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Lattice Boltzmann Modeling on Convective Heat Transfer of Nanofluids through Highly Conductive Metal Foams
Published in K.R.V. Subramanian, Tubati Nageswara Rao, Avinash Balakrishnan, Nanofluids and Their Engineering Applications, 2019
H.J. Xu, Z.B. Xing, X. Fang, W. Zhang, Z.Z. Zhou
Figure 9.6a shows the comparison of the vertical velocity (uy) distribution for different Rayleigh numbers with the nanoparticle volume fraction 5% at y = 0.5 H. From Figure 9.6a, compared with other situations, the vertical velocity for Ra = 103 is very small, which means that the flow is very weak. Compared with the isotherm in Figure 9.5a, the temperature difference in vertical direction is almost zero, so the buoyancy due to temperature difference is very small. Figure 9.6b shows the comparison of temperature distribution for different Rayleigh numbers at y = 0.5 H. The temperature at Ra = 103 is approximately linear, indicating that heat conduction dominates the heat transfer. A large Rayleigh number corresponds to the large coefficient of thermal expansion, large temperature difference, or the small viscosity. Therefore, an increase in Rayleigh number facilitates fluid flow and heat diffusion. From Figure 9.6, as Ra increases, the velocity gradually increases, and the temperature profile and the isotherm begin to bend. Due to the intensified flow, the temperature gradient near the wall is large, and heat transfer is enhanced. For Ra = 105, the vertical velocity is negative in the left half of x < 0.5, and the temperature is smaller than the average temperature, indicating that the vortex brought by vortex at large Rayleigh number corresponds to the intensified local flow. This is conducive to enhancing natural convective heat transfer.
Climate effects
Published in Bernardo Caicedo, Geotechnics of Roads: Fundamentals, 2018
The Rayleigh number, Ra, is the relation used to estimate whether conduction or convection is the main method of heat transport in a fluid. This non-dimensional number depends on acceleration due to gravity, g, the thermal expansion coefficient, β, kinematic viscosity, ν, thermal diffusivity, κ, the surface temperature, Ts, the quiescent temperature which is Tsky in atmospheric processes, and the characteristic length, L: Ra=gβνκ(Ts-Tsky)L3
Dynamics of Partially Mixed Estuaries
Published in Björn Kjerfve, Hydrodynamics of Estuaries, 1988
Their solution for circulation in the central regime of the estuary in which both forced and free convection are important was expressed as the sum of three modes: a river discharge mode, a wind stress mode, and a gravitational convection mode. Aside from wind stress effects, they found that the structure of the nontidal velocity was controlled by an estuarine Rayleigh number Ra = gk SoD3/AvKHo where k is defined by Equation 8, So is the salinity at the head of the estuary, D is the depth, and KHo is the coefficient of longitudinal eddy diffusion at the head of the estuary. The Rayleigh number is a measure of the tendency for bouyancy-induced convection to develop against the retarding effects of friction (due to the vertical eddy viscosity) and diffusion (longitudinal eddy diffusion which tends to reduce the density gradient). Figure 3 shows that the strength of the convection increases with Rayleigh number; in this figure Uf is the freshwater velocity equal to the river flow divided by the area of the cross section.
Mechanistic assessment of aerosol transport in an SFR cover gas space under operating condition
Published in Aerosol Science and Technology, 2023
Parthkumar Rajendrabhai Patel, Amit Kumar, A. John Arul
In a typical enclosure heated from the bottom, due to the density difference, the hot air near the heated surface rises due to buoyancy forces; simultaneously, the higher density cold air comes downward due to higher density and gravitational forces acting on it. During downward and upward transitions, the fluid is resisted by viscous forces. When the buoyancy and gravitational forces are dominant compared to fluid viscous forces, convection is formed. The Rayleigh number at which convection is formed is known as the critical Rayleigh number (∼ 1708). Just above the critical Rayleigh number, two dimensional counter rolling roll-like structure is expected in the flow domain. This two-dimensional roll-like structure is known as a Bénard cell. As the Rayleigh number increases, the two-dimensional rolls break into three-dimensional rolls. If such a structure is viewed from the top, distinguishable hexagonal patterns can be visible (Adrian Bejan, 2013).
Conjugate heat transfer due to conduction, natural convection, and radiation from a vertical hollow cylinder with finite thickness
Published in Numerical Heat Transfer, Part A: Applications, 2021
Vikrant Chandrakar, Jnana Ranjan Senapati, Aurovinda Mohanty
The variation of velocity magnitude with the cylinder centerline is shown in Figure 18 for different Rayleigh number cases. For a particular Rayleigh number, the velocity goes on increasing along the length of the centerline. The variation of velocity magnitude along the axis is observed significantly for higher Rayleigh number cases, i.e., Ra = 5.7 × 106 or 5.7 × 107. Whereas the change along the centerline is found to be insignificant for lower Rayleigh number cases. In natural convection, the surrounding air is heated by the high-temperature cylinder wall, moving up in the direction against gravity. So, the buoyant plume builds up along the centerline far away from the cylinder when surrounding air drawn from all sides mixes with the core fluid. This phenomenon is noticed in the vector plots. For a fixed position on the centerline, the greater the Rayleigh number, the greater is the velocity magnitude. As the natural convection strength increases with the Rayleigh number, the flow velocity also increases. This is well made out of the vector plots. Therefore, the vector magnitude is seen to be more appreciable for higher Rayleigh number cases. From Figure 18, a local rise and fall of the velocity magnitude are noticed in between 0 to 0.2 m length.
Modelling of surface and inner wall temperatures in the analysis of courtyard thermal performances in Mediterranean climates
Published in Journal of Building Performance Simulation, 2021
V.P. López-Cabeza, F.J. Carmona-Molero, S. Rubino, C. Rivera-Gómez, E.D. Fernández-Nieto, C. Galán-Marín, T. Chacón-Rebollo
Let us recall that the Prandtl number is the ratio between the kinematic viscosity and the thermal diffusion. The Rayleigh number is associated with the heat transfer in the fluid and measures the ratio between buoyancy and viscous forces. When the Rayleigh number is below a critical value ( = 105), heat transfer is primarily in the form of conduction, but when it exceeds this critical value, heat transfer is primarily in the form of convection (Benítez and Bermúdez 2011; Chacón Rebollo et al. 2018). Moreover, in the last case, if the Rayleigh number exceeds a certain threshold ( = 108) the flow is unstable (Rabinowitz 1968). This instability is called Rayleigh-Bénard instability (Schlichting and Gertesten 2004).