An exact solution of the Boussinesq equations for an infinite wall in a stratified fluid
Abstract
An exact solution of the twodimensional NavierStokes equations in the Boussinesq approximation is developed for the case of an infinite vertical wall boundary and an infinite halfspace of fluid. The wall and distant fluid are assumed to be linearly stratified in the vertical direction with different stratifications. By assuming a solution of a given form, the problem is reduced to the solution of two ordinary differential equations, which was numerically evaluated. The numerical results show that as the stratification ratio increases, the boundary layer thickness decreases and heat transfer increases. In this respect, the linearized theory shows close agreement with the exact results. As Prandtl number increases for fixed stratification ratio, the damping effect of viscosity becomes more pronounced and the boundary layer thickness decreases.
 Publication:

ASME Journal of Heat Transfer
 Pub Date:
 November 1977
 Bibcode:
 1977ATJHT..99..676J
 Keywords:

 Boussinesq Approximation;
 Stratified Flow;
 Two Dimensional Flow;
 Wall Flow;
 Half Spaces;
 NavierStokes Equation;
 Partial Differential Equations;
 Prandtl Number;
 Temperature Distribution;
 Thermal Boundary Layer;
 Fluid Mechanics and Heat Transfer