NATURAL CONVECTION WITHIN A SIMPLIFIED MODEL OF THE HUMAN EYE

Abstract

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.