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In this semester we have considered two "transport equations" -- equations that describe something moving across space as a result of differences in the value of some variable:

- the Hagen-Poisseuile
(HP) equation that describes how pressure drops in a pipe are associated
with the motion of a volume of fluid, Δ
*P*=*ZQ*, where*P*is the pressure,*Z*is the resistance to flow, and*Q*is the volume of fluid per second, and - Fourier's law that described
how the flow of heat energy is associate with changes in temperature, Δ
*T*=*ZΦ*where*T*is the temperature,*Z*is the thermal resistance, and*Φ*is heat energy per second.

(a) In both of these cases, the resistance depends on the shape of the material,
but they depend on it in different ways. For each case describe how the resistance
depends on the shape of the object doing the resisting (length along the flow,
*L*, and area perpendicular to the flow, *A*) and explain the mechanism of
why each behaves the way it does.

(b) Fourier's law is often written as Δ*T* = *Rφ* where *φ* = *Φ/A*.
If we do this, how does *R* depend on *L* and *A*? Considering
situations where we want to manage heat flow, discuss why this form of the
equation might be more convenient that the one quoted above.

Page last modified December 13, 2008: M24