**DPS Meeting, Madison, October 1998**

*Session 42. Comets IV*

Contributed Oral Parallel Session, Thursday, October 15, 1998, 2:30-3:50pm, Madison Ballroom C
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## [42.08] Heat Conduction through Surface Structures and Mixtures using Electric Circuits as Analogs

*W. F. Huebner, D. C. Boice (SwRI), J. R. Green (JPL)*

We present a mathematical model using electric analogs to
simulate vertical and lateral conductive heat flow in
surface layers of planetary bodies with topography. The
model can also be used to determine average electric and
thermal conductivities of small-scale granular mixtures (as
opposed to molecular mixtures). The algorithm is general and
applicable to complex compositions. Analogies between
thermal and electric conductivities are basic and well
known. The model uses Kirchhoff's rules for electric
networks.

If a temperature difference is maintained across a solid
body, the thermal energy transported per unit time and unit
area, (the vector heat current per unit area, {\bf Q}), is
proportional to the negative temperature gradient, such that
{\bf Q} = - \kappa \nabla T. Here \kappa is the heat (or
thermal) conductivity of the material. For the electric
analogy we use Ohm's law. If a potential difference is
maintained in a resistive (ohmic) body, the electric charge
transported per unit time and unit area (the vector current
density, {\bf i}) is proportional to the electric field,
such that {\bf i} = \sigma {\bf E} = - \sigma \nabla V.
Here \sigma is the electric conductivity (or specific
conductance) of the material and V is the electric
potential. With {\bf i} replacing {\bf Q} and V
replacing T the parallel nature of thermal and electric
conductivity is established. The thermal conductivity,
\kappa, is a direct analog to the electric conductivity,
\sigma.

The model will be used to verify heat flow measured through
porous mixtures of ice and dust as an analog of comet matter
in the laboratory. Heat flow is simulated by electric
currents through a three-dimensional network of resistors
with emfs representing temperatures at boundaries. We
illustrate our model, for simplicity, with a two-dimensional
network. Each type of material with given conductivity is
represented by a corresponding value for the electric
resistance. The {\it number} of each type of resistor is
proportional to the relative abundance of each material
type. For mixtures, resistors are selected randomly.

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