What is Heat conduction: Definition and 109 Discussions

Thermal conduction is the transfer of internal energy by microscopic collisions of particles and movement of electrons within a body. The colliding particles, which include molecules, atoms and electrons, transfer disorganized microscopic kinetic and potential energy, jointly known as internal energy. Conduction takes place in all phases: solid, liquid, and gas.
Heat spontaneously flows from a hotter to a colder body. For example, heat is conducted from the hotplate of an electric stove to the bottom of a saucepan in contact with it. In the absence of an opposing external driving energy source, within a body or between bodies, temperature differences decay over time, and thermal equilibrium is approached, temperature becoming more uniform.
In conduction, the heat flow is within and through the body itself. In contrast, in heat transfer by thermal radiation, the transfer is often between bodies, which may be separated spatially. Also possible is the transfer of heat by a combination of conduction and thermal radiation. In convection, the internal energy is carried between bodies by a moving material carrier. In solids, conduction is mediated by the combination of vibrations and collisions of molecules, of propagation and collisions of phonons, and of diffusion and collisions of free electrons. In gases and liquids, conduction is due to the collisions and diffusion of molecules during their random motion. Photons in this context do not collide with one another, and so heat transport by electromagnetic radiation is conceptually distinct from heat conduction by microscopic diffusion and collisions of material particles and phonons. But the distinction is often not easily observed unless the material is semi-transparent.
In the engineering sciences, heat transfer includes the processes of thermal radiation, convection, and sometimes mass transfer. Usually, more than one of these processes occurs in a given situation.
The conventional symbol for thermal conductivity is k.

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  1. B

    Calculator Question: Graphing an Equation for Heat Conduction in a Rod

    Homework Statement For the rod in Problem 10 (already solved this, see below): (a) plot u vs. x for t= 5, 10, 20, 40, 100, and 200 (b) plot u vs. t for x= 10, 20, and 30 (c) how long does it take for the entire rod to cool off to a temp. of no more than 1 degree C? Homework...
  2. B

    Heat Conduction Equation - BVP

    Homework Statement Folks, I am self studying through a heat conduction problem involving a 2nd order linear homogenous differential equation which has the solution of the form ##\theta (x)=C_1\cosh mx+ C_2\sinh mx## (1) where ##m \equiv \sqrt \frac{c}{a}= \sqrt{\frac{\beta P}{k A}} ##...
  3. S

    Speed of heat conduction through glass

    Is anyone here familiar with the speed of a temperature wave through Si02 or other electrical insulators? Thanks, S.L.
  4. Z

    Something About My Deduction On the Fourier's Law of Heat Conduction

    My hypothesis is to use two different stable heat sources with different tempreature T1 and T2 (T1>T2) transmits the heat . Then I let the distance between this two heat sourse filled with idea gas or ideal metal in a tube. So if the distance is L, the heat capacity is Cv (Constant). So the...
  5. S

    Heat conduction in a beam with variable x-section

    Say we have a laterally insulated beam and some boundary conditions at either end, be it convective or fixed-temperature, but the cross-sectional area is variable. If the cross-section were constant I'd just say it were a 1-D problem, but I'd imagine that having the cross-sectional area be a...
  6. T

    Derivation of Heat Conduction in Spherical Co-Ordinates

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  7. I

    Transient heat conduction in a slab

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  8. L

    Heat conduction in gravity field without convection

    I used to think that the heat does rise even in solid metals with no gas/liquid around (No density argument is possible then.) But couldn't find anything describing or even verifying it. I'am pretty sure the gravitationally induced anharonicity in the atomic core potentials should have at...
  9. A

    Heat conduction in hollow cilinder.

    Homework Statement Given is a hollow cilinder with inner radius R1 and outer radius R2. The heat conductivity of the material is k. The cilinder has length l and an inner temperature of T1 and outer temperature T2. Determine the temperature gradient in the cilinder and the heat flow that leaks...
  10. A

    Analytical Solutions for 1D Transient Heat Conduction in Cylindrical Coordinates

    Hi, I have written a numerical code to solve the 1D heat equation in cyclindrical coordinates: \frac{\partial T}{\partial t}=\kappa\left(\frac{\partial^{2}T}{\partial r^{2}}+\frac{1}{r}\frac{\partial T}{\partial r}\right) The problem I'm considering is a hollow cylinder in an infinite...
  11. E

    What is the Solution to a Heat Conduction Problem in a Rod?

    Homework Statement Find the solution of the heat conduction problem: 100Uxx=Ut, 0<x<1, t>0; U(0,t)=0, U(1,t)=0, t>0; U(x,0)=sin(2\pix)-sin(5\pix), 0\leqx\leq1 Homework Equations U(x,t)=\sumcne(-n2\pi2\alpha2t)/L2sin((n\pix)/L)...
  12. T

    Heat Conduction with a nuclear source

    In Bird, Stewart, Lightfoot "Transport Phenomena", they post the following equation for heat conduction with a nuclear heat source: Sn=Sn0 [1+b(r/R)^2] where Sn is volumetric thermal energy, r is radius and R is radius of the fuel pellet. The text state that b is a dimensionless...
  13. G

    Modeling 2D Heat Conduction Using Matlab & Central Divided Difference Method

    1. The problem statement I'd like to use Matlab to help me model and solve a simple 2D steady state heat conduction problem: A square section duct is buried in the Earth some distance below the surface. This duct is at a steady temperature of 60 degrees C. I need to use the central divided...
  14. R

    Heat conduction through a slab with internal heat generation

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  15. G

    Heat Conduction of Metal Rod (Differential Equations)

    Hi everyone, I recently started studying heat conduction using differential equations and this has been stumping me for a while. I am having trouble understanding what type of heat conduction problem this is. We are given a 100cm long copper rod with ends maintained at 0 C. The center of the...
  16. K

    Heat Conduction with Insulated Ends

    Homework Statement Let the ends of a copper rod 100 cm long be maintained at 0 degrees C. Suppose that the center of the bar is heated to 100 degrees C by an external heat source and that this situation is maintained until a steady state results. Find this steady-state temperature...
  17. J

    Boundary value problem for heat conduction (HELP)

    Hi, I am trying to work this problem out but I don't know how to solve the boundary value. here is the problem statement thanks in advance
  18. R

    Heat conduction coefficient in tungsten

    Homework Statement Hello! I am supposed to explain the behaviour of the thermal conductivity of tungsten. I have plotted the relation http://img340.imageshack.us/img340/9776/heatcond.jpg is also experimental data Temp[0 10 50 100 300 500 1000 2000 3400] and thermal conductivity...
  19. T

    Archived How Does Fourier's Law Apply to Heat Flux in a Uniformly Heated Slab?

    Homework Statement a) A slab of thickness L and constant thermal conductivity \lambda generates heat at a constant rate throughout of g W m–3. The heat is dissipated from both sides of the slab by convection into the ambient air at a temperature Tf with a heat transfer coefficient h. The...
  20. R

    Doubt in Fourier's Law of Heat conduction

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  21. C

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  22. M

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  23. B

    Heat conduction problem with variable temperature

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  24. B

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  25. T

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  26. M

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  27. A

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  28. J

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  29. J

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  30. D

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  31. D

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    Describe the physics behind an engineering system where heat conduction phenomena plays an important role. (a familiar system)
  32. U

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    Homework Statement A cubical box 22cm on a side is constructed from 1.3cm -thick concrete panels. A 100 W lightbulb is sealed inside the box. What is the air temperature inside the box when the light is on if the surrounding air temperature is 20 C? Homework Equations rate of heat transfer...
  33. N

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  34. A

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  35. N

    Calculate Heat Loss Through House Wall - R19 & Brick Layer

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  36. P

    Deriving Steady-State Heat Conduction Equation in a Sphere

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  37. cepheid

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  38. F

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  39. T

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  40. P

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  41. S

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  42. B

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  43. Somefantastik

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  44. U

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  45. P

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  46. P

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  47. M

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  48. L

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  49. C

    How Does Steady State Heat Conduction Impact Home Heating System Design?

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  50. D

    Question about heat conduction equation.

    I know how to solve a 1-D heat conduction equation when both ends are kept at 0 temperature(using separation of variables and Fourier series.). In the notes, the prof asked us to solve for one end kept at zero and the other insulated (at x=L) and referred to a non-existent chapter in our...
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