JET OVER A HOT SPHERE

Heat Transfer in the Flow of a Cold, Axisymmetric Jet Over a Hot Sphere

The heat-transfer characteristics of thin film flow over a hot sphere resulting from a cold vertical jet of liquid falling onto the surface have been investigated. The underlying physical features have been illustrated by numerical solutions of high accuracy based on the modified Keller box method. The solutions for film thickness distribution are good agreement with those obtained approximatel...

Rubber rolling over a sphere

“Rubber” coated rolling bodies satisfy a no-twist in addition to the no slip satisfied by “marble” coated bodies [28]. Rubber rolling has an interesting differential geometric appeal because the geodesic curvatures of the curves on the surfaces at the corresponding points are equal. The associated distribution in the 5 dimensional configuration space has 2-3-5 growth (these distributions were f...

Numerical Integration Over a Sphere*

Minimizing a Quadratic Over a Sphere

A new method, the sequential subspace method (SSM), is developed for the problem of minimizing a quadratic over a sphere. In our scheme, the quadratic is minimized over a subspace which is adjusted in successive iterations to ensure convergence to an optimum. When a sequential quadratic programming iterate is included in the subspace, convergence is locally quadratic. Numerical comparisons with...

Quadrature over the Sphere

Consider integration over the unit sphere in , especially when the integrand has singular behaviour in a polar region. In an earlier paper [4], a numerical integration method was proposed that uses a transformation that leads to an integration problem over the unit sphere with an integrand that is much smoother in the polar regions of the sphere. The transformation uses a grading parameter . Th...