Heat Transfer and Pipe Geometry
Date: Spring 2013
Does the orientation of a solid object, such as a metal pipe, affect the rate heat is conducted through it? For example, if heat is applied to the lower end of a vertical pipe, will the upper end become warm sooner than the lower end would if the upper end was heated? Disregard any affect of heated air rising along the pipe when the lower end is heated. My question is aimed at determining whether heat from Earth's core is conducted upward faster than the actual speed of fluid mantle material.
The orientation of an amorphous, or a multicrystalline solid object, has
no effect whatsoever on its heat conductivity. However, there are
certain types of crystals that do in fact conduct heat somewhat better
in one orientation of the crystal's structure than others. But for this to
be useful, an object would have to be made of a very large single
crystal. Earth's core is clearly, however, not a single crystal, and
hence a preferential direction for heat conductivity is not possible.
Generally, gravity is not a consideration except in the case you point out, convective heat flow due to rising air. When we look at a solid pipe, its orientation is not used to calculate the rate of heat flow within the pipe. Most important is the thermal conductivity, i.e., how well the material conducts heat through it.
Kyle J. Bunch, PhD, PE
Your pipe example is problematic relative to Earth's dynamics. I think
you are convoluting a lot of different factors. First, you have to
separate intrinsic anisotropy of materials (anisotropic means the
orientation of the material affects its properties). Simple pipe
metals are macroscopically anisotropic. But Earth's interior is
not such a simple material. It has layers that may differ in
orientation, and fluid convection moving heat, not just conduction.
You also must consider two separate force fields that exist in Earth's core: magnetic and gravitational. When dealing with iron, for
example, both of these fields will influence the convection of
material (and may impact conduction through anisotropy). Over long
time periods that matter in geophysical dynamics, Earth is very
much not a static solid. In short, I do not think the pipe analogy is
But, to try to answer your question, the answer depends on your
assumptions. Diffusion and turbulence will cause heat to move faster
at the front edge of a fluid front. This is true for pseudo-plug-flow,
an impinging jet, etc. However, the same occurs at the back end of a
plug -- so while there is some heat moving 'ahead of the front',
there'\ is some heat behind the front that is lagging behind. So the
'average' could be no change. The specific circumstances of a given
system govern if there is a net increase in 'speed' of heat flow or if
there is not. In solids (where you neglect mass diffusion and
convection), and if you assume the materials are isotropic, and if you
neglect force fields, then the heat will flow equally in all
directions. But these assumptions effectively ruin this model as an
analog for dynamics of Earth's core.
Hope this helps,
Thanks for the question. Yes, the orientation of a solid object affects the rate of heat flow through an object. Generally speaking, the more material that the heat has to travel through, the slower the rate of heat conduction.
To answer your second question, both ends will become warm at the same rate as gravity will have negligible affect on heat flow. Of course, we are assuming the pipe is a short distance, much less than the radius of Earth.
For the last question, the travel of hot mantle fluid from the core to the surface does increase the total rate of heat transfer from the core to the surface. Convection is the process of heat transfer and fluid transfer. All else being equal, convection is one of the fastest methods of heat transfer.
I hope this helps. Please let me know if you have more questions.
Conduction of heat in a solid is not affected by gravity.
For fluids, the situation is quite different.
Dr. Ali Khounsary
Advanced Photon Source
Argonne National Laboratory
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