Page 22 - Packed bed columns for absorption, desorption, rectification and direct heat transfer

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2
c.pJV—dt = AV t,dV.dT (43)
8

1
After simplifying and introducing the symbol a a = , called
c.p
coefficient of temperature conductivity, from Eq. (43) it is obtained

^ = a aV"t (44)

The equation (44) is called Fourier differential equation of conductivity
in immovable medium.

1.2.1.2.2. Differential equation of heat convection
Convective heat transfer is the transfer of heat from a moving fluid flow
to a solid surface. Because the viscosity of the liquid is many times greater than
that of the gas phase, the same phenomenon takes place also at the interface of
two phases moving with different velocities.
There are two types of convection, forced one at which the moving is
due to the action of outside mechanical energy, and free convection due to
temperature difference in the fluid volume and resulting difference of the fluid
density. The buoyancy force per unit volume in this case is

(45)

where pand p , are the fluid density in two points with two different
temperatures t and tj.
The acceleration due to this force is

(46)
Pi

To obtain the differential equation of convective heat transfer, let us
consider a parallelepiped in the moving fluid with edge dimensions dx, dy and
dz. Let us assume that this is a steady state process without changing of the