Thermal Resistance to Heat Flow:

The Thermal Resistance to Heat Flow between two points in a medium (e.g. insulation) is equal to temperature difference between these points divided by the heat flowing between them in a unit time i e.

In SI units, heat flowing in a unit time is measured in watts.

Clearly, the SI unit of thermal resistance is °C per watt. This is also called thermal ohm.

Like electrical resistance, thermal resistance is directly proportional to length l in the direction of transmission of heat and inversely proportional to the cross-section area a at right angles to that direction.

where k is the constant of proportionality and is known as thermal resistivity.

Thermal Resistance of Dielectric of a Single Core Cable:

Let us now find the thermal resistance of the dielectric of a single-core cable.

Let               

r = radius of the core in metre

r₁ = inside radius of the sheath in metre

k = thermal resistivity of the insulation (i.e. dielectric)

Consider 1m length of the cable. The thermal resistance of small element of thickness dx at radius x is (See Fig. 11.21)

Thermal resistance of the dielectric is

The thermal resistance of lead sheath is small and is generally neglected in calculations.

Permissible Current Loading:

When considering heat dissipation in underground cables, the various thermal resistances providing a heat dissipation path are in series. Therefore, they add up like electrical resistances in series. Consider a cable laid in soil.

Let

I = permissible current per conductor

n = number of conductors

R = electrical resistance per metre length of the conductor at the working temperature

S = total thermal resistance (i.e. sum of thermal resistances of dielectric and soil) per metre length

t = temperature difference (rise) between the conductor and the soil

Neglecting the dielectric and sheath losses, we have,

Permissible current per conductor is given by;

It should be noted that when cables are laid in proximity to each other, the permissible current is reduced further on account of mutual heating.