These are basically applicable to steady state conduc­tion in one direction through a uniform cross-section, e. g., a flat plate as illustrated in Fig 1.17.

Qt = total heat passing per unit time

A = area of plate perpendicular to direction of

heat flow

x = plate thickness

11 = temperature of hot face

i; = temperature of cold face

к = coefficient of thermal conductivity of the

plate material.

If we assume that к remains constant and that the relationship between heat and temperature is linear:

Qj/A = k(t] — t2)/x (1.1)

= q known as the heat flux.

This expression is sometimes written as:

Qt — (ti — t2)/(x/kA)

where x/kA is known as the thermal resistance.

This term is analogous to electrical resistance, its value depending upon the material properties and the geo­metry. It can, be applied in a similar manner to the application of’Ohm’s Law to electrical circuits. Thus to obtain a high rate of heat transfer through a solid fuel element we would endeavour to have a large tem­perature differential and a low thermal resistance, although of course there may be other non-heat trans­fer limitations to achieving this objective. The simple Equation (1.1) can only be applied directly to a flat plate geometry. The majority of fuel elements used in reactors are cylindrical and it will be useful when we apply the laws of conduction to fuel elements if we have the equation in a form which can be directly related to a cylindrical shape, e. g., a hollow cylinder or pipe (Fig 1.18).

By rewriting Equation (1.1) in the form Qt = — 2x к dt/dx we can apply it to Fig 1.18 and arrive at an expression:

Qt = (tі — t2)/(I/2irk) loge (R2/Ri) (1.2)

and as in Equation (i. l), (1/2тгк) Ioge (R2/Rj) is the ‘thermal resistance’.

Equation (1.2) is used extensively in calculations to obtain the heat loss through the walls of steam pipes, etc., due to conduction.