Heat Conduction of Zinc Specimen Femlab Simulation Measurement Calibration Technique: Effects of Heat Loss Through Specimen Surface Area

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.

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

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)

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

Visual Of V.I. Instrumentation Block Diagram

Visual Of V.I. Instrumentation Temperature Output Interface

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.

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

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 Thermally Insulated Surface Heat Loss Effects Through Sides Heat Loss Effects Through Sides 2 Sensor 1 Sensor 2 Actual to Model Scaling: 1 unit = 50mm

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

FEMLAB RESULTS Phase I – Velocity Solution

Phase I – Velocity Solution (cont)

Cylinder Boundary Viscous Drag Vs. Arc Length

Phase I – Velocity Solution (cont) Cylinder Boundary Vorticity Profiles Vortex Strength Vs. Arc Length Vortex Strength Vs. X - Distance

Phase II – Temperature Solution (Thermally Insulated) ∆T = degrees

Phase II – Temperature Solution (Convective Heat Loss Effects) ∆T = degrees

Phase II – Temperature Solution (Convective Heat Loss Effects) Heat Flux Profile Vs. Z – Direction

Simulation Results When accounting for the heat flux through the side surfaces of the cylinder, the temperature difference is decreased by the following ratio: Π = / = Which yields a percent reduction from the thermally insulated case to heat losses of: Ψ = 1 – Π = %

Measurement Results Room Temperature Results Temperature Vs Time (for each Thermocouple)

Room Temperature Results (cont) Temperature Difference Vs. Time (steady–state time)

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

Liquid Nitrogen Results ( ≈77 K ) (cont) Temperature Difference Vs. Time (note: Drastic Drop when heat source was turned off ≈9500 sec

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. θ 1 =(T 1 –To)/(T 1 –T 2 ) & θ 2 =(T 2 –To)/(T 1 –T 2 )

Thermal Conductivity TO BE CONTINUED…

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