Defining the reduced length (1), the temperature distribution is approximated (2) by making use of the splines ξ and Q(ξ).

With (4), the left and right heat fluxes are given by (5), and the corresponding edge temperatures by (6).

On the other hand, (7) gives the temperature drops in the films, where rf represents the film resistance (1/hf).

Defining composite thermal resistances by (8) (replace i by j to obtain corresponding j values),

Eliminating b, c, ui, uj leads to heat flux (9).

The thermal balance (10) may be written as (11) where a "composite" coolant temperature t defined by (12).

(11) is (u-implicit) time-discretized by (13), where u1 and u2 are the bos and eos values of the average metal temperature and (t-explicit) t1 the bos value of the composite coolant temperature (12).

Once u2 updated from (13), qi is obtained from (14) and qj by ij permutation.