Search

This study presents an innovative visualization tool for the analysis of the mixed convection in a lid-driven air filled cubical cavity heated from below. The total energy of the flow in the cavity isvisualized based on the energy stream functions or energy streamlines. Also the heat transfer enhancement in the cavity is presented with an analogy between conduction and convection, namely, the field synergy principle. Flow is assumed to be driven by the vertical temperature gradient and by the top lid of the cavity, which is assumed to slide on its own plane at a uniform speed. The top and bottom walls are assumed to be isothermal and all other walls are thermally insulated. Non dimensional governing equations of this problem are solved by using the finite volume method. Established open source CFD package OpenFOAM is utilized to investigate the flow with respect to the control parameters arising in the system. The nonlinear terms arising in the governing equations are discretized with the NVD schemes. The convection differencing schemes namely, UPWIND, QUICK, SUPERBEE and SFCD discussed and are used to simulate the flow using MPI code. It is observed that the computational cost for all the differencing schemes get reduced tremendously when the MPI code is implemented. Also SFCD scheme gave the Nuseelt number values close to those available in the literature. Extensive numerical flow visualization is conducted for the Reynolds number (Re = 100, 400, 1000) and the Richardson number (Ri = 0.001, 1, 10), which categorize the free and forced convective flow, respectively. It is observed that for a fixed value of Re, as Ri increases, the average Nusselt number (Nu¯), decreases. This shows that the natural convection starts to prevail with an increasing of Ri. But, for a fixed Ri, as Re increases (Nu¯) increases and the forced convection mode becomes dominant, leading to a chaotic flow. Plots demonstrating the influences of Re and Ri in termsof the contours of the fluid streamlines, isotherms, vortex corelines, and field synergy principle. The synergy angle of buoyant-aiding flow is high while the buoyant-opposing flow is significantly less than that of forced convection flow.

The problem of rotating natural convective flow about the vertical axis, with variable viscosity confined between the two horizontal plates, is investigated via linear stability analysis. The transformed governing equations are solved numerically by using the Galerkin method. The computed results are compared for special cases with the results of earlier research by Chandrasekhar and Stengel et al., and are found to be in good agreement. We studied both stationary convection and oscillatory convection. The threshold values of Rayleigh number and wavenumber are computed and presented for various boundary conditions viz. rigid-rigid, rigidfree, free-rigid and free-free, and for different values of physical parameters viz. Taylor number Ta, viscosity ratio c and Prandtl number Pr. For rigid-rigid boundary conditions we studied the effect of c, Ta and Pr on the vertical velocity and temperature eigenfunctions at the onset. It is observed that the rotation rate stabilizes the dynamical system. The occurrence of the co-dimension two bifurcation point (CTP) is shown for various boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, linear and nonlinear properties of thermohaline convection at the onset with the stress-free boundary conditions are investigated using perturbation analysis relevant to oceanic water and ground water. The nonlinear governing equations are expanded using linear stability solutions, related to the temperature, motion, and concentration in the series of nonhomogeneous linear equations. The proposed method yields finite amplitude steady solutions by means of successive approximations. The rate of heat transfer is studied up to sixth-order using an expansion of thermal Rayleigh number (Ra1) as proposed by Kuo (1961, "Solution of the Non-Linear Equations of the Cellular Convection and Heat Transport," J. Fluid Mech., 10(04), pp. 611-630). The heat transfer rate of the system depends on Lewis number, Prandtl number, and thermal (Ra1) as well as solutal (Ra2) Rayleigh number. The result for the heat transport (N) in the system fits a power law of exponent of 0.288, i.e., N≃(Ra1/Ra1o)0.288 for Ra2=0 ⁠, Pr = 10 and Ra1>4Ra1o ⁠. This power law of exponent value of 0.288 is close to the results (0.25) obtained by Kuo (1961, "Solution of the Non-Linear Equations of the Cellular Convection and Heat Transport," J. Fluid Mech., 10(04), pp. 611-630), and also to the experimental results for laminar convection by Jakob (1949, Heat Transfer, Vol. 1, Wiley, New York.). The characteristics of heat transfer and flow field results are depicted by means of isotherms and streamlines, respectively. The path of convective heat transport and the comprehensive analysis of energy distribution by means of heatlines are explained using the concept of heat function. Laminar natural convection using entropy generation analysis due to fluid friction and heat transfer is also being studied. The numerical simulation for total entropy generation has been carried out for Prandtl numbers pertaining to ground water for different Ra1 and Ra2. [ABSTRACT FROM AUTHOR]

Thermal convection of binary mixtures in a porous medium is studied with stress-free boundary conditions. The linear stability analysis is studied by using the normal mode method. The effects of the material parameters have been studied at the onset of convection. Using a multiple scale analysis near the onset of the stationary convection, a cubic-quintic amplitude equation is derived. The influence of the Lewis number and the separation ratio on the supercritical-subcritical transition is discussed. Stationary front solutions and localized states are analyzed at the Maxwell point. Near the threshold of the oscillatory convection, a set of two coupled complex cubic-quintic Ginzburg-Landau type amplitude equations is derived, and implicit analytical expressions for the coefficients are given.