On a class of exact solutions of the NavierStokes equations for a Boussinesq fluid
Abstract
The paper shows the existence of an analytical onedimensional solution of the NavierStokes equations for a differentially heated annulus of infinite vertical extent whose wall temperatures increase linearly with height. The general solution can be expressed in terms of Bessel and modified Bessel functions of zeroth order and of complex argument. It depends on five constants which are determined from the boundary conditions and from the integral relation expressing mass conservation. This solution closely corrresponds to the flow structure found in a tall finite vertical annulus heated with a uniform flux from the side.
 Publication:

Academie des Sciences Paris Comptes Rendus Serie Sciences Mathematiques
 Pub Date:
 February 1990
 Bibcode:
 1990CRASM.310..353L
 Keywords:

 Boussinesq Approximation;
 Convective Heat Transfer;
 Fluid Mechanics;
 NavierStokes Equation;
 Bessel Functions;
 Flow Distribution;
 Heat Flux;
 Incompressible Flow;
 Temperature Distribution;
 Fluid Mechanics and Heat Transfer