C. J. Ho

A study of natural convection heat transfer in a vertical rectangular enclosure with two-dimensional discrete heating: Effect of aspect ratio

Natural convection heat transfer inside a vertical rectangular enclosure with four two-dimensional discrete flush-mounted heaters is investigated numerically and experimentally to unveil primarily the influence of aspect ratio of the enclosure. Numerical simulations for the problem have been conducted for the aspect ratio varying from 1 to 10 and the modified Rayleigh number in the range between 103 and 107 with a given relative heater size and location. Numerical results reveal that the increase of the aspect ratio leads to substantial degradation of convective dissipation from the discrete heaters. The highest heater surface temperature occurs usually at the top heater for Ra∗ ≥ 104 regardless the aspect ratio of enclosure. Correlation in terms of the modified Rayleigh number and the aspect ratio of the enclosure has been generated for the average Nusselt numbers for each heater as well as the maximum surface temperature at the discrete heaters. Holographic interferometry and a smoke flow visualization are employed to map the temperature and flow fields within an enclosure of aspect ratio 10. The predicted temperature and flow fields are found to be in good agreement with the experiments.

A numerical study of natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions

Abstract Numerical solutions are presented for steady laminar two-dimensional natural convection in concentric and eccentric horizontal cylindrical annuli with constant heat flux on the inner wall and a specified isothermal temperature on the outer wall. The heat and fluid flow patterns in the annuli are vividly visualized by means of the contour maps of streamlines and heatlines. Results of the parametric study conducted further reveal that the influence of the Prandtl number is quite weak; the heat and fluid flows are primarily dependent on the modified Rayleigh number and the eccentricity of the annulus. Above all, the specification of different thermal boundary conditions has a significant effect on the average heat transfer rate across the annulus.

Heat transfer of solid-liquid phase-change material suspensions in circular pipes: Effects of wall conduction

This article considers the problem of conjugate heat transfer in circular pipes with finite heated length to examine the effects of wall conduction on the heat transfer characteristics of solid–liquid phase-change material suspension flow. A mixture continuum approach is adopted in the formulation of the energy equation, with an approximate enthalpy model describing the phase-change process in the phase-change material particles. From numerical simulations via the finite-volume approach, it was found that the conduction heat transfer propagating along the pipe wall results in significant preheating of the suspension flow in the nondirectly heated region upstream of the heated section, where melting of the particles may occur and therefore the contribution of the latent heat transfer to convection heat dissipation over the heated section is markedly attenuated. Contributions of the sensible and latent heat transfer to the total heat transfer rate of the suspension flow over the heated section were delineated quantitatively for various sets of the relevant dimensionless parameters, including the particle volumetric concentration, the modified Stefan number, the Peclet number of suspending fluid, the wall thickness ratio, and the wall-to-fluid thermal conductivity ratio.

Conjugate natural convection heat transfer in an air-filled rectangular cavity

A numerical study of conjugate natural convection heat transfer in an air-filled rectangular cavity has been performed. Results clearly indicate that the heat transfer rate is considerably attenuated in a partitioned cavity in comparing with that for nonpartitioned cavity.

Numerical simulation of melting of ice around a horizontal cylinder

Abstract The problem of outward melting of ice around a horizontal isothermal cylinder is considered. A numerical model in which natural convection induced in the molten water encompassing density inversion is taken into consideration has been developed. Via finite-difference solution of the melting model, numerical simulation of melting of ice has been performed for the cylinder surface temperature T i = 4, 6, 8, 9 and 10°C with cylinder radius of 25.4 mm. The results of the present simulation were found qualitatively valid when compared with the existing experimental data.

Numerical simulation of heat penetration through a vertical rectangular phase change material/air composite cell

Abstract In this paper a numerical simulation of transient heat penetration through a vertical rectangular composite cell, filled with a solid-liquid phase change material (PCM) and air layer, is presented. Inside the composite cell the PCM layer is separated from the air layer by a solid partition of finite thickness. The buoyancy-induced flows developed in both the air-filled layer and the molten PCM zone inside the PCM layer were modeled as two-dimensional laminar Newtonian fluid flow adhering to the Boussinesq approximation. Meanwhile, two-dimensional conduction heat transfer accounted for the unmelted solid PCM region as well as the solid partition. The numerical results for the composite cell with a thin diathermal partition demonstrate that by means of the latent-heat absorption inside the PCM layer, heat penetration across the composite cell can be greatly retarded over an effective duration until a critical instant, around which the melting front of the PCM reaches the partition wall. Such an effective thermal protection duration is found to be a strong function of the modified Rayleigh number, the modified Stefan number, the subcooling factor, the relative PCM thickness ratio, and the aspect ratio of the composite cell. A geometry of a shallow rectangular composite cell having a larger PCM/air thickness ratio is found to be preferable fer effective thermal protection applications. In addition, the effect of a solid partition of finite thickness and conductivity on thermal protection efficacy of the PCM/air composite cell is examined.

Analysis of buoyancy-aided convection heat transfer from a horizontal cylinder in a vertical duct at low Reynolds number

This paper reports a numerical study on buoyancy-aided steady convection heat transfer from a horizontal cylinder situated in a vertical adiabatic duct. Numerical results have been generated forH1/D=2.5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6, 20≤Re≤60, andRi up to 4. The placing of a horizontal cylinder in a vertical duct of smaller width results in significantly enhanced pure forced convection due to the blockage effect, but degrades appreciably the extent of buoyancy-aided enhancement in the heat transfer rate. Nevertheless, the presence of a vertical duct leads to an overall enhancement of mixed convection heat transfer coefficient relative to that without the confining duct. Moreover, the average Nusselt number is rather insensitive to the variation of either the position of the cylinder in the duct or the duct height in the investigated ranges of these geometric parameters.ZusammenfassungDieser Artikel beschreibt eine numerische Studie über auftriebsunterstützte konvektive Wärmeübertragung von einem horizontalen Zylinder der in einem vertikalen adiabaten Kanal positioniert ist. Die numerischen Ergebnisse sind fürH1/D=2, 5, 4, 8,H/D=8, 16, 24,S/D=2, 4, 6 sowie 20≤Re≤60 undRi bis 4 berechnet worden. Die Anordnung des horizontalen Zylinders in einem schmaleren vertikalen Kanal führt auf Grund des Blockierungs-effektes zu einem deutlichen Anstieg der reinen Zwangskonvektion. Aber sie verschlechtert deutlich den Betrag der auftriebsbedingten Steigerung in der Wärmeübergangsrate. Trotzdem führt die Anwesenheit des vertikalen Kanals insgesamt zu einer Steigerung des Wärmeübergangskoeffizienten bei Mischkonvektion im Vergleich zur Abwesenheit des begrenzenden Kanals. Des weiteren ist die durchschnittliche Nusseltzahl von der Variation der Zylinderposition im Kanal oder der Kanalhöhe abhängig.

Periodic melting within a square enclosure with an oscillatory surface temperature

Abstract This paper presents a numerical study dealing with the natural convection-dominated melting process of a pure metal (tin) from a hot vertical wall, having a uniform surface temperature with a timedependent sinusoidally varying perturbation, of a square enclosure. The enthalpy method is adopted to model the latent heat absorption/release at the moving solid-liquid interface and the Boussinesq approximation is adhered to to simulate the natural convection flow in the melt region. Parametric simulations via a finite difference method have been directed towards the response of the melting process in the enclosure to the imposed oscillatory wall temperature. The ranges of the relevant parameters covered in the present study are Ra = 10 3 −5 × 10 5 , Sie = 0.007 and 0.07, Sc = 0.2–0.5, p = 0.5—8 , and A = 0–0.69 . Results clearly demonstrate that a steady periodic melting regime arises following a period of transient oscillatory melting. The heat transfer rates at the vertical hot and cold walls as well as the melting rate exhibit a regular temporal oscillation at a frequency equal to that of the imposed wall temperature perturbation but with phase difference. The effects of relevant parameters on the oscillatory melting behavior are investigated.

The melting process of ice from a vertical wall with time-periodic temperature perturbation inside a rectangular enclosure

Abstract A numerical investigation of natural-convection-dominated melting process of ice from a vertical wall of a square enclosure is reported. Time-dependent sinusoidal temperature perturbation is imposed on the vertical hot wall of the enclosure, and its effects on the heat transfer and buoyancy-driven flow during the melting process of ice are examined. For all the simulations conducted in the present study, a steady periodic melting regime at a frequency of the imposed time-periodic temperature perturbation emerges following a period of transient oscillatory melting process. The synchronous response of the melting process of ice to the imposed time-periodic perturbation on the hot wall temperature is found to be strongly affected by the density inversion phenomenon of water. Parametric simulations have been performed to unveil the effects of the relevant parameters on the heat transfer characteristics during the steady periodic melting regime of ice inside the enclosure. Results clearly demonstrate the feasibility of controlling the melting heat transfer in an ice-filled enclosure by means of the time-periodic perturbation of the wall temperature in conjunction with the density inversion phenomenon of water near 4°C.

Thermal convection heat transfer of air/water layers enclosed in horizontal annuli with mixed boundary conditions

This paper presents a numerical study for thermal convection of air/water layers enclosed in a horizontal concentric/eccentric cylindrical annulus with the inner wall subjected to a constant heat flux and an isothermal condition at the outer wall. Results are generated for an annulus of radius ratio of 2.6 with three different vertically eccentric positions of the inner cylinder, the modified Rayleigh number up to 107, and the modified Marangoni number varying from 0.0 to 104. The heat transfer characteristics and fluid flow patterns driven by buoyancy and/or thermocapillary effects in air/water-filled annulus are illustrated by means of contour maps of healtline and streamline respectively. Under the mixed thermal boundary conditions considered, significant heat exchange across the air-water interface is found and appears to be unaffected by the thermocapillary convection.ZusammenfassungEs wird eine numerische Untersuchung der thermischen Konvektion von Luft/Wasser-Schichten, die von horizontalen konzentrischen/exzentrischen zylindrischen Ringkanälen umschlossen sind, deren innere Wand einer konstanten Wärmestromdichte und deren äußere Wand isothermen Bedingungen ausgesetzt sind, dargestellt. Ergebnisse werden für einen Ringkanal mit einem Radiusverhältnis von 2,6 mit drei verschiedenen senkrechten exzentrischen Positionen des inneren Zylinders, für die modifizierte Rayleigh-Zahl bis 107 und für die modifizierte Marangoni-Zahl zwischen 0,0 und 104 erhalten. Die Charakteristiken der Wärmeübertragung und des Fluid-Stromlinienbildes, hervorgerufen durch Auftriebskräfte und/oder thermokapillare Effekte in mit Luft/Wasser gefüllten Ringkanälen wurden mittels Schichtlinienplänen der Isothermen und der Stromlinien dargestellt. Bei den untersuchten gemischten thermischen Randbedingungen wurde ein signifikanter Wärmeaustausch über der Luft/Wasser-Grenzfläche gefunden, der scheinbar nicht durch die thermokapillare Konvektion gestört wird.