Thermal Resistance to Heat Flow

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.

Thermal Resistance to Heat Flow

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

Thermal Resistance to Heat Flow

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.

Thermal Resistance to Heat Flow

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

Thermal Resistance to Heat Flow

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

r= 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 to Heat Flow

Thermal Resistance to Heat Flow

Thermal resistance of the dielectric is

Thermal Resistance to Heat Flow

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,

Thermal Resistance to Heat Flow

Permissible current per conductor is given by;

Thermal Resistance to Heat Flow

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.

Updated: June 3, 2018 — 12:00 am