Steady thermal-solutal capillary convection in a shallow annular pool with the radial temperature and concentration gradients

Using asymptotical analysis, we investigate the characteristics of the coupled thermal and solutal capillary convection with the radial temperature and solute concentration gradients in a shallow annular pool with the free surface. The pool is heated from the outer cylinder with high solutal concentration and cooled at the inner cylinder with low solutal concentration. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the depth to the width of the pool, goes to zero. The comparison with the previous work certifies that the asymptotic solution is right and believable. The influences of the solutal capillary force, the buoyant force, the Soret effect and the geometric parameters on the fluid flow are analyzed.