of Fins

Fin is nothing but an extended surface found on the heat exchanging devices such as radiators in Car, Bike engines, Computer CPU heatsinks and Heat exchangers in power plants. An efficient Fin can really increase the performance of a system. There are various types of Fin and analyzing those theoretically takes a lot of effort. So, researchers around the world take help of numerical methods to analyze complex problem such as heat transfer through Fin. In this project, you will work on solving the various type of fin using numerical methods and compare it with a theoretical solution where it exists.

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In this project, you will study conductive heat transfer under one dimensional & two dimensional, steady-state conditions. The term one-dimensional refers to the fact that only one coordinate is needed to describe the spatial variation of the dependent variables. Hence, in a one-dimensional system, temperature gradients exist along only a single coordinate direction, and heat transfer occurs exclusively in that direction, whereas in a two-dimensional system, temperature gradients exist along two coordinate directions. The system is characterized by steady-state conditions if the temperature at each point is independent of time. Considering steady-state conduction by discussing heat transfer with no internal generation of thermal energy. The objective is to determine expressions for the temperature distribution and heat transfer rate in the different cross-sectional area of Fins.

Finally, using 1-D heat conduction, 2-D heat conduction, and convective heat transfer, you will analyze various types of fins (straight fin of the uniform cross-sectional area and non-uniform cross-sectional area, annular fin and pin fin) using both Analytical and Numerical methods. After solving you have to compare the numerical result with the theoretical result to check the accuracy of your solution and validating your numerical solution.

• Fin: These are extended surfaces from an object which helps in increasing heat transfer rate to or from the environment by increasing convection.
• Conductive Heat Transfer: Heat transfer is classified into various mechanisms, such as conduction, convection, radiation. The simplest mode of heat transfer is by conduction. Conductive heat transfer is the phenomena in which heat is transferred from one body to another due to temperature difference when they came in contact.

• Convective Heat Transfer: Convective heat transfer is a mechanism where the transfer of heat occurs because of intermolecular interaction and movement of matter. This mode of heat transfer will occur only when there will be contact between solid and liquid or liquid and liquid.
• FDM: This is one of the discretization techniques used in numerical analysis to solve differential equation by approximating the derivatives. Here we discretize both space and time into N no of data points, where we store the data and keep updating as we move forward in time.
• Taylors Series Expansion: To implement the finite difference method, Taylor series representation of a function should be known. In mathematics, Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function’s derivatives at a single point. That is, if a function is continuous and we know its derivative at a point, then we can easily determine its value on the next neighboring point in the domain by using Taylor series.

Project Implementation:

1. At first do some research on numerical methods, types of Fins and governing equation for heat transfer through Fins.
2. Then, according to the boundary conditions solve governing equations of heat transfer through the Fin. In this step, you also need to write C programming codes to calculate the temperature distribution over the Fin at a no. of points. Save the result data in a text file for post-processing purpose.
3. Then, find a Numerical solution to those equations using FDM. Chose Forward in time and center in space discretization (FTCS) to get a better result. In this step, you have to write codes to discretize the domain and interact the solution for a number of times until you get an accuracy of 10e-5. Don’t forget to save the result data in a text file.
4. Plot the result data using Gnuplot or Minitab. For plotting, contours use Minitab for ease and convenience.
5. Compare your result for an analytical solution and numerical solution by plotting them simultaneously. If both of your solutions are coinciding or nearer to coincide then your numerical solution is correct.
6. After solving the one-dimensional problem, go for more complex problems involving variable cross-section area.

Project Brief: At the end of this project you will have good knowledge of heat transfer through fins, mathematical modeling, and numerical methods. You can use this experience to model fluid flow problems (CFD) and solve them using numerical methods.

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Software requirements:

1. DevC++: You will be needing DevC++ software to write logic and interact the solution for a number of times.

2. Gnuplot: Also, you will be needing plotting software such as Gnuplot to plot the result data and compare the solution.

Programming language: C programming language

• Dev-C++
• Gnuplot

• Numerical Methods
• CFD

A Numerical Study on Different Types of Fins