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

The effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment has been investigated numerically. The reduced equations are integrated by employing the implicit finite difference scheme or Ke1ler-box method and obtained the effect of heat due to viscous dissipation on the local skin-friction and loca1 Nusselt number at various stratification levels, for fluids having Prandtl number equals 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters and compared with the Finite Difference solutions. Effect of the heat transfer due to viscous dissipation and the temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region. A numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium is also considered for this study. Solutions are obtained using the implicit Finite Difference method and compared with the local non-similarity method. The velocity and temperature distributions for different values of stratification parameter are shown graphically. The results show many interesting aspects of complex interaction of the two buoyant mechanisms.

Scaling analysis of the unsteady natural convection boundary layer adjacent to an inclined plate for Pr > 1 following instantaneous heating

The unsteady natural convection boundary layer adjacent to an instantaneously heated inclined plate is investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer following instantaneous heating may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. Major scaling relations of the velocity and thicknesses and the flow development time of the natural convection boundary layer are obtained using triple-layer integral solutions and verified by direct numerical simulations over a wide range of flow parameters.

Periodically forced natural convection through the roof of an attic-shaped building

In this study, numerical simulations of natural convection in an attic space subject to diurnal temperature condition on the sloping wall have been carried out. An explanation of choosing the period of periodic thermal effect has been given with help of the scaling analysis which is available in the literature. Moreover, the effects of the aspect ratio and Rayleigh number on the fluid flow and heat transfer have been discussed in details as well as the formation of a pitchfork bifurcation of the flow at the symmetric line of the enclosure.

Natural convection flow in a porous enclosure with localized heating from below

Natural convection flow in a two-dimensional fluid saturated porous enclosure with localized heating from below, symmetrical cooling from the sides and the top and rest of the bottom walls are insulated, has been investigated numerically. Darcy’s law for porous media along with the energy equation based on the 1st law of thermodynamics has been considered. Implicit finite volume method with TDMA solver is used to solve the governing equations. Localized heating is simulated by a centrally located isothermal heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5 and 4/5 are considered. The effect of heat source length and the Rayleigh number on streamlines and isotherms are presented, as well as the variation of the local rate of heat transfer in terms of the local Nusselt number from the heated wall. Finally, the average Nusselt number at the heated part of the bottom wall has been shown against Rayleigh number for the non-dimensional heat source length.

Natural convection from a vertical plate embedded in a stratified medium with uniform heat source

Natural convection flow from an isothermal vertical plate with uniform heat source embedded in a stratified medium has been discussed in this paper. The resulting momentum and energy equations of boundary layer approximation are made non-similar by introducing the usual non-similarity transformations. Numerical solutions of these equations are obtained by an implicit finite difference method for a wide range of the stratification parameter, X. The solutions are also obtained for different values of pertinent parameters, namely, the Prandtl number, Pr and the heat generation or absorption parameter, λ and are expressed in terms of the local skin-friction and local heat transfer, which are shown in the graphical form. Effect of heat generation or absorption on the streamlines and isotherms are also shown graphically for different values of λ.

Effects of corrugation frequency and aspect ratio on natural convection within an enclosure having sinusoidal corrugation over a heated top surface

Natural convection of a two-dimensional laminar steady-state incompressible fluid flow in a modified rectangular enclosure with sinusoidal corrugated top surface has been investigated numerically. The present study has been carried out for different corrugation frequencies on the top surface as well as aspect ratios of the enclosure in order to observe the change in hydrodynamic and thermal behavior with constant corrugation amplitude. A constant flux heat source is flush mounted on the top sinusoidal wall, modeling a wavy sheet shaded room exposed to sunlight. The flat bottom surface is considered as adiabatic, while the both vertical side walls are maintained at the constant ambient temperature. The fluid considered inside the enclosure is air having Prandtl number of 0.71. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results in terms of isotherms, streamlines and average Nusselt numbers are obtained for the Rayleigh number ranging from 10^3 to 10^6 with constant physical properties for the fluid medium considered. It is found that the convective phenomena are greatly influenced by the presence of the corrugation and variation of aspect ratios.

Prandtl number scaling of natural convection of an inclined flat plate due to uniform surface heat flux

A new scaling analysis has been performed for the unsteady natural convection boundary layer under a downward facing inclined plate with uniform heat flux. The development of the thermal or viscous boundary layers may be classified into three distinct stages including a start-up stage, a transitional stage and a steady stage, which can be clearly identified in the analytical as well as numerical results. Earlier scaling shows that the existing scaling laws of the boundary layer thickness, velocity and steady state time scale for the natural convection flow on a heated plate of uniform heat flux provide a very poor prediction of the Prandtl number dependency of the flow. However, those scalings performed very well with Rayleigh number and aspect ratio dependency. In this study, a new Prandtl number scaling has been developed using a triple-layer integral approach for Pr > 1. It is seen that in comparison to the direct numerical simulations, the new scaling performs considerably better than the previous scaling.

Free convection in a triangular enclosure with fluid-saturated porous medium and internal heat generation

Unsteady natural convection inside a triangular cavity has been studied in this study. The cavity is filled with a saturated porous medium with non-isothermal left inclined wall while the bottom surface is isothermally heated and the right inclined surface is isothermally cold. An internal heat generation is also considered which is dependent of the fluid temperature. The governing equations are solved numerically by finite element method. The Prandtl number of the fluid is considered as 0.7 (air) while the aspect ratio and the Rayleigh number are considered as 0.5 and 105 respectively. The effect of the porosity of the medium and heat generation on the fluid flow and heat transfer have been presented as a form of streamlines and isotherms. The rate of heat transfer through three surfaces of the enclosure is also presented.

Natural convection in a triangular enclosure due to non-uniform cooling on top

Natural convection in a triangular enclosure subject to non-uniformly cooling at the inclined surfaces and uniformly heating at the base is investigated numerically. The numerical simulations of the unsteady flows over a range of Rayleigh numbers and aspect ratios are carried out using Finite Volume Method. Since the upper surface is cooled and the bottom surface is heated, the air flow in the enclosure is potentially unstable to Rayleigh Benard instability. It is revealed that the transient flow development in the enclosure can be classified into three distinct stages; an early stage, a transitional stage and a steady stage. It is also found that the flow inside the enclosure strongly depends on the governing parameters, Rayleigh number and aspect ratio. The asymmetric behaviour of the flow about the geometric centre line is discussed in detailed. The heat transfer through the roof and the ceiling as a form of Nusselt number is also reported in this study.

Mixed convection laminar flow along a horizontal plate subject to streamwise sinusoidal surface temperature

Mixed convection of a two-dimensional laminar incompressible flow along a horizontal flat plate with streamwise sinusoidal surface temperature has been numerically investigated for different values of Rayleigh number and Reynolds number for constant values of Prandtl number, amplitude and frequency of periodic temperature. The numerical scheme is based on the finite element method adapted to rectangular non-uniform mesh elements by a non-linear parametric solution algorithm. The fluid considered in this study is air. The results are obtained for the Rayleigh number and Reynolds number ranging from 102 to 104 and 1 to 100, respectively, with constant physical properties for the fluid medium considered. Velocity and temperature profiles, streamlines, isotherms, and average Nusselt numbers are presented to observe the effect of the investigating parameters on fluid flow and heat transfer characteristics. The present results show that the convective phenomena are greatly influenced by the variation of Rayleigh numbers and Reynolds number.

Free convection heat transfer through coupled thermal boundary layers in a partitioned triangular enclosure

A numerical investigation has been carried out for the coupled thermal boundary layers on both sides of a partition placed in an isosceles triangular enclosure along its middle symmetric line. The working fluid is considered as air which is initially quiescent. A sudden temperature difference between two zones of the enclosure has been imposed to trigger the natural convection. It is anticipated from the numerical simulations that the coupled thermal boundary layers development adjacent to the partition undergoes three distinct stages; namely an initial stage, a transitional stage and a steady state stage. Time dependent features of the coupled thermal boundary layers as well as the overall natural convection flow in the partitioned enclosure have been discussed and compared with the non-partitioned enclosure. Moreover, heat transfer as a form of local and overall average Nusselt number through the coupled thermal boundary layers and the inclined walls is also examined. The details results will be discussed in the full paper.

Effect of differentially heating and consequent transient behaviour for natural convection within an enclosure of sinusoidal corrugated side walls

Unsteady natural convection due to differentially heating of the sinusoidal corrugated side walls of a modified square enclosure has been numerically investigated. The fluid inside the enclosure is air, initially as quiescent. The flat top and bottom surfaces are considered as adiabatic. The numerical scheme is based on the finite element method adapted to triangular non-uniform mesh element by a non-linear parametric solution algorithm. The results are obtained for the Rayleigh number, Ra ranging from 1e+05 to 1e+08 for different corrugation amplitude and frequency with constant physical properties for the fluid medium considered. The streamlines, isotherms and average Nusselt numbers are presented to observe the effect of sudden heating and its consequent transient behavior on fluid flow and heat transfer characteristics for the range of governing parameters. The present results show that the transient phenomena are greatly influenced by the variation of the aforementioned parameters.