Analysis of Conduction Heat Transfer in Semi-Infinite Slabs and Infinite Quadrants with Discrete Heat Generation Sources Using Green’s Function Integral Methods – Experimental Approach

Carlos J. Rodríguez Feijoo* Prof.Omar E. Meza Castillo cjavier523@gmail.com

Inter American University of Puerto RicoBayamón Campus

Abstract

The main goal of this project is to create a physical model that will allow us to conduct experiments in a controlled environment so that we can determine how the heat is transferred by conduction into an aluminum slab.

As a starting point for this model, we have decided that our experiment will consist of a discrete source of heat that will transfer heat through a slab of aluminum that will have a set of calibrated thermocouples. This will permit us to acquire live data from the experiment as the heat from the source begins to transfer throughout the slab.

This data will be collected through an interface using the program Labview 2010. The results are going to be compared with analytical results provided by Green’s Function Integral Method. This experimental approach will enable us to conclude if the data we have gathered is correct or if there is some external interference interrupting in our experimental design.

Discussion:

The first step was to select the material that can be easy to work with but will be hard enough to stand to the experimental process without failing. By conducting a little research we determined to use aluminum because it is a malleable material that can be easily shaped to conform to our design. We then selected a slab with a width of ¼ of an inch, and 9 inches by 7 inches since we considered this to be an adequate size to conduct the experiment. The heating source that we are going to use will have to be able to generate a substantial amount of heat to elevate the temperature of the slab so we can measure the difference with our equipment. But this source cannot heat the slab to a point where it reaches a uniform temperature because we will not be able to conduct our experiment. During the experimental process we have tried different methods to heat the plate but many worked better in theory than in practice, this had led us to adapt a soldering gun to our experiment since it can generate and maintain a steady temperature that is sufficient for our experiment. Since the experiment was based on heat transfer, we needed an instrument that could adequately measure the temperature. For this we used thermocouples type (T) that where calibrated according to the procedure to obtain an accurate temperature measurement and determine how the heat dispersed through the material. A vacuum chamber will be used to ensure that no outside contaminant will affect our experiment. This will also prevent the heat from escaping by convection through the air that surrounds the slab. This will ensure that the result we get are constant and do not get any outside interference that can lead to a wrong conclusion.

Literature Cited:

Nellore S. Venkataraman, Omar E. Meza Castillo, “Conduction Heat Transfer in Semi-infinite and Infinite Regions with Discrete Heat Sources”, Acta Astronautica 58 (2006) 15-37.

Acknowledgements:

I will like to Acknowledge Prof. Omar Meza for his collaboration on this project and PR-LSAMP who made possible this opportunity by providing the funding for this investigation.

Introduction: The bases of this experiment are to recreate the results obtained in

Professor Omar Meza’s thesis during his Master degree. Since these results were obtained using an analytical process we have been assigned the task of creating a physical model that will replicate the results as closely as possible.

The main objective is to be able to obtain real time data collection (temperature) of the process of heat transfer by conduction in our experiment.

These will serve as proof of thesis' results and will allow us to conduct further experiments involving the basic geometry of the heating source itself and the relation that exist between this variant and the area that the heat covers in the slab.

Conclusions:

To conclude this project we still need to adapt the physical model to the vacuum chamber to be certain that the results are not being contaminated with some outside interference. But the results obtained so far are conforming to the analytical results that we are trying to replicate. This serves as motivation to continue following our goals with this project.

Results

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Vol

tage

Voltage acros the slab

Voltage_A3

Voltage_A2

Voltage_A1

Voltage_A0

Methods:

The method used is experimental, where the collection of the data will be performed through an LabView interface. The results are represented in a graphical form since it is easier to see that as we get nearer to the heat source the temperature increases considerably. It is this same pattern of data that we are trying to replicate in our physical model. To achieve this we will have to take in consideration radiation and convection heat transfer, a vacuum chamber will be considered for future tests.

Voltage across the slab