2 - CHG 2314 Heat Transfer Part 2a Introduction to...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
University of Ottawa, CHG 2314, B. Kruczek 1 CHG 2314 Heat Transfer Part 2a Introduction to Conduction - Fourier’s Law - Heat diffusion equation - Thermal properties
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
University of Ottawa, CHG 2314, B. Kruczek 2 Fourier’s Law | Fourier’s law is a rate equation that allows determination of the conduction heat flux from knowledge of the temperature distribution in a medium | In most general (vector) form for multidimensional conduction Fourier’s law is: | Implications of Fourier’s law: z Heat transfer is in the direction of decreasing temperature (basis for negative sign) z Fourier’s law servers to define the thermal conductivity of the medium: z Direction of heat transfer is perpendicular to the lines of constant temperature (isotherms) z Heat flux vector may be resolved into orthogonal components q" k T = −∇ G JG kq " T G
Background image of page 2
University of Ottawa, CHG 2314, B. Kruczek 3 Fourier’s Law in different coordinates | Cartesian coordinates: T ( x,y,z ) | Cylindrical coordinates: T ( r, φ ,z ) | Spherical coordinates: T ( r, , θ ) (2.3) " TTT qk i kj k k xyz →→→ ∂∂∂ =− x q ′′ y q z q (2.22) i k j k k rr z →→ ∂∂ r q q z q (2.25) sin TT T i k j k k r θφ r q q q
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
University of Ottawa, CHG 2314, B. Kruczek 4 Fourier’s Law and heat rate | Cartesian coordinates ( x,y,z ) are all equivalent z When Fourier law is simplified to one dimension, it can be written in terms of x, y, or z coordinate z In Cartesian coordinates typically the area for heat conduction does not change in the direction of flow so that analysis in terms of heat flux and heat flow are the same | Angular (cylindrical or spherical) coordinates are not equivalent z When Fourier law in angular coordinates is simplified to one dimension, it becomes: z In one-dimensional heat conduction in angular coordinates, the area for heat conduction changes in the direction of flow: " dT qk dr =− "" ' ' " " Cylinder: 2 or 2 rr r r r r qA q r L q q r q ππ == "2" Sphere: 4 2 r r q r r L q () or , φ φθ NB: In angular coordinates , the temperature gradient is still based on temperature change over a length scale and hence has units of ° C/m and not ° C/deg. ( ) or ,
Background image of page 4
University of Ottawa, CHG 2314, B. Kruczek 5 Heat (Diffusion) Equation | A differential equation whose solution provides the temperature distribution in stationary medium. | Based on applying conservation of energy to a differential control volume through which energy transfer is exclusively by conduction. | Cartesian coordinates: (2.17) p TTT T kkk q c xx yy zz t ρ ⎛⎞ ∂∂ +++ = ⎜⎟ ⎝⎠ ± Net transfer of thermal energy into the control volume (inflow-outflow) Thermal energy generation Change in thermal energy storage z Applying conservation law for closed system to the control volume: (1.11) in out g st E EE E −+ = ±± z Leads eventually to:
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
University of Ottawa, CHG 2314, B. Kruczek 6
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/30/2011 for the course CHG 2314 taught by Professor Kruz. during the Spring '10 term at University of Ottawa.

Page1 / 17

2 - CHG 2314 Heat Transfer Part 2a Introduction to...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online