Showing papers on "Natural convection published in 2010"

Boundary layer structure in turbulent thermal convection and its consequences for the required numerical resolution

Abstract: Results on the Prandtl–Blasius-type kinetic and thermal boundary layer (BL) thicknesses in turbulent Rayleigh–Benard (RB) convection in a broad range of Prandtl numbers are presented. By solving the laminar Prandtl–Blasius BL equations, we calculate the ratio between the thermal and kinetic BL thicknesses, which depends on the Prandtl number only. It is approximated as for and as for , with . Comparison of the Prandtl–Blasius velocity BL thickness with that evaluated in the direct numerical simulations by Stevens et al (2010 J. Fluid Mech. 643 495) shows very good agreement between them. Based on the Prandtl–Blasius-type considerations, we derive a lower-bound estimate for the minimum number of computational mesh nodes required to conduct accurate numerical simulations of moderately high (BL-dominated) turbulent RB convection, in the thermal and kinetic BLs close to the bottom and top plates. It is shown that the number of required nodes within each BL depends on and and grows with the Rayleigh number not slower than . This estimate is in excellent agreement with empirical results, which were based on the convergence of the Nusselt number in numerical simulations

Infrared thermography for convective heat transfer measurements

Abstract: This paper deals with the evolution of infrared (IR) thermography into a powerful optical tool that can be used in complex fluid flows to either evaluate wall convective heat fluxes or investigate the surface flow field behavior. Measurement of convective heat fluxes must be performed by means of a thermal sensor, where temperatures have to be measured with proper transducers. By correctly choosing the thermal sensor, IR thermography can be successfully exploited to resolve convective heat flux distributions with both steady and transient techniques. When comparing it to standard transducers, the IR camera appears very valuable because it is non-intrusive, it has a high sensitivity (down to 20 mK), it has a low response time (down to 20 μs), it is fully two dimensional (from 80 k up to 1 M pixels, at 50 Hz) and, therefore, it allows for better evaluation of errors due to tangential conduction within the sensor. This paper analyses the capability of IR thermography to perform convective heat transfer measurements and surface visualizations in complex fluid flows. In particular, it includes the following: the necessary radiation theory background, a review of the main IR camera features, a description of the pertinent heat flux sensors, an analysis of the IR image processing methods and a report on some applications to complex fluid flows, ranging from natural convection to hypersonic regime.

The onset of convection in a horizontal nanofluid layer of finite depth

Abstract: This paper presents a linear stability analysis for the onset of natural convection in a horizontal nanofluid layer. The employed model incorporates the effects of Brownian motion and thermophoresis. Both monotonic and oscillatory convection for free–free, rigid–rigid, and rigid–free boundaries are investigated. The oscillatory instability is possible when nanoparticles concentrate near the bottom of the layer, so that the density gradient caused by such a bottom-heavy nanoparticle distribution competes with the density variation caused by heating from the bottom. It is established that the instability is almost purely a phenomenon due to buoyancy coupled with the conservation of nanoparticles. It is independent of the contributions of Brownian motion and thermophoresis to the thermal energy equation. Rather, the Brownian motion and thermophoresis enter to produce their effects directly into the equation expressing the conservation of nanoparticles so that the temperature and the particle density are coupled in a particular way, and that results in the thermal and concentration buoyancy effects being coupled in the same way.

Mhd free convection flow of a nanofluid past a vertical plate in the presence of heat generation or absorption effects

Abstract: This work is focused on the numerical solution of steady natural convection boundary-layer flow of a nanofluid consisting of a pure fluid with nanoparticles along a permeable vertical plate in the presence of magnetic field, heat generation or absorption, and suction or injection effects The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis The governing boundary-layer equations of the problem are formulated and transformed into a non-similar form The obtained equations are then solved numerically by an efficient, iterative, tri-diagonal, implicit finite-difference method Comparisons with previously published work are performed and are found to be in excellent agreement Representative results for the longitudinal velocity, temperature, and nanoparticle volume fraction profiles as well as the local heat transfer rates for various values of the physical parameters are displayed in both graphical and tabular forms

Effect of Local Thermal Non-equilibrium on the Onset of Convection in a Porous Medium Layer Saturated by a Nanofluid

Abstract: The onset of convection in a horizontal layer of a porous medium saturated by a nanofluid is analytically studied. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. For the porous medium, the Darcy model is employed. The effect of local thermal non-equilibrium among the particle, fluid, and solid-matrix phases is investigated using a three-temperature model. The analysis reveals that in some circumstances the effect of LTNE can be significant, but for a typical dilute nanofluid (with large Lewis number and with small particle-to-fluid heat capacity ratio) the effect is small.

Topological design of heat dissipating structure with forced convective heat transfer

Abstract: This paper discusses the use of the topology optimization formulation for designing a heat dissipating structure that utilizes forced convective heat transfer. In addition to forced convection, there is also natural convection due to natural buoyancy forces induced by local heating inside fluid. In the present study, the temperature distribution due to forced convection, neglecting buoyancy and viscous dissipation inside fluid, was simulated and optimized. In order to analyze the heat transfer equation with forced convective heat loss and the Navier-Stokes equation, a common sequential computational procedure for this thermo/hydraulic characteristic was implemented. For topology optimization, four material properties were interpolated with respect to spatially defined density design variables: the inverse permeability in the Navier-Stokes equation, the conductivity, density, and the specific heat capacity of the heat transfer equation. From numerical examples, it was found that the balance between the conduction and convection of fluid is of central importance to the design of heat dissipating structures.

The Onset of Double-Diffusive Nanofluid Convection in a Layer of a Saturated Porous Medium

Abstract: The paper develops a theory of double-diffusive nanofluid convection in porous media. This theory is applied to investigating the onset of nanofluid convection in a horizontal layer of a porous medium saturated by a nanofluid for the case when the base fluid of the nanofluid is itself a binary fluid such as salty water. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis, while the Darcy model is used for the porous medium. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. Both non-oscillatory and oscillatory cases are investigated by using Galerkin method; the stability boundaries for these cases are approximated by simple and useful analytical expressions.

Laminar natural convection of Bingham fluids in a square enclosure with differentially heated side walls

Abstract: In this study, two-dimensional steady-state simulations of laminar natural convection in square enclosures with differentially heated sidewalls have been carried out where the enclosures are considered to be completely filled with a yield stress fluid obeying the Bingham model. Yield stress effects on heat and momentum transport are investigated for nominal values of Rayleigh number (Ra) in the range 103–106 and a Prandtl number (Pr) range of 0.1–100. It is found that the mean Nusselt number N u ¯ increases with increasing values of Rayleigh number for both Newtonian and Bingham fluids. However, N u ¯ values obtained for Bingham fluids are smaller than that obtained in the case of Newtonian fluids with the same nominal value of Rayleigh number Ra due to weakening of convective transport. The mean Nusselt number N u ¯ in the case of Bingham fluids is found to decrease with increasing Bingham number, and, for large values of Bingham number Bn, the value settles to unity ( N u ¯ = 1.0 ) as heat transfer takes place principally due to thermal conduction. The effects of Prandtl number have also been investigated in detail and physical explanations are provided for the observed behaviour. New correlations are proposed for the mean Nusselt number N u ¯ for both Newtonian and Bingham fluids which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of N u ¯ in response to changes in Ra, Pr and Bn.