The Brinkman-Fourier system with ideal gas equilibrium

<p style='text-indent:20px;'>In this work, we will introduce a general framework to derive the thermodynamics of fluid mechanical system, which guarantees consistence between energetic variational approaches with laws thermodynamics. In particular, focus on coupling thermal and forces. We follow for classical gas ideal equilibrium present existences weak solutions thermodynamic system coupled Brinkman-type equation govern velocity field.</p>