Convection of a micropolar fluid with stretch - U. Walzer (Annals of Geophysics, 1976)
As a model for the Bénard convection in the asthenosphere the problem of the hydrodynamic stability of an infinite horizontal layer is calculated. The layer consists of a micropolar fluid with streich. The field equations for the velocity vector, microrotation vector, microstretch, microinertia, density, temperature, and pressure form a system of eleven partial differential equations for the determination of eleven unknown scalar functions. We succeed in decoupling the system and reducing the problem to an ordinary differential equation. The analytical solution can be given for the special case of a micropolar Boussinesq fluid.