Heat Conduction of Zinc Specimen

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Heat Conduction of Zinc Specimen

• Femlab Simulation Measurement Calibration
  Technique Effects of Heat Loss Through Specimen
  Surface Area

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Experiment Objectives

• The main objective in this experiment is to
  measure the effective thermal conductivities of a
  material within a temperature range of 77K-350K.
• This will allow us to classify and identify any
  similarities discovered by the experimental data
  compared with published data on the specific
  material.
• To familiarize ourselves with the concepts and
  principles that govern similar thermodynamic
  systems.
• To gain insight and knowledge of various
  measurement techniques associated with thermal
  transport.
• Also to become familiar with setup and use of
  various pieces of equipment needed to perform the
  experiment.

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Theory and Concepts
(2)
---------------------------------------
(Short-Hand Notation)
(Conduction along x-direction) These expressions
lead to the 2nd Order Time Dependant Heat
Diffusion Differential Equation, which has the
following form (non-linear, 3-D general form)
----------------------- (General Heat Diffusion
Relation)
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Experiment Overview

• Heat source Used a resistor with a voltage
  running through it. Causes heat dissipation in
  the form of power (i.e ? heat flux)
• Measurement Device (Thermocouples) Carefully
  placed 2 thermo-sensors (30mm apart) in order to
  record data for at least two different spatial
  locations.
• LABVIEW Easily Recorded Measurements using the
  DAQ Assistant Box
• GNU Octave (Data Analysis)

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Data Acquisition

• LABVIEW Data Acquisition Software
• Recorded Measurements using a virtual instrument
  based software.
• Directly converts measurements into temperatures
  rather than direct voltages.
• Shell Script, GNU Octave
• Shell script for command execution and file
  manipulation
• GNU Octave for data manipulation, plotting, and
  analysis

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Visual Of V.I. Instrumentation
Block Diagram
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Visual Of V.I. Instrumentation
Temperature Output Interface
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Experiment CAD Model
Shows a rough CAD Model of the measurement
apparatus. Consists of Zinc cylinder, hot plate
(inward heat flux), and wiring to the LABVIEW DAQ
box for measurement recording.
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Application of FEMLAB

• Problem
• Recorded measurements do not account for loss of
  energy due to convective heat flux through
  surface of cylinder.
• Solution
• FEMLAB simulation was performed to adjust
  measurements to include convective energy losses.
  The results were used to compute the thermal
  conductivity of the material.

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FEMLAB GEOMETRY

• Sensor 1 was placed at z .6 in the FEMLAB model
  of the system.
• Sensor 2 was placed at z 1.2, which gives a
  total separation distance .6.
• This will allow us to compare the temperature
  differences between the two sensors for the two
  cases
• Thermally Insulated Surface
• Heat Loss Effects Through Sides

Actual to Model Scaling 1 unit 50mm
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FEMLAB Simulation Parameters

• Modules
• 2D Incompressible Navier Stokes
• 2D Heat Diffusion Equation (Energy Transfer)
• Simulation Geometry
• Cylinder encapsulated by a rectangle box
  representing systems physical boundaries. (I)
• 2D Axial Symmetric rectangle (cylinder) that
  was used for the energy transfer equation with
  the velocity solution of part 1. (II)

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FEMLAB RESULTS

• Phase I Velocity Solution

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• Phase I Velocity Solution (cont)

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• Phase I Velocity Solution (cont)
• Cylinder Boundary

• Viscous Drag Vs. Arc Length

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• Phase I Velocity Solution (cont)
• Cylinder Boundary

Vorticity Profiles Vortex Strength Vs. Arc
Length Vortex Strength Vs. X - Distance
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• Phase II Temperature Solution
• (Thermally Insulated)

?T 1.034483 degrees
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• Phase II Temperature Solution
• (Convective Heat Loss Effects)

?T .732588 degrees
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• Phase II Temperature Solution
• (Convective Heat Loss Effects)

Heat Flux Profile Vs. Z Direction
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Simulation Results

• When accounting for the heat flux through the
  side surfaces of the cylinder, the temperature
  difference is decreased by the following ratio
• ? .732588 / 1.034483 0.708168
• Which yields a percent reduction from the
  thermally insulated case to heat losses of
• ? 1 ? 29.183

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Measurement Results

• Room Temperature Results

Temperature Vs Time (for each Thermocouple)
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• Room Temperature Results (cont)

Temperature Difference Vs. Time (steadystate
time)
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• Liquid Nitrogen Results ( 77 K )

Heat Source was turned off at kink at about 9500
sec
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• Liquid Nitrogen Results ( 77 K ) (cont)

Temperature Difference Vs. Time (note Drastic
Drop when heat source was turned off 9500 sec
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Non-Dimensional Temperature Profile

• Non-Dimensional Profile of Thermo1. Notice the
  spike at about 9540 sec. This is when T1 T2
  for a split second as a consequence of turning
  the heat source off and instant cooling occurs.

?1(T1To)/(T1T2) ?2(T2To)/(T1T2)
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Thermal Conductivity

• TO BE CONTINUED

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