Heat Conduction in a Body Subject to an Oscillating Heat Source
Download
1 / 33

Heat Conduction in a Body Subject to an Oscillating Heat Source - PowerPoint PPT Presentation


  • 130 Views
  • Uploaded on

Heat Conduction in a Body Subject to an Oscillating Heat Source. By Seth Flaxman Evanston Township High School. Problem Statement. Copper plate in contact with an oscillating heat source Tests at various velocities Measured temperature distribution Computer simulations Physical experiments.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Heat Conduction in a Body Subject to an Oscillating Heat Source' - garrett-clarke


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Heat Conduction in a Body Subject to an Oscillating Heat Source

By Seth Flaxman

Evanston Township High School


Problem Statement Source

  • Copper plate in contact with an oscillating heat source

  • Tests at various velocities

  • Measured temperature distribution

  • Computer simulations

  • Physical experiments


Purpose Source

  • Heat conduction problems

  • Novel problem: oscillating heat sources at various velocities

  • Importance


Background Source

Heat flow is a part of everyday life.

Examples:

Radiation: Heat transfer due to the sun

Convection: Hot air currents in an oven

Conduction: Touching something that is hot


Heat Flux Source

Fourier’s Law of Conduction

q - heat flux

k - thermal conductivity

T -temperature distribution, dependent on time and space


Heat Conduction Source

Heat Equation

k - thermal conductivity

q - heat generation term

ρ - density of the material

c - heat capacity of the material

T - temperature distribution


Previous Work Source

  • Work by Krishnamurthy on oscillating heat sources

  • Computer model developed by Backstrom

A steel bar heated by a moving torch


Methods Source

Computer Simulation and Laboratory Experiment

  • Copper plate

  • Heat source

  • Heat source velocity

  • Boundary conditions

  • Time period



Thermistor positions in the copper plate Source

Laboratory Experiment




Laboratory Experiment Source

  • Each run lasted 120 seconds

  • Temperature readings recorded every 5 milliseconds


Computer Model Source

  • Heat equation

  • Boundary conditions

    • Insulated

    • Initial temperature

    • Heat flux

Contact area in the laboratory

Contact area in the computer model


Results Source

Temperature vs. Time at 0.40 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results Source

Temperature vs. Time at 0.040 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results Source

Temperature vs. Time at 0.0079 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results Source

Temperature vs. Time at 0.0040 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results Source

Laboratory Results

Temperature vs. Time at 0.40 m/sec

Temperature vs. Time at 0.0040 m/sec

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Laboratory Results Source

Temperature Change by Probe (ºC)


Discussion Source

  • Interesting behavior at low velocities

  • Computer simulations and experimental results agree

  • Average rise in temperature is independent of velocity

  • New results, not in literature


Further Research Source

  • Analytic solution

  • Other types of oscillatory motion: simple harmonic motion

  • Slower velocities

  • Different materials


Acknowledgments Source

Special thanks to Dr. Mark Vondracek, my parents, my brothers, Dr. Russell Kohnken, and Ms. Lisa Oberman.

Also, thanks to David L. Vernier of Vernier Software and Technology and Marcus H. Mendenhall, author of the Python Laboratory Operations Toolkit.


Results Source

Heat Vector Field Plot

Heat Vector Field Plot (0.040 m/sec.)

Location of heat source

y (cm)

x (cm)


Methods Source

P = IV

P = 2.12 * 10 = 21.2 W

Heat flux = 21.2 / (.023 * .0275) = 33,517 W / m2

2.75 cm


Methods Source

Heat Source Velocities (m/sec.)



FlexPDE Descriptor File Source

TITLE 'Temperature vs. Time at 0.0040 m/sec' { intel.pde }

SELECT errlim=1e-3 spectral_colors

VARIABLES

temp( range=400)

DEFINITIONS

Lx = .2286 { in meters }

Ly = .1294 { in meters }

RealHeight = .1524 { in meters }

d0 = .0275 { length of heat source in meters }

heat_flux = -33517 { W / m^2 }

time_interval = 120

vx = .0040 { Moving heat source velocity in m/sec }

period = (Lx - d0) / vx

oscillations = time_interval / period

length = Lx

heat = 0

tempi = 26.5 { degrees Celsius }

k = 386 {Thermal conductivity of copper }

rcp= 8954 * 383.1

{ Density of copper times specific heat }

{ Source: p. 657 of Heat Conduction Ed. 2 by Ozisik [7] }

fluxd_x = -k*dx(temp)

fluxd_y = -k*dy(temp)

fluxd = vector(fluxd_x, fluxd_y)

fluxdm = magnitude(fluxd)

step = abs(ustep( mod(t, period * 2) - period)

* period - mod(t, period) )

{ In FlexPDE, mod does accept floats. This means repeated subtraction rather than remainder. }

fluxd0 = heat_flux * [ustep(vx* step + d0 - x)

- ustep(vx * step - x)]

INITIAL VALUES

temp = tempi

EQUATIONS

div(fluxd) + rcp * dt(temp) = 0

BOUNDARIES

region 'domain'

start (0,0) natural(temp) = 0 line to (Lx,0)

natural(temp) = 0 line to (Lx,Ly)

natural(temp) = fluxd0 line to (0,Ly)

natural(temp)= 0 line to finish

TIME

from 0 to oscillations * period

PLOTS

for t=0 by period * .1 to

oscillations * period

contour( temp) painted

vector( fluxd) norm

elevation( fluxd0 ) from (0,0) to (Lx,0)

HISTORIES

HISTORY(temp) at

(Lx/5,2*RealHeight/3) (2*Lx/5, 2*RealHeight/3)

(3*Lx/5,2*RealHeight/3) (4*Lx/5, 2*RealHeight/3)

(Lx/5,RealHeight/3) (2*Lx/5, RealHeight/3)

(3*Lx/5,RealHeight/3) (4*Lx/5, RealHeight/3)

END


Boundary Conditions Source

Initial temperature (26.5 ºC):

Insulated on all sides:

Subject to oscillating heat flux on top:

fluxd0 = heat_flux * [ustep(vx * step + d0 - x) - ustep(vx * step - x)]


Presentation Outline Source

  • Problem Statement

  • Purpose

  • Methods

  • Results

  • Further Research


ad