A computer code for enclosed natural convection in the boundary layer regime

A computer code is developed for the numerical prediction of natural convection in rectangular two-dimensional cavities at high Rayleigh numbers. The governing equations are retained in the primitive variable form. The numerical method is based on finite differences and an ADI scheme. Convective terms may be approximated with either central or hybrid differencing for greater stability. A non-uniform grid distribution is possible for greater efficiency. The pressure is dealt with via a SIMPLE type algorithm and the use of a fast elliptic solver for the solenoidal velocity correction field significantly reduces computing times. Preliminary results indicate that the code is reasonably accurate, robust and fast compared with existing benchmarks and finite difference based codes, particularly at high Rayleigh numbers. Extension to three-dimensional problems and turbulence studies in similar geometries is readily possible and indicated.

The laminar boundary layer regime for natural convection of air in a square cavity

Numerical predictions are obtained for laminar natural convection of air in a square two dimensional cavity at high Rayleigh numbers. Proper resolution of the core reveals weak multi-cellular structure which varies in a complex manner as the effects of convection are increased. The end of the steady laminar regime is numerically estimated to occur at Ra=2.2x10^8.

Laminar and turbulent natural convection in rectangular cavities

A computer program has been developed for the prediction of buoyancy-driven laminar and turbulent flow in rectangular air-filled two-dimensional cavities with differentially heated side walls. Laminar flow predictions for a square cavity and Rayleigh numbers from Ra = 10^3 up to the onset of unsteady flow have been obtained. Accurate solutions for Ra = 5 x 10^6, 10^7, 5 x 10^7 and 10^8 are presented and an estimate for the critical Rayleigh number at which the steady laminar flow becomes unsteady is given for this geometry. Numerical predictions of turbulent flow have been obtained for RaH~0(10^9 -10^11 ) and compared with existing experimental data. A previously developed second moment closure model (Behnia et al. 1987) has been used to model the turbulence. Results indicate that a second moment closure model is capable of predicting the observed flow features.

Laminar and turbulent natural convection in rectangular cavities

"This chapter discusses laminar and turbulent natural convection in rectangular cavities. Natural convection in rectangular two-dimensional cavities has become a standard problem in numerical heat transfer because of its relevance in understanding a number of problems in engineering. Current research identified a number of difficulties with regard to the numerical methods and the turbulence modeling for this class of flows. Obtaining numerical predictions at high Rayleigh numbers proved computationally expensive such that results beyond Ra ∼ 1014 are rarely reported. The chapter discusses a study in which it was found that turbulent computations in square cavities can't be extended beyond Ra ∼ O (1012) despite having developed a code that proved very efficient for the high Ra laminar regime. As the Rayleigh number increased, thin boundary layers began to form next to the vertical walls, and the central region became progressively more stagnant and highly stratified. Results obtained for the high Ra laminar regime were in good agreement with existing studies. Turbulence computations, although of a preliminary nature, indicated that a second moment closure model was capable of predicting the experimentally observed flow features."--Publisher Summary

Effect of surface radiation on conjugate natural convection in a horizontal annulus driven by inner heat generating solid cylinder

This paper reports a numerical study of the laminar conjugate natural convection heat transfer with and without the interaction of the surface radiation in a horizontal cylindrical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal circular boundary. Numerical solutions are obtained by solving the governing equations with a pressure correction method on a collocated (non-staggered) mesh. Steady-state results are presented for the flow and temperature distributions and Nusselt numbers for the heat generation based Grashof number ranging from 10(7) to 10(10), solid-to-fluid thermal conductivity ratios of 1, 5, 10, 50 and 100, radius ratios of 0.226 and 0.452 and surface emissivities of 0-0.8 with air as the working medium. It is observed that surface radiation reduces the convective heat transfer in the annulus compared to the pure natural convection case and enhances the overall Nusselt number.

Unsteady Natural Convection Flow over a Heated Cylinder Buried in a Fluid Saturated Porous Medium

Transient natural convection flow on a heated cylinder buried in a semi-infinite liquid-saturated porous medium has been studied. The unsteadiness in the problem arises due to the cylinder which is heated (cooled) suddenly and then maintained at that temperature. The coupled partial differential equations governing the flow and heat transfer are cast into stream function-temperature formulation, and the solutions are obtained from the initial time to the time when steady state is reached. The heat transfer is found to change significantly with increasing time in a small time interval immediately after the start of the impulsive change, and steady state is reached after some time. The average Nusselt number is found to increase with Rayleigh number When the surface of the cylinder is suddenly cooled, there is a change in the direction of the heat transfer in a small time interval immediately after the start of the impulsive change in the surface temperature;however when the surface temperature is suddenly increased, no such phenomenon is observed.

Unsteady natural convection from a horizontal annulus filled with a porous medium

The unsteady natural convection flow from a horizontal cylindrical annulus filled with a non-Darcy porous medium has been studied. The unsteadiness in the problem arises due to the impulsive change in the wall temperature of the outer cylinder. The Navier–Stokes equations along with the energy equation governing the unsteady natural convection flow have been solved by the finite-volume method. The effect of time variation on the heat transfer is more pronounced only in a small time interval immediately after the start of the impulsive motion and the steady state is reached after certain time. The results show that the annulus completely filled with a porous medium has the best insulating effectiveness. Convection in the horizontal annulus is confined mostly at top and bottom regions. Hence, only these regions should be insulated. In case of annulus partially filled with a porous material, insulating the region near the outer cylinder is more effective than insulating the region near the inner cylinder. The effect of Darcy number on the heat transfer is more pronounced than that of the Grashof number.

Natural Convection on a Horizontal Cone in a Porous Medium with Non-Uniform Wall Temperature/Concentration or Heat/Mass Flux and Suction/Injection

The steady natural convection flow on a horizontal cone embedded in a saturated porous medium with non-uniform wall temperature/concentration or heat/mass flux and suction/injection has been investigated. Non-similar solutions have been obtained. The nonlinear couple differential equations under boundary layer approximations governing the flow have been numerically solved. The Nusselt and Sherwood numbers are found to depend on the buoyancy forces, suction/injection rates, variation of wall temperature/concentration or heat/mass flux, Lewis number and the non-Darcy parameter.

Non-Boussinesq conjugate natural convection in a vertical annulus

Non-Boussinesq conjugate natural convection in a vertical annulus with a centrally located vertical heat generating rod is studied numerically, taking into account variable transport properties. Results are presented for maximum solid temperatures, average Nusselt numbers and average pressure. In general, the Boussinesq model predicts higher temperatures in the solid and lower average Nusselt numbers on the inner and outer boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Natural Convection Heat Transfer From an Isothermal Vertical Surface to a Stable Thermally Stratified Fluid

Natural convection from an isothermal vertical surface to a thermally stratified fluid is studied numerically. A wide range of stratification levels is considered. It is shown that at high levels of ambient thermal stratification, a portion at the top of the plate absorbs heat, while a horizontal plume forms around a location where the plate temperature equals the ambient temperature. The plume is shown to be inherently unsteady, and its transient nature is investigated in detail. The effect of the temperature defect in striating the plume is discussed. Average Nusselt number data are presented for Pr = 6.0 and 0.7.

Effective thermal conductivity of a heat generating rod bundle dissipating heat by natural convection and radiation

A numerical study of conjugate natural convection and surface radiation in a horizontal hexagonal sheath housing 19 solid heat generating rods with cladding and argon as the fill gas, is performed. The natural convection in the sheath is driven by the volumetric heat generation in the solid rods. The problem is solved using the FLUENT CFD code. A correlation is obtained to predict the maximum temperature in the rod bundle for different pitch-to-diameter ratios and heat generating rates. The effective thermal conductivity is related to the heat generation rate, maximum temperature and the sheath temperature. Results are presented for the dimensionless maximum temperature, Rayleigh number and the contribution of radiation with changing emissivity, total wattage and the pitch-to-diameter ratio. In the simulation of a larger system that contains a rod bundle, the effective thermal conductivity facilitates simplified modelling of the rod bundle by treating it as a solid of effective thermal conductivity. The parametric studies revealed that the contribution of radiation can be 38-65% of the total heat generation, for the parameter ranges chosen. Data for critical Rayleigh number above which natural convection comes into effect is also presented. (C) 2011 Elsevier B.V. All rights reserved.