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

Unsteady laminar boundary layers in a compressible stagnation flow

The unsteady laminar compressible boundary-layer flow in the immediate vicinity of a two-dimensional stagnation point due to an incident stream whose velocity varies arbitrarily with time is considered. The governing partial differential equations, involving both time and the independent similarity variable, are transformed into new co-ordinates with finite ranges by means of a transformation which maps an infinite interval into a finite one. The resulting equations are solved by converting them into a matrix equation through the application of implicit finite-difference formulae. Computations have been carried out for two particular unsteady free-stream velocity distributions: (1) a constantly accelerating stream and (2) a fluctuating stream. The results show that in the former case both the skin-friction and the heat-transfer parameter increase steadily with time after a certain instant, while in the latter they oscillate thus responding to the fluctuations in the free-stream velocity.

Rocket Propellant Combustion Studies in a Constant Volume Bomb

A constant volume window bomb has been used to measure the characteristic velocity (c*) of rocket propellants. Analysis of the combustion process inside the bomb including heat losses has been made. The experiments on double base and composite propellants have revealed some (i) basic heat transfer aspects inside the bomb and (ii) combustion characteristics of Ammonium Perchlorate-Polyester propellants. It has been found that combustion continues even beyond the peak pressure and temperature points. Lithium Fluoride mixed propellants do not seem to indicate significant differences in c*) though the low pressure deflagration limit is increased with percentage of Lithium Fluoride.

The problem of liquid droplet combustion-reexamination

The simple quasi-steady analysis of the combustion of a liquid fuel droplet in an oxidising atmosphere provides unsatisfactory explanations for several experimental observations. It's prediction of values for the burning constant (K), the flame-to-droplet diameter ratio ( ) and the flame temperature (Tf) have been found to be amgibuous if not completely inaccurate. A critical survey of the literature has led us to a detailed examination of the effects of unsteadiness and variable properties. The work published to date indicates that the gas-phase unsteadiness is relatively short and therefore quite insignificant.A new theoretical analysis based on heat transfer within the droplet is presented here. It shows that the condensed-phase unsteadiness lasts for about 20â??25% of the total burning time. It is concluded that the discrepancies between experimental observations and the predictions of the constant-property quasi-steady analysis cannot be attributed either to gas-phase or condensed-phase unsteadiness.An analytical model of quasi-steady droplet combustion with variable thermodynamic and transport properties and non-unity Lewis numbers will be examined. Further findings reveal a significant improvement in the prediction of combustion parameters, particularly of K, when consideration is given to variations of cp and λ with the temperature and concentrations of several species. Tf is accurately predicted when the required conditions of incomplete combustion or low ( ) at the flame are met. Further refinement through realistic Lewis numbers predicts ( ) meaningfully.

Nonsimilar incompressible laminar boundary layers with magnetic field.

The solution of the steady laminar incompressible nonsimilar magneto-hydrodynamic boundary layer flow and heat transfer problem with viscous dissipation for electrically conducting fluids over two-dimensional and axisymmetric bodies with pressure gradient and magnetic field has been presented. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. The computations have been carried out for flow over a cylinder and a sphere. The results indicate that the magnetic field tends to delay or prevent separation. The heat transfer strongly depends on the viscous dissipation parameter. When the dissipation parameter is positive (i.e. when the temperature of the wall is greater than the freestream temperature) and exceeds a certain value, the hot wall ceases to be cooled by the stream of cooler air because the ‘heat cushion’ provided by the frictional heat prevents cooling whereas the effect of the magnetic field is to remove the ‘heat cushion’ so that the wall continues to be cooled. The results are found to be in good agreement with those of the local similarity and local nonsimilarity methods except near the point of separation, but they are in excellent agreement with those of the difference-differential technique even near the point of separation.

Thermal performance of magnesium oxide wall board using numerical modelling

Fire resistance of light-gauge steel frame (LSF) walls can be enhanced by lining them with single or multiple layers of wall boards. This research is focused on the thermal per-formance of Magnesium Oxide (MgO) wall boards in comparison to the conventional gypsum plasterboards exposed to standard fire on one side. Thermal properties of MgO board and gypsum plasterboard were measured first and then used in the finite element heat transfer models of the two types of panels. The measured thermal property results show that MgO board will perform better than the gypsum plasterboards due to its higher specific heat values at elevated temperatures. However, MgO board loses 50% of its ini-tial mass at about 500 °C compared to 16% for gypsum plasterboard. The developed finite element models were validated using the fire test results of gypsum plasterboards and then used to study the thermal performance of MgO board panels. Finite element analysis re-sults show that when MgO board panels are exposed to standard fire on one side the rate of temperature rise on the ambient side is significantly reduced compared to gypsum plas-terboard. This has the potential to improve the overall thermal performance of MgO board lined LSF walls and their fire resistance levels (FRL). However, full scale fire tests are needed to confirm this. This paper presents the details of this investigation and the results.

Compressible magnetohydrodynamic boundary layer swirling nozzle and diffuser flows with a magnetic field

The flow, heat and mass transfer problem for boundary layer swirling flow of a laminar steady compressible electrically conducting gas with variable properties through a conical nozzle and a diffuser with an applied magnetic field has been studied. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme after they have been transformed into dimensionless form using the modified Lees transformation. The results indicate that the skin friction and heat transfer strongly depend on the magnetic field, mass transfer and variation of the density-viscosity product across the boundary layer. However, the effect of the variation of the density-viscosity product is more pronounced in the case of a nozzle than in the case of a diffuser. It has been found that large swirl is required to produce strong effect on the skin friction and heat transfer. Separationless flow along the entire length of the diffuser can be obtained by applying appropriate amount of suction. The results are found to be in good agreement with those of the local nonsimilarity method, but they differ quite significantly from those of the local similarity method.

Unsteady Incompressible Three-Dimensional Asymmetric Stagnation-Point Boundary Layers

The unsteady laminar incompressible boundary-layer flow near the three-dimensional asymmetric stagnation point has been studied under the assumptions that the free-stream velocity, wall temperature, and surface mass transfer vary arbitrarily with time. The partial differential equations governing the flow have been solved numerically using an implicit finite-difference scheme. It is found that in contrast with the symmetric flow, the maximum heat transfer occurs away from the stagnation point due to the decrease in the boundary-layer thickness. The effect of the variation of the wall temperature with time on heat transfer is strong. The skin friction and heat transfer due to asymmetric flow only are comparatively less affected by the mass transfer as compared to those of symmetric flow.

Steady mixed convection stagnation-point flow of upper convected Maxwell fluids with magnetic field

The steady MHD mixed convection flow of a viscoelastic fluid in the vicinity of two-dimensional stagnation point with magnetic field has been investigated under the assumption that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary layer theory is used to simplify the equations of motion. induced magnetic field and energy which results in three coupled non-linear ordinary differential equations which are well-posed. These equations have been solved by using finite difference method. The results indicate the reduction in the surface velocity gradient, surface heat transfer and displacement thickness with the increase in the elasticity number. These trends are opposite to those reported in the literature for a second-grade fluid. The surface velocity gradient and heat transfer are enhanced by the magnetic and buoyancy parameters. The surface heat transfer increases with the Prandtl number, but the surface velocity gradient decreases.

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.

An investigation into the thermophysical and rheological properties of nanofluids for solar thermal applications

Considered to be the next generation of heat transfer fluids, nanofluids have been receiving a growing amount of attention in the past decade despite the controversy and inconsistencies that have been reported. Nanofluids have great potential in a wide range of fields, particularly for solar thermal applications. This paper presents a comprehensive review of the literature on the enhancements in thermophysical and rheological properties resulting from experimental works conducted on molten salt nanofluids that are used in solar thermal energy systems. It was found that an increase in specific heat of 10–30% was achieved for most nanofluids and appeared independent of particle size and to an extent mass concentration. The specific heat increase was attributed to the formation of nanostructures at the solid–liquid interface and it was also noted that the aggregation of nanoparticles has detrimental effects on the specific heat increase. Thermal conductivity was also found to increase, though less consistently, ranging from 3% to 35%. Viscosity was seen to increase with the addition of nanoparticles and is dependent on the amount of aggregation of the particles. An in-depth micro level analysis of the mechanisms behind the thermophysical property changes is presented in this paper. In addition, possible trends are discussed relating to current theorised mechanisms in an attempt to explain the behaviour of molten salt nanofluids.

Numerical studies on channel formation and growth during solidification: Effect of process parameters

In the present work, solidification of a hyper-eutectic ammonium chloride solution in a bottom-cooled cavity (i.e. with stable thermal gradient) is numerically studied. A Rayleigh number based criterion is developed, which determines the conditions favorable for freckles formation. This criterion, when expressed in terms of physical properties and process parameters, yields the condition for plume formation as a function of concentration, liquid fraction, permeability, growth rate of a mushy layer and thermophysical properties. Subsequently, numerical simulations are performed for cases with initial and boundary conditions favoring freckle formation. The effects of parameters, such as cooling rate and initial concentration, on the formation and growth of freckles are investigated. It was found that a high cooling rate produced larger and more defined channels which are retained for a longer durations. Similarly, a lower initial concentration of solute resulted in fewer but more pronounced channels. The number and size of channels are also found to be related to the mushy zone thickness. The trends predicted with regard to the variation of number of channels with time under different process conditions are in accordance with the experimental observations reported in the literature.

Effects of climate and morphology on temperature conditions of lakes

To a large extent, lakes can be described with a one-dimensional approach, as their main features can be characterized by the vertical temperature profile of the water. The development of the profiles during the year follows the seasonal climate variations. Depending on conditions, lakes become stratified during the warm summer. After cooling, overturn occurs, water cools and an ice cover forms. Typically, water is inversely stratified under the ice, and another overturn occurs in spring after the ice has melted. Features of this circulation have been used in studies to distinguish between lakes in different areas, as basis for observation systems and even as climate indicators. Numerical models can be used to calculate temperature in the lake, on the basis of the meteorological input at the surface. The simple form is to solve the surface temperature. The depth of the lake affects heat transfer, together with other morphological features, the shape and size of the lake. Also the surrounding landscape affects the formation of the meteorological fields over the lake and the energy input. For small lakes the shading by the shores affects both over the lake and inside the water body bringing limitations for the one-dimensional approach. A two-layer model gives an approximation for the basic stratification in the lake. A turbulence model can simulate vertical temperature profile in a more detailed way. If the shape of the temperature profile is very abrupt, vertical transfer is hindered, having many important consequences for lake biology. One-dimensional modelling approach was successfully studied comparing a one-layer model, a two-layer model and a turbulence model. The turbulence model was applied to lakes with different sizes, shapes and locations. Lake models need data from the lakes for model adjustment. The use of the meteorological input data on different scales was analysed, ranging from momentary turbulent changes over the lake to the use of the synoptical data with three hour intervals. Data over about 100 past years were used on the mesoscale at the range of about 100 km and climate change scenarios for future changes. Increasing air temperature typically increases water temperature in epilimnion and decreases ice cover. Lake ice data were used for modelling different kinds of lakes. They were also analyzed statistically in global context. The results were also compared with results of a hydrological watershed model and data from very small lakes for seasonal development.

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.

Factors controlling the surface energy budget over snow and ice

Polar Regions are an energy sink of the Earth system, as the Sun rays do not reach the Poles for half of the year, and hit them only at very low angles for the other half of the year. In summer, solar radiation is the dominant energy source for the Polar areas, therefore even small changes in the surface albedo strongly affect the surface energy balance and, thus, the speed and amount of snow and ice melting. In winter, the main heat sources for the atmosphere are the cyclones approaching from lower latitudes, and the atmosphere-surface heat transfer takes place through turbulent mixing and longwave radiation, the latter dominated by clouds. The aim of this thesis is to improve the knowledge about the surface and atmospheric processes that control the surface energy budget over snow and ice, with particular focus on albedo during the spring and summer seasons, on horizontal advection of heat, cloud longwave forcing, and turbulent mixing during the winter season. The critical importance of a correct albedo representation in models is illustrated through the analysis of the causes for the errors in the surface and near-surface air temperature produced in a short-range numerical weather forecast by the HIRLAM model. Then, the daily and seasonal variability of snow and ice albedo have been examined by analysing field measurements of albedo, carried out in different environments. On the basis of the data analysis, simple albedo parameterizations have been derived, which can be implemented into thermodynamic sea ice models, as well as numerical weather prediction and climate models. Field measurements of radiation and turbulent fluxes over the Bay of Bothnia (Baltic Sea) also allowed examining the impact of a large albedo change during the melting season on surface energy and ice mass budgets. When high contrasts in surface albedo are present, as in the case of snow covered areas next to open water, the effect of the surface albedo heterogeneity on the downwelling solar irradiance under overcast condition is very significant, although it is usually not accounted for in single column radiative transfer calculations. To account for this effect, an effective albedo parameterization based on three-dimensional Monte Carlo radiative transfer calculations has been developed. To test a potentially relevant application of the effective albedo parameterization, its performance in the ground-based retrieval of cloud optical depth was illustrated. Finally, the factors causing the large variations of the surface and near-surface temperatures over the Central Arctic during winter were examined. The relative importance of cloud radiative forcing, turbulent mixing, and lateral heat advection on the Arctic surface temperature were quantified through the analysis of direct observations from Russian drifting ice stations, with the lateral heat advection calculated from reanalysis products.