NATURAL CONVECTION WITHIN A SIMPLIFIED MODEL OF THE HUMAN EYE

A finite difference solution for steady natural convective flow within the human eye, modelled as a sphere with a specified temperature distribution over its surface, has been obtained. The stream function-vorticity formulation of the equations of motion for the unsteady axisymmetric flow is used; interest lying in the final steady solution. Forward differences are used for the time derivatives and second-order central differences for the space derivatives. The alternating direction implicit method is used for solution of the discretization equations. Local one-dimensional grid adaptation is used to resolve the steep gradients in some regions of the flow at large Rayleigh numbers. The break-up into multi-cellular flow is found at high Rayleigh numbers. Results identify regions of stagnant fluid in locations similar to those of blind spots in the eye.