Natural convection in enclosures with partial partitions

Laminar and turbulent natural convection in enclosures with partial partitions has been studied by a numerical method. Vertical boundaries were isothermal and horizontal boundaries were adiabatic. Two dimensional equations of conservation of mass, momentum and energy, with the Boussinesq approximation are solved using the Simpler method. Various geometrical parameters were: aspect ratio A=0.3 to 0.4, partition position D=0.5−0.6, height of the partitions C=D=0 to 0.15. The Rayleigh number was varied from 10⁴ to 10¹¹. The results are reduced in terms of the normalized Nusselt number as a function of the Rayleigh number, and other non dimensional geometrical parameters. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions. Heat transfer correlations useful for practical design problems have been derived.     

Natural convection in porous triangular enclosures with a solid adiabatic fin attached to the horizontal wall

A numerical analysis has been performed to investigate the effects of fin location onto the bottom wall of a triangular enclosure filled with porous media whose height base ratio is 1. The temperature of the bottom wall is higher than that of the inclined wall while the vertical wall is insulated. Thus, the fin divides the heated bottom wall to two separate regions. Finite difference method was applied to solve governing equations which are written using Darcy method. Solutions of algebraic equations were made by Successive Under Relaxation (SUR) technique. The effective parameters on flow and temperature fields are: Rayleigh number, location center of fin, dimensionless fin height, and dimensionless fin width. The obtained results indicated that the fin can be used as a control element for heat transfer and fluid flow.     

Free convection in porous media filled right-angle triangular enclosures

Steady-state free convection heat transfer in a right-angle triangular enclosure, whose vertical wall insulated and inclined and bottom walls are differentially heated, is performed in this study. The governing equations are obtained using Darcy model. In this study, the governing equations were solved by finite difference method and solution of algebraic equations was made via Successive Under Relaxation method. The effect of aspect ratios ranging from 0.25 to 1.0 and Rayleigh numbers 50 ≤ Ra ≤ 1000 is investigated as governing parameters on heat transfer and flow field. It is observed that heat transfer is increased with the decreasing of aspect ratio and multiple cells are formed at high Rayleigh numbers.     

Natural convection in partitioned air-filled rectangular enclosures

This work is a study on the effect a vertical partition has on steady-state natural convection in air-filled rectangular enclosures. A finite-difference scheme was used to solve the governing equations. Computed Nusselt numbers are presented as a function of the governing parameters. It was found that placing a partition midway between the vertical walls of an enclosure produces the greatest reduction in heat transfer and often compares favorably with fully insulating the enclosure with a porous material.     

Natural convection solar dryer with biomass back-up heater

A direct-type natural convection solar dryer and a simple biomass burner have been combined to demonstrate a drying technology suitable for small-scale processors of dried fruits and vegetables in non-electrified areas of developing countries. From a series of evaluation trials of the system, the capacity of the dryer was found to be 20–22 kg of fresh pineapple arranged in a single layer of 0.01-m-thick slices. The overall drying efficiency of the unit was calculated to be 9%. During the same trial, the drying efficiency of the solar component alone was found to be 22%. Other trials estimated the efficiency of the burner in producing useful heat for drying to be 27%. Key features of the biomass burner were found to be the addition of thermal mass on the upper surface, an internal baffle plate to lengthen the exhaust gas exit path and a variable air inlet valve. Further modifications to further improve the performance of both the solar and biomass components of the dryer are suggested.     

Natural convection of nanofluids in enclosures with low aspect ratios

This paper analyzes heat transfer and fluid flow of natural convection in inclined cavity filled with CuO-water nanofluid heated from one side and cooled from the ceiling. The transport equations for the flow are solved numerically by the finite volume element method using the SIMPLER algorithm Based on numerical predictions. The effects of Rayleigh number and aspect ratio on flow pattern and energy transport are investigated for Rayleigh numbers ranging from 10⁴ to 10⁷ volume fraction of solid varied to 0%–4% and for five different aspect ratios of 0.08, 0.1, 0.125, 0.25 and 0.5. It is found that the effect of Rayleigh number on heat transfer is less significant when the enclosure is shallow (AR = 0.5) and the influence of aspect ratio is stronger when the enclosure is tall and the Rayleigh number is high.     

Natural convection of microparticle suspensions in thin enclosures

Natural convection experiments were performed with aluminum oxide microparticle aqueous suspensions in thin enclosures of circular planform at angles of inclination to the horizontal of 90°, 30° and 0°. The average size of the aluminum oxide particles was about 250 nm, and volume fractions of 1.31% and 2.72% were used. The aspect ratio varied from 50.7 to 10.9, and the maximum Raleigh number was 3 × 10⁵. No effect of particles on the Nusselt number–Rayleigh number relation was found for the vertical enclosure at 90°. However at 30° and 0° (horizontal) there was a decrease in Nusselt number compared to pure water, which was pronounced at lower Rayleigh number and higher particle concentrations. This anomalous behavior is attributed to sedimentation.     

Effects of thin fin on natural convection in porous triangular enclosures

A two-dimensional solution of natural convection in solid adiabatic thin fin attached to porous right triangular enclosures has been analyzed numerically. The vertical wall of the enclosure is insulated while the bottom and the inclined walls are isothermal. The temperature of the bottom wall is higher than the temperature of the inclined wall. Governing equations, which are written using Darcy model, are solved via the finite difference technique. The Successive Under Relaxation (SUR) method was used to solve linear algebraic equations. Dimensionless location of the thin fin from 0.2 to 0.6, the aspect ratio of triangular enclosure from 0.25 to 1, Rayleigh number from 100 to 1000 and the dimensionless height of the fin from 0.1 to 0.4 are used as governing parameters that are effective on heat transfer and fluid flow. Results for the mean Nusselt number, velocity profiles, the contour maps of the streamlines and isotherms are presented. It is observed that the thin fin can use as a passive control element for flow field, temperature distribution and heat transfer.     

Control of mixed convection in lid-driven enclosures using conductive triangular fins

Control of mixed convection (combined forced and natural convection) in a lid-driven square cavity is performed using a short triangular conductive fin. A numerical technique is used to simulate the flow and temperature fields. The vertical walls of the cavity are differentially heated. Both the top lid and the bottom wall are adiabatic. The fin is located on one of the motionless walls of the cavity. Three different cases have been studied based on the location of the fin. In this context, Cases I, II and III refer to the fin on the left, bottom and right walls, respectively. Results are presented for +x and −x directions of the top lid in horizontal axis and different Richardson numbers as Ri = 0.1, 1.0 and 10.0. It is observed that the triangular fin is a good control parameter for heat transfer, temperature distribution and flow field.     

Natural convection flow in porous enclosures with heating and cooling on adjacent walls and divided by a triangular massive partition

The problem of steady, laminar, natural convection flow in a porous enclosure divided by a triangular massive partition has been formulated. The massive triangular partition is a solid adiabatic body which is located to the right and top wall. Bottom and left vertical wall of porous enclosure are isothermally heated and cooled, respectively. Remaining wall is adiabatic. Governing equations using Darcy model are solved numerically by the finite-difference method and the Successive Under Relaxation (SUR) technique is used to solve linear algebraic equations. Thanks to massive partition, two different enclosure are formed, depends on dimensions of the triangular body, as triangle and trapezoidal. Flow patterns and temperature distributions were presented at different aspect ratios (0 ≤ AR ≤ 1) and Rayleigh numbers (100 ≤ Ra ≤ 1000). Results are given for different aspect ratios (AR) for AR = 0, 0.25, 0.50, 0.75 and 1. A parametric study is conducted and a set of representative results for flow and temperature characteristics are presented and discussed.     

Natural convection flows in porous trapezoidal enclosures with various inclination angles

Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles $(\phi )$. Parametric study has been carried out for a wide range of Rayleigh number $(\mathit{Ra})({10}^3?\mathit{Ra}?{10}^6)$, Prandtl number $(\mathit{Pr})(0.026?\mathit{Pr}?988.24)$ and Darcy number $(\mathit{Da})({10}^{-3}?\mathit{Da}?{10}^{-5})$. Numerical results are presented in terms of stream functions, isotherm contours and Nusselt numbers. The heat transfer is primarily due to conduction at lower values of Darcy number $(\mathit{Da})$ and convection dominant heat transfer is observed at higher Da values. The intensity of circulation increases with increase in Darcy number. Increase in the intensity of circulations and larger temperature gradient are also observed with increase in $\phi$ from 0° to 45° especially at larger Pr and Ra. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating at all Rayleigh and Darcy numbers, but average Nusselt number is lower for non-uniform heating. Local heat transfer rates are found to be relatively greater for $\phi =0°$. It is observed that the local heat transfer rate at the central portion of bottom wall is larger for non-uniform heating case. Average Nusselt number plots show higher heat transfer rates at the bottom wall for $\phi =0°$ as compared to $\phi =45°$ and $\phi =30°$. It is observed that the average heat transfer rate at the bottom wall is found to be invariant with respect to $\phi$ at higher Ra for non-uniform heating. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and the power law correlations between average Nusselt number and Rayleigh numbers are presented for convection dominated regimes.     

Natural convection from isothermal flat surfaces

Local heat-transfer coefficients along a flat plate in natural convection in air were measured using Boelter-Schmidt type heat flux meters. Experiments were carried out for different temperature differences in heating and cooling, and with inclinations varying from the horizontal “facing upwards” position, through the vertical position, to the horizontal “facing downwards” position.

The results are presented in terms of local Nusselt number as a function of the local Grashof number “tangential component”. All runs were in the range accepted as that of laminar boundary layer flow. However, under certain conditions when the normal velocity component of the air is directed away from the surface, separated flow is indicated along the trailing part of the surface, well before turbulence sets in in the boundary layer. Separation starts at a certain point along the surface. This point is nearer to the leading edge the higher the temperature difference, and the larger the inclination of the surface to the vertical.

In a separation region, the flux density is uniform. In all other regions the results agreed closely with established theories of laminar boundary layer flow.

A leading adiabatic section, used in some of the experiments, did not affect the results. An appendix gives relations recommended for engineering calculations.     

Entropy production due to free convection in partially heated isosceles triangular enclosures

A numerical analysis of the entropy production has been performed due to natural convection heat transfer and fluid flow in isosceles triangular enclosures with partially heated from below and symmetrically cooled from sloping walls. Governing equations are solved by finite difference method. Governing parameters on flow and temperature fields are Rayleigh number (10³  Ra  8.8 × 10⁵), dimensionless length of heater (0.25  (ℓ′ = ℓ/L)  1.0), dimensionless location of heater (0.25  (c′ = c/L)  0.75) and inclination angle of slopping walls (30°  β  60°). Heat transfer results are presented in terms of local and mean Nusselt numbers (Nu) while entropy production results are shown with entropy production number (N_s) and Bejan number (Be). Isotherms, streamlines, contours of entropy production due to heat transfer and fluid friction irreversibility are plotted. It is observed that entropy production number increases but Bejan number decreases with increasing of Rayleigh number. However, both entropy production due to heat transfer and fluid friction irreversibility are affected by higher inclination angle of triangle and length of heater.     

Natural convection heat transfer from a discrete protruding surface

Steady heat transfer from a two dimensional discrete protruding copper block mounted on a vertical wall has been experimentally studied here. The buoyant flow around theblock has been visualized using an interferometer. The average Nusselt number for the heater is found to be considerably larger than values reported in the literature. Local Nusselt numbers derived from the interferograms, however justify the magnitude of the average Nusselt number.     

Analysis of entropy generation during natural convection in tilted triangular enclosures with various base angles

ABSTRACT

This paper presents a study of entropy generation during natural convection in a triangular enclosure with various configurations (cases 1 and 2 symmetric about Y-axis, and case 3 symmetric about X-axis) for the linearly heated inclined walls. The detailed analysis and comparison for the various base angles (φ = 45° and 60°) of the triangular enclosures have been carried out for Pr = 0.015 ? 1,000 and Ra = 10³ ? 10⁵. The results show that, case 3 configuration with the tilt angle φ = 60° may be the optimal shape based on the minimum total entropy generation (S_total) with the high heat transfer rate at Ra = 10⁵, irrespective of Pr.     

Natural convection in enclosures with floor cooling subjected to a heated vertical wall

Natural convection in enclosures is extensively investigated due to its importance in many applications, such as heat transfer through double glazing windows, electronic cooling devices, geophysical applications, etc. Two configurations that have been extensively explored in the literature are the differentially heated enclosures and the Rayleigh–Benard problems. In the present work, a different kind of problem is investigated, namely the cross thermal boundary conditions. Three dimensional analyses were performed for an enclosure cooled from below with one vertical wall heated, and the other connecting walls were assumed to be adiabatic. The thermal condition at the ceiling is varied from an adiabatic one to a different degree of heating. The objective of this study is to simulate the comfort provided by floor cooling in a room. For comfort requirements, the interest is on determining the rate of heat transfer and the temperature distribution in the room. Also, the results have importance for other cooling applications such as electronic cooling and natural convection in freezers. Furthermore, the problem is academically interesting for understanding the fundamentals of natural convection. Based on the authors’ knowledge, the physics of this problem has not been explored by other people in such a detail. However, the application has been in practice from ancient times.The predicted results are interesting and have practical applications. For a certain configuration, where strong three dimensional recirculations were predicted, the flow is three dimensional, hence the two dimensional assumption is not valid. Also, it is found that the rate of rate transfer from the floor is a weak function of the investigated parameters, such as Rayleigh number.     

Natural convection in tilted rectangular enclosures with a vertically situated hot plate inside

A numerical study of laminar natural convection in tilted rectangular enclosures that contain a vertically situated hot plate is performed. The plate is very thin and isothermal on both lateral ends, and it acts as a heat source within the medium. Three surfaces of the rectangular enclosure are insulated while one lateral surface is cold. Navier–Stokes equations, continuity equation and the energy equation, along with the Boussinesq approximation, are expressed in the form of vorticity-transport equations. All the pertinent equations are solved using the finite volume method with SIMPLE algorithm. The Rayleigh numbers and the tilt angle of the enclosure are ranged from 10⁵ to 10⁷ and from 0° to 90°, respectively. The aspect ratios of the rectangular enclosures that are considered in this study are A = 1 and A = 2. The isotherms and streamlines are produced for various Rayleigh numbers and geometrical conditions, and steady-state Nusselt numbers are computed. The steady-state plate-surface-averaged Nusselt numbers are computed for each case as a function of Rayleigh number and other non-dimensional geometrical parameters and a correlation useful for practical problems was derived.     

Natural convection in porous triangular enclosure with a centered conducting body

A numerical work was performed to examine the heat transfer and fluid flow due to natural convection in a porous triangular enclosure with a centered conducting body. The center of the body was located onto the gravity center of the right-angle triangular cavity. The Darcy law model was used to write the governing equations and they were solved using a finite difference method. Results are presented by streamlines, isotherms, mean and local Nusselt numbers for the different parameters such as the Rayleigh number, thermal conductivity ratio, and height and width of the body. It was observed that both height and width of the body and thermal conductivity ratio play an important role on heat and fluid flow inside the cavity.