AN EXPERIMENTAL RESEARCH ON THE INSTABILITY OF NATURAL CONVECTION BOUNDARY LAYER AROUND A VERTICAL HEATED FLAT PLATE

Experimental results on the instability of the isothermal natural-convection boundary layer around a vertical heated flat plate are presented. It is demonstrated that the characteristics of the instability wave in the outer layer is consistent with the calculation of Brewster & Gebhart. Aft;er an initial growth of its low frequency components at the downstream side of the turning point of the neutral curve (Gr approximate to 120) its comparatively higher frequency components develop and become turbulent subsequently with a buoyancy subrange in its power spectra. Simultaneously, in the measurement at the inner layer near the wail a viscous instability signal the same as the Tollmien-Schlichting waves in ordinary boundary layer and its subharmonics in a much higher frequency domain is discovered and an inertial subrange can be observed in the spectra at Gr approximate to 378.6.

基于亏量校正求解自然对流问题的后验误差估计子

本文给出NC方程基于亏量校正方法的恢复型误差估计子。我们在亏量步求解人工黏性系数的稳定非线性问题;在校正步通过线性化方程来校正这个残量,在亏量和校正步我们都采用Oceen迭代。考虑应力张量σ = ?u ? pI + ?T ,若我们采用最低阶协调速度和压力有限元对P1- P0- P1求解离散NC问题,应力张量的有限元逼近σh = ?uh ? p h I + ?Th 是不连续的分片常数。我们利用超收敛片恢复技巧构造连续空间的量 G (σ h) ,得到了局部恢复型误差估计子(σh-G ( σh)K 。最后,通过数值实验验证了基于亏量校正方法的恢复型误差估计子是有效的。

Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall

The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.

Tiwari-Das nanofluid model for magnetohydrodynamics(MHD)natural-convective flow of a nanofluid adjacent to a spinning down-pointing vertical cone

In this article,the natural-convective flow of an electrically conducting nanofluid adjacent to a spinning down-pointing vertical cone in the presence of transverse magnetic field is studied.The mathematical model has been formulated based on Tiwari-Das nanofluid model.Three different types of water-based nanofluid with copper,aluminum oxide(alumina)and titanium dioxide(titania)as nanoparticles are considered in this investigation.Two cases of heat transfer analysis are discussed.These are:(i)the spinning cone with prescribed surface temperature and(ii)the spinning cone with prescribed surface heat flux.Using appropriate transformations,the system of partial differential equations is transformed into an ordinary differential system of three equations,which is solved numerically using the fourth-order Runge-Kutta method with shooting technique.The current solution demonstrates very good agreement with those of the previously published studies in the especial cases.The effects of the three key thermophysical parameters governing the flow;the nanoparticle volume fraction,the magnetic parameter and the spin parameter on dimensionless velocity and temperature distributions,skin friction coefficient,Nusselt number and entropy generation number are presented graphically and discussed in details.Our results demonstrate that,the enhancement of heat transfer is a function of particle concentration,small fraction of metallic particles leading to significant changes in all three quantities of skin friction coefficient,local Nusselt number and entropy generation number.The results illustrate that selecting alumina and copper as the nanoparticle leads to the minimum and maximum amounts of skin friction coefficient value,and also copper and titania nanoparticles have the largest and lowest local Nusselt number.Moreover,it is observed that the magnetic parameter has a decreasing effect on both skin friction coefficient and local Nusselt number and an increasing effect on entropy generation number.In addition,our computation shows that all three quantities of skin friction coefficient,local Nusselt number and entropy generation number are the increasing functions of spin parameter.Finally,this simulation represents the feasibility of using magnetic rotating body drives in novel nuclear space propulsion engines and this model has important applications in heat transfer enhancement in renewable energy systems and industrial thermal management.

The Crank-Nicolson/Explicit Scheme for the Natural Convection Equations with Nonsmooth Initial Data

In this article,a Crank-Nicolson/Explicit scheme is designed and analyzed for the time-dependent natural convection problem with nonsmooth initial data.The Galerkin finite element method(FEM)with stable MINI element is used for the velocity and pressure and linear polynomial for the temperature.The time discretization is based on the Crank-Nicolson scheme.In order to simplify the computations,the nonlinear terms are treated by the explicit scheme.The advantages of our numerical scheme can be list as follows:(1)The original problem is split into two linear subproblems,these subproblems can be solved in each time level in parallel and the computational sizes are smaller than the origin one.(2)A constant coefficient linear discrete algebraic system is obtained in each subproblem and the computation becomes easy.The main contributions of this work are the stability and convergence results of numerical solutions with nonsmooth initial data.Finally,some numerical results are presented to verify the established theoretical results and show the performances of the developed numerical scheme.