Heat Conduction in a Body Subject to an Oscillating Heat Source
Sponsored Links
This presentation is the property of its rightful owner.
1 / 33

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


  • 102 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Heat Conduction in a Body Subject to an Oscillating Heat Source

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

  • Copper plate in contact with an oscillating heat source

  • Tests at various velocities

  • Measured temperature distribution

  • Computer simulations

  • Physical experiments


Purpose

  • Heat conduction problems

  • Novel problem: oscillating heat sources at various velocities

  • Importance


Background

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

Fourier’s Law of Conduction

q - heat flux

k - thermal conductivity

T -temperature distribution, dependent on time and space


Heat Conduction

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

  • Work by Krishnamurthy on oscillating heat sources

  • Computer model developed by Backstrom

A steel bar heated by a moving torch


Methods

Computer Simulation and Laboratory Experiment

  • Copper plate

  • Heat source

  • Heat source velocity

  • Boundary conditions

  • Time period


Laboratory Experiment


Thermistor positions in the copper plate

Laboratory Experiment


Laboratory Experiment


Laboratory Experiment


Laboratory Experiment

  • Each run lasted 120 seconds

  • Temperature readings recorded every 5 milliseconds


Computer Model

  • Heat equation

  • Boundary conditions

    • Insulated

    • Initial temperature

    • Heat flux

Contact area in the laboratory

Contact area in the computer model


Results

Temperature vs. Time at 0.40 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results

Temperature vs. Time at 0.040 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results

Temperature vs. Time at 0.0079 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results

Temperature vs. Time at 0.0040 m/sec

Computer Simulation

Laboratory Results

Temperature (ºC)

Temperature (ºC)

Time (sec.)

Time (sec.)


Results

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

Temperature Change by Probe (ºC)


Discussion

  • 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

  • Analytic solution

  • Other types of oscillatory motion: simple harmonic motion

  • Slower velocities

  • Different materials


Acknowledgments

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

Heat Vector Field Plot

Heat Vector Field Plot (0.040 m/sec.)

Location of heat source

y (cm)

x (cm)


Methods

P = IV

P = 2.12 * 10 = 21.2 W

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

2.75 cm


Methods

Heat Source Velocities (m/sec.)


Thermistor Circuit


FlexPDE Descriptor File

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

SELECTerrlim=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

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

  • Problem Statement

  • Purpose

  • Methods

  • Results

  • Further Research


  • Login