TITLE.PM5

782 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th15-1.pm5

where, k 0 = Thermal conductivity at 0°C, and

β= Temperature coefficient of thermal conductivity, 1/°C (It is usually positive

for non-metals and insulating materials (magnesite bricks being the

exception) and negative for metallic conductors (aluminium and certain

non-ferrous alloys are the exceptions).

6. In case of solids and liquids, thermal conductivity (k) is only very weakly dependent on
   pressure ; in case of gases the value of k is independent of pressure (near standard
   atmospheric).


7. In case of non-metallic solids :
   — Thermal conductivity of porous materials depends upon the type of gas or liquid
   present in the voids.
   — Thermal conductivity of a damp material is considerably higher than that of the dry
   material and water taken individually.
   — Thermal conductivity increases with increase in density.


8. The Wiedemann and Franz law (based on experiment results), regarding thermal and
   electrical conductivities of a material, states as follows :
   ‘‘The ratio of the thermal and electrical conductivities is the same for all metals at the
   same temperature ; and that the ratio is directly proportional to the absolute temperature
   of the metal.’’

Mathematically,

k T

σ

∝

or

k

T

C

σ

= ...(15.3)

where, k = Thermal conductivity of metal at temperature T(K),

σ = Electrical conductivity of metal at temperature T(K), and

C = Constant (for all metals) is referred to as Lorenz number

(= 2.45 × 10–8 WΩ/K^2 ; Ω stands for ohms).

This law conveys that the materials which are good conductors of electricity are also

good conductors of heat.

15.2.3. Thermal resistance (Rth)

When two physical systems are described by similar equations and have similar boundary
conditions, these are said to be analogous. The heat transfer processes may be compared by anal-
ogy with the flow of electricity in an electrical resistance. As the flow of electric current in the
electrical resistance is directly proportional to potential difference (dV) ; similarly heat flow rate,Q,
is directly proportional to temperature difference (dt), the driving force for heat conduction through
a medium.
As per Ohm’s law (in electric-circuit theory), we have

Current (I) =

Potential

Electrical

difference ( )

resistance ( )

dV

R ...(15.4)

By analogy, the heat flow equation (Fourier’s equation) may be written as

Heat flow rate (Q) =

Temperature difference ( )dt

dx

kA

F

HG

I

KJ

...(15.5)