A NUMERICAL METHOD FOR SOLVING THE EQUATIONS OF NATURAL CONVECTION IN A NARROW CONCENTRIC CYLINDRICAL ANNULUS WITH A HORIZONTAL AXIS

Abstract

A numerical method is given for solving the equations of steady laminar natural convection in a narrow concentric cylindrical annulus with a horizontal axis. The method involves an iterative scheme of partial differential equations, but only linear algebraic equations. Once two matrices have been inverted successive iterates use just matrix multiplication, and even the matrix inversions for a new case are unnecessary if the ratio between the radii of the cylinders is unchanged. The present method gives results for a related problem agreeing with published results obtained by a less convenient, though more general, method; and an analytical check on part of the calculation is also satisfied. The iterations are found to converge if the quantity (gap/inner radius)³ × (Grashof number) is less than some critical value. The problem has an application to the cabin insulation of high speed aircraft.