Rotating Translating Cones

A first attempt has been made to confirm experimentally a theoretical concept, recently published, involving a rigid cone rotating about its long axis under still water: it should tend to translate along that axis blunt end leading and apex trailing. Two identical hollow cones, neutrally buoyant, with equal weights attached to the apexes, were released simultaneously at the surface of a swimming pool. One cone had a thin light weight spiral vane vertically attached to the cone’s outside surface in order to cause it to rotate as it sank. Several trial runs were made in the shallow and deep ends of the pool, and in every case, the non-rotating cone without a vane hit the bottom of the pool first. These comparisons qualitatively and indirectly validate the prediction.

Numerical investigation of magnetohydrodynamic(MHD)radiative flow over a rotating cone in the presence of Soret and chemical reaction

Present study is a numerical investigation of the flow,heat and mass transfer behaviour of magnetohydrodynamic flow over a vertical rotating cone through porous medium in the presence of thermal radiation,chemical reaction and Soret effects.Further,the numerical solutions are elucidated by using Runge-Kutta based shooting technique.Obtained results are validated with open literature and found an excellent agreement.The influence of non-dimensional governing parameters on velocity,temperature and concentration profiles along with the friction factor,local Nusselt and Sherwood numbers are determined and discussed with the help of graphs and tables.Results proved that the variable porosity parameter have tendency to enhance the heat and mass transfer rate.An increase in the buoyancy parameter depreciates the thermal and concentration boundary layer thicknesses.

A mathematical analysis of time dependent flow on a rotating cone in a rheological fluid

In the present study we have explored the time dependent combined convectional flow on a rotating cone in a rotating Jeffrey fluid with the combined effects of heat and mass transfer.The governing equations of motion,energy and mass transfer for unsteady flow are presented and simplified using similar variables.The reduced coupled nonlinear differential equations are solved analytically with the help of strong analytical technique homotopy analysis method.The heat transfer analysis for prescribed wall temperature is considered.Numerical results for Nusselt number and Sherwood number have computed and discussed.The physical features of pertinent parameters are discussed by plotting the graphs of velocity,heat transfer,concentration,skin friction,Nusselt number and Sherwood number.

Truncated Smoothing Newton Method for l_∞ Fitting Rotated Cones

In this paper, the rotated cone fitting problem is considered. In case the measured data are generally accurate and it is needed to fit the surface within expected error bound, it is more appropriate to use l∞ norm than 12 norm. l∞ fitting rotated cones need to minimize, under some bound constraints, the maximum function of some nonsmooth functions involving both absolute value and square root functions. Although this is a low dimensional problem, in some practical application, it is needed to fitting large amount of cones repeatedly, moreover, when large amount of measured data are to be fitted to one rotated cone, the number of components in the maximum function is large. So it is necessary to develop efficient solution methods. To solve such optimization problems efficiently, a truncated smoothing Newton method is presented. At first, combining aggregate smoothing technique to the maximum function as well as the absolute value function and a smoothing function to the square root function, a monotonic and uniform smooth approximation to the objective function is constructed. Using the smooth approximation, a smoothing Newton method can be used to solve the problem. Then, to reduce the computation cost, a truncated aggregate smoothing technique is applied to give the truncated smoothing Newton method, such that only a small subset of component functions are aggregated in each iteration point and hence the computation cost is considerably reduced.