Natural convection adjacent to an inclined flat plate and in an attic space under various thermal forcing conditions

Saha, Suvash Chandra (2008) Natural convection adjacent to an inclined flat plate and in an attic space under various thermal forcing conditions. PhD thesis, James Cook University.

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Abstract

The natural convection thermal boundary layer adjacent to an inclined flat plate and inclined walls of an attic space subject to instantaneous and ramp heating and cooling is investigated. Attention in this study has been given to fluid having a Prandtl number less than unity. A scaling analysis has been performed to describe the flow behaviour and heat transfer. Major scales quantifying the flow velocity, flow development time, heat transfer and the thermal and viscous boundary layer thicknesses at different stages of the flow development are established.

In Chapter 3, an investigation of the natural convection boundary layer adjacent to an inclined plate subject to sudden heating and a temperature boundary condition which follows a ramp function up until a specified time and then remains constant is reported. The development of the flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. Different flow regimes based on the Rayleigh number are discussed with numerical results for both boundary conditions. For ramp heating, the boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating.

In Chapter 4, the natural convection boundary layer adjacent to an inclined plate subject to sudden and ramp cooling boundary conditions is reported. It is found that the cold boundary layer adjacent to the plate is potentially unstable to a Rayleigh-Bénard instability if the Rayleigh number exceeds a certain critical value. A scaling relation for the onset of instability of the boundary layer is achieved. For the ramp cooling case, the onset of instability may set in at different stages of the boundary layer development. A proper identification of the time when the instability may set in is discussed. A numerical verification of the time for the onset of instability is presented in this chapter. Different flow regimes based on the stability of the boundary layer have also been discussed with numerical results.

In Chapters 5 and 6, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The sudden and ramp heating/cooling boundary conditions are applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up/cooling-down of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

Further, a periodic temperature boundary condition is also considered in Chapter 7 to show the basic flow features in the attic space over diurnal cycles. The numerical results reveal that, during the daytime heating stage, the flow in the attic space is stratified; whereas at the night-time cooling stage, the flow becomes unstable. A symmetrical solution can be seen for relatively low Rayleigh numbers. However, as the Ra is gradually increased, a transition occurs at a critical value of Ra. Above this critical value, an asymmetrical solution exhibiting a pitchfork bifurcation arises at the night-time. It is also found that the calculated heat transfer rate at the night-time cooling stage is much higher than that during the daytime heating stage.

Item ID: 12138
Item Type: Thesis (PhD)
Keywords: natural convection, attic space, inclined plate, heat transfer, flow behaviour, boundary layer, scaling analysis, fluid dynamics, fluid mechanics, ramp heating, ramp cooling, thermal forcing, buoyancy, stability
Date Deposited: 29 Oct 2010 05:47
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 33%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091508 Turbulent Flows @ 33%
09 ENGINEERING > 0915 Interdisciplinary Engineering > 091505 Heat and Mass Transfer Operations @ 34%
SEO Codes: 85 ENERGY > 8507 Energy Conservation and Efficiency > 850704 Residential Energy Conservation and Efficiency @ 50%
96 ENVIRONMENT > 9606 Environmental and Natural Resource Evaluation > 960604 Environmental Management Systems @ 50%
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