How to solve the following PDEs in Freefem

Dear freefem team, I am currently trying to implement the following method in freefem. In the section 2.1 of the paper, it includes 3 pdes for solving. The last one is the elasticity equation which is clear to me, however I am not sure if it possible to solve the first 2 PDEs in Freefem [N-S with boby force and engery equation]. Thank you for the help.

Three-dimensional topology optimization of thermal-fluid-structural problems for cooling system design.pdf (7.5 MB)

You can apply Newton’s method as described in

The source is available at

You have to adapt the method to include temperature (this should not lead to serious difficulties).

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