Physical Chemistry of Foods

5.2.3 Heat Transfer

If a temperature gradient exists in a liquid—and this is also valid for a
solid—heat motion of the molecules will cause the temperature to become
equal throughout; after all, temperature is proportional to the average
kinetic energy of the molecules (Section 4.3.1), and the molecules collide
with each other, thereby transferring momentum and thus smoothing out
temperature differences. Thisdiffusion of heat(or conduction) proceeds in
the same way as diffusion of mass. The diffusion coefficient for heatDHis
generally called the thermal diffusivity. Equations (5.18), (5.20), and (5.21)
remain valid, replacingcbyT. For the transport of heat, the quantity of
heat per unit volume ðrcpTÞhas to be used instead of concentration
(quantity of mass per unit volume). Thereby, Fick’s first equation is
transformed into theFourier equation

dq

dt

¼
DHA

qðrcpTÞ

qx



t

¼
lA

qT

qx



t

l¼DHrcp ð 5 : 22 Þ

where q is the amount of heat (J), l the thermal conductivity
ðW?K
^1 ?m
^1 Þ,rthe mass densityðkg?m
^3 Þ,andcpthe specific heat at
constant pressureðJ?kg
^1 ?K
^1 Þ. The diffusion equations for heat also
apply to solids, since momentum transfer between molecules in a solid is
about as frequent as in liquids.
DH equals about 10
^7 m^2 ?s
^1 ; for most food components this is
correct within a factor of two. For crystalline material the value tends to be
higher than for a liquid, and ice even hasDH& 10
^6 m^2 ?s
^1 (most metals
are in the range 10
^5 –10
^4 ). Since the mass diffusion coefficient nearly
always is< 10
^9 m^2 ?s
^1 , the diffusion of heat is at least 100 times as fast as
the diffusion of mass. Nevertheless, it is still slow at distances longer than a
few mm.
Heat can also be transferred by other mechanisms. The most common
way is byconvection, where cold and hot masses of liquid are mixed, so that
heat diffusion is merely needed at very small distances; the rate of transfer is
thereby greatly enhanced. Heat can be transported byradiationfrom a hot
to a cold surface, where both surfaces are separated by a gas phase or by
vacuum. We will not discuss the theory but merely mention that the rate of
transfer is proportional toðT 14
T 24 Þ, whereT 1 andT 2 are the (absolute)
temperatures of both surfaces.
Another mechanism is heat transfer bydistillation. It is illustrated by
the heat transport into a loaf of bread during baking. Applying Eq. (5.21)
with x^0 ¼4 cm and DH¼ 10
^7 m^2 ?s
^1 , gives a halving time for heat