  The prohibitive cost and low fidelity of experimental data in industry scale
thermofluid systems limit the usefulness of pure data-driven machine learning
methods. Physics-informed neural networks (PINN) strive to overcome this by
embedding the physics equations in the construction of the neural network loss
function. In the present paper, the mixed-variable PINN methodology is applied
to develop steady-state and transient surrogate models of incompressible
laminar flow with heat transfer through a 2D internal domain with obstructions.
Automatic spatial and temporal differentiation is applied to the partial
differential equations for mass, momentum and energy conservation, and the
residuals are included in the loss function, together with the boundary and
initial values. Good agreement is obtained between the PINN and CFD results for
both the steady-state and transient cases, but normalization of the PDEs proves
to be crucial. Although this proves the ability of the PINN approach to solve
multiple physics-based PDEs on a single domain, the PINN takes significantly
longer to solve than the traditional finite volume numerical methods utilized
in commercial CFD software.
