The Scalar Curvature Problem on the Four Dimensional Half Sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature to a metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.Comment: 19 page

Experimental study of the heat transfer enhancement by corona wind in a square channel

Paper presented at the 7th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Turkey, 19-21 July, 2010.Convective heat transfer is still the major heat transfer mode in bio and food processes where air is commonly used as the heat transfer medium. Alternative processes should be investigated in order to enhance heat transfer. This work concerns the ElectroHydroDynamic (EHD) enhancement of the convective heat transfer in a square channel. An experimental set-up was designed in order to determine the local heat transfer coefficient at the surface of a heated plate. Conditioned air (controlled temperature and humidity) was introduced in a square channel at a velocity ranging from 0 to 5 m/s. A corona electrode was placed in the channel in order to generate an ionic wind. The applied voltage was ranging from 0 to 20 kV. An infrared camera was used to measure the surface temperature of the heated plate at the bottom surface of the channel. This original experimental device was used to determine the local heat transfer coefficients for different configurations (various inlet air velocities and applied voltages). Results showed that the electrical body force and the inertial force had synergetic effects for low Reynolds number. It was demonstrated that the corona wind could lead to a fourth increase of the mean heat transfer coefficient. Nevertheless, at higher Reynolds number, the corona wind had no more effect on the heat transfer.ksb201