Experimental investigation of mixed convection from an array of discrete heat sources at the bottom of a horizontal channel

Mixed convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally under various operating conditions for air. The lower surface of the channel was equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux, sidewalls and the upper wall are insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR = 10, Reynolds numbers 241 Re_Dh 980, and modified Grashof numbers Gr^* = 9.53 × 10⁵ to 1.53 × 10⁷ . From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers, with emphasis on changes obtained for different discrete heat source locations. From these results, the buoyancy affected secondary flow and the onset of instability have been discussed. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit, especially for low Reynolds numbers.     

Experimental investigation of mixed convection in a rectangular duct with a heated plate in the middle of cross section

The flow and heat transfer in an inclined and horizontal rectangular duct with a heated plate longitudinally mounted in the middle of cross section was experimentally investigated. The heated plate and rectangular duct were both made of highly conductive materials, and the heated plate was subjected to a uniform heat flux. The heat transfer processes through the test section were under various operating conditions: Pr ≈ 0.7, inclination angle ϕ = −60° to +60°, Reynolds number Re = 334–1,911, Grashof number Gr = 5.26 × 10²–5.78 × 10⁶. The experimental results showed that the average Nusselt number in the entrance region was 1.6–2 times as large as that in the fully developed region. The average Nusselt numbers and pressure drops increased with the Reynolds number. The average Nusselt numbers and pressure drops decreased with an increase in the inclination angle from −60° to +60° when the Reynolds number was less than 1,500. But when the Reynolds number increased to over about 1,800, the heat transfer coefficients and pressure drops were independent of inclination angles.     

Mixed convection from a cylinder oscillating vertically in a quiescent fluid

 The problem of heat convection from a vertically oscillating cylinder in a quiescent fluid is investigated. The governing equations of motion and energy are solved numerically in a non-inertial frame of references to determine the flow field and heat transfer characteristics under different conditions. The main dominating parameters are Keulegan–Carpenter number, KC, frequency parameter, β, Grashof number, Gr and Prandtl number, Pr. The ranges considered for these parameters are KC ≤ 10, β≤40 and Gr ≤ 10⁵ while Prandtl number is kept constant. The study revealed that the effect of amplitude and frequency of oscillation on heat transfer is strongly influenced by the Grashof number range. In the forced convection regime (Gr = 0), the increase of KC creates extensive vortex motion at all cylinder positions that leads to a significant increase in heat transfer. A similar trend, but with a lesser extent, is also observed for the increase of β. However, at high Grashof numbers, the effect of oscillation on heat convection is only significant at large values of KC. Received on 5 June 2000 / Published online: 29 November 2001     

3D Numerical study of the effect of aspect ratio on mixed convection air flow in upward solar air heater

A 3D Numerical study of mixed convection air flow in upward solar air heater with large spanwise aspect ratio (A = 10 to 40) was performed using CFD commercial code Fluent 14.5 (ANSYS). The main objective of this study is to investigate the channel height's effect (aspect ratio) on flow pattern and heat transfer in upward solar air heater in the particular case of low Re and high aspect ratio. The bottom plate (absorber) was submitted to Constant Heat Flux (CHF) in the range of 200 to 1000 W/m² and Reynolds number was varied from 50 to 1000. Our results are in concordance with most of authors conclusions about Poiseuille–Rayleigh–Benard flows. In mixed convection, increasing heat flux enhances heat transfer unlike forced convection flows. Simulation results of flow visualizations and Nusselt number calculations have shown that depending on Ri*, the velocity and temperature distributions in SAH vary greatly with the channel's height. The obtained results were different from previous studies. Indeed, our investigation of channel's height was achieved for the same heat flux but different Grashof numbers. For low channel's heights (high aspect ratio), increasing heat flux has not a significant effect but for higher channel's heights, an augmentation of heat flux enhances buoyancy effects in the flow and causes high turbulence. Also, increasing Reynolds number in low channel's heights (high A), can enhance substantially heat transfer. For higher channel's heights (low A), increasing Reynolds number decreases Ri* and thus buoyancy forces. Heat transfer is reduced and so Nusselt number. The obtained results may be very useful for engineers in designing and testing solar collectors.     

Steady and transient liquid sphere heating in a convective gas stream

 A finite-difference scheme has been developed to solve the equations governing the laminar forced convection heat transfer around and inside a spherical fluid droplet moving steadily in another immiscible fluid for both steady and transient thermal conditions. For large values of the external flow Reynolds number (Re), results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ^*). Detailed results over a wide range of viscosity ratio (μ^*) and for 200≤Re≤1000 are presented for the temperature profiles outside and inside the sphere, Nusselt number, the time required to attain a uniform surface temperature and the time required to reach the steady-state temperature. Results show that convective heating is dependent on the external flow Reynolds number (Re) and the interior-to-exterior viscosity ratio (μ^*) where increasing Re or decreasing μ^* result in increasing heat transfer rate convected to the liquid sphere. Received on 1 March 1999     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Numerical study of transient laminar natural convection heat transfer over a sphere subjected to a constant heat flux

Transient laminar natural convection over a sphere which is subjected to a constant heat flux has been studied numerically for high Grashof numbers (10⁵ ≤ Gr ≤ 10⁹) and a wide range of Prandtl numbers (Pr = 0.02, 0.7, 7, and 100). A plume with a mushroom-shaped cap forms above the sphere and drifts upward continuously with time. The size and the level of temperature of the transient cap and plume stem decrease with increasing Gr and Pr. Flow separation and an associated vortex may appear in the wake of the sphere depending on the magnitude of Gr and Pr. A recirculation vortex which appears and grows until “steady state” is attained was found only for the very high Grashof numbers (10⁵ ≤ Gr ≤ 10⁹) and the lowest Prandtl number considered (Pr = 0.02). The appearance and subsequent disappearance of a vortex was observed for Gr = 10⁹ and Pr = 0.7. Over the lower hemisphere, the thickness of both the hydrodynamic (δ_H) and the thermal (δ_T) boundary layers remain nearly constant and the sphere surface is nearly isothermal. The surface temperature presents a local maximum in the wake of the sphere whenever a vortex is established in the wake of the sphere. The surface pressure recovery in the wake of the sphere increases with decreasing Pr and with increasing Gr. For very small Pr, unlike forced convection, the ratio δ_T/δ_H remains close to unity. The results are in good agreement with experimental data and in excellent agreement with numerical results available in the literature. A correlation has also been presented for the overall Nusselt number as a function of Gr and Pr.     

A numerical study of the steady forced convection heat transfer from an unconfined circular cylinder

Forced convection heat transfer from an unconfined circular cylinder in the steady cross-flow regime has been studied using a finite volume method (FVM) implemented on a Cartesian grid system in the range as 10 ≤ Re ≤ 45 and 0.7 ≤ Pr ≤ 400. The numerical results are used to develop simple correlations for Nusselt number as a function of the pertinent dimensionless variables. In addition to average Nusselt number, the effects of Re, Pr and thermal boundary conditions on the temperature field near the cylinder and on the local Nusselt number distributions have also been presented to provide further physical insights into the nature of the flow. The rate of heat transfer increases with an increase in the Reynolds and/or Prandtl numbers. The uniform heat flux condition always shows higher value of heat transfer coefficient than the constant wall temperature at the surface of the cylinder for the same Reynolds and Prandtl numbers. The maximum difference between the two values is around 15–20%.     

Heat transfer and friction factor of turbulent flow through a horizontal semi-circular duct

Forced convection heat transfer and pressure drop characteristics of air flow inside a horizontal semi-circular duct are investigated experimentally. The experiments are carried out on a semi-circular duct of 23 mm inner radius, 2 mm thickness, and 2,000 mm length within a range of Reynolds number (8,242 ≤ Re ≤ 57,794)., under uniform wall heat flux conditions. The friction factor is determined by measuring the axial static pressure at different selected axial stations along the semi-circular duct. The variations of surface and mean air temperatures, local heat transfer coefficient, local Nusselt number, and the friction factor with the axial dimensionless distance are presented. It is observed that, for a given value of Reynolds number, each of the local heat transfer coefficient and the friction factor has a relatively high value near the entrance of the semi-circular duct then it decreases with increasing the dimensionless axial distance until it approaches a nearly constant value at the fully developed region. Also, it is found that, with increasing the Reynolds number the average heat transfer coefficient is increased and the friction factor is decreased. Moreover, empirical correlations for the heat transfer coefficient and friction factor as a function of the Reynolds number are obtained.     

Transient combined natural convection-conduction in open-ended vertical concentric annuli

Transient conjugate natural convection heat transfer in open-ended vertical concentric annuli is investigated numerically. The governing equations of an induced laminar flow for a fluid of Pr=0.7 are solved using a finite-difference technique. The heating is achieved by a step change in the temperature of the outer surface of the outer tube while the inner surface of the inner tube is kept adiabatic. The range of Grashof number considered is 500≤Gr^*≤10⁵. The effects of solid-fluid conductivity ratio and diffusivity ratio on the transient induced flow characteristics are presented. Received on 25 March 1998     

Heat transfer due to a round jet impinging normal to a circular cylinder

An experimental investigations of heat transfer for a stationary isothermal circular cylinder exposed normal to an impinging round air-jet has been reported. The circumferential heat transfer distributions as well as axial Nusselt number is measured. The measurements are taken as a function of the Reynolds number ranging from 3.8 × 10³ to 4 × 10⁴, the cylinder separation distance to the nozzle diameter (z/d) varying from 7 to 30, and the nozzle to cylinder diameter ratio (d/D) changing from 0.06 to 0.14. The output results indicated that the axial and radial distributions of the local heat transfer peaked at the impingement point. The heat transfer rate increases as the values of z decreases, for the same d and Re. The drop-off of the Nusselt number with increasing axial distance or radial angle from the impingement point was more pronounced for smaller z and d. The peripheral and surface average Nusselt numbers were determined by integration. The experimental data was used to produce correlations for both average and stagnation point heat transfer. Received on 4 January 1999     

Forced convection of turbulent flow in triangular ducts with different angles and surface roughnesses

The experimental investigations were consisting of two parts. The first part was carried out to study the effect of corner geometry on the steady-state forced convection inside horizontal isosceles triangular ducts with sharp corners. The electrically-heated triangular duct was used to simulate the triangular passage of a plate-fin compact heat exchanger. The isosceles triangular ducts were manufactured with duralumin, and fabricated with the same length of 2.4 m and hydraulic diameter of 0.44 m, but five different apex angles (i.e. θ _a =15^∘,30^∘, 40^∘,60^∘, and 90^∘) respectively. The investigation was performed under turbulent flow condition covering a wide range of Reynolds number (i.e. 7000≤Re _D ≤20000). It was found that the best thermal performance is achieved with the apex angle of 60^∘. The second part was performed to investigate the effect of surface roughness on the forced convection of the same system. Horizontal equilateral triangular ducts with an apex angle of 60^∘ were fabricated with the same length and hydraulic diameter, but different average surface roughnesses of 1.2 m,3.0 m and 11.5 m respectively. It was concluded that the duct with a higher surface roughness will have a better heat transfer performance. Non-dimensional expressions for the determination of the heat transfer coefficient of the triangular ducts with different apex angles and surface roughnesses were also developed. Received on 15 December 1997     

Experimental study on heat transfer of thermally developing and developed, turbulent, horizontal pipe flow of dilute air-solids suspensions

Heat transfer characteristics of a turbulent, dilute air-solids suspension flow in thermally developing/developed regions were experimentally studied, using a uniformly heated, horizontal 54.5 mm-ID pipe and 43-μm-diameter glass beads. The local heat transfer was measured at 27 locations from the inlet to 120-dia downstream of the heated section over a range of Reynolds numbers 3×10⁴−1.2×10⁵ and solids loading ratio 0–3, and the fully developed profiles of air velocity/temperature and particle mass flux were measured at a location 140-dia downstream of the heated section using specially designed probes, inserted into the suspension flow. The effects of the Reynolds number, solids loading ratio, and azimuthal/longitudinal locations on the heat transfer characteristics and their interactions are discussed through comparison of the present results with the data obtained by other investigators. Received on 14 October 1996     

Experimental study of air natural convection on metallic foam-sintered plate

The natural convection on metallic foam-sintered plate at different inclination angles was experimentally studied. Seven copper foam samples with different pore densities (10–40 pore per inch), porosities (0.90–0.95), and aspect ratios (the ratio of foam thickness to sample length, 0.1–0.5) were measured at inclination angles of 0° (vertical orientation), 15°, 30°, 45°, 60°, 75°, 90° (horizontal orientation). The heat conduction and natural convection inside the foam both contributed to the total heat transfer. Although, the form and viscous drag, which are influenced by permeability and viscous friction in the thermal boundary layer respectively, tend to suppress the natural convection, the heat transfer was finally enhanced by the foam sintered surface due to large surface area extension. Optimum inclination range 60–75° corresponding to maximum average Nu number was found in the heat flux range of 600–1800 W/m². The sintered foam surface with lower porosity and pore density was recommended for heat transfer enhancement. Particularly, the sample with porosity 0.9, pore density of 10 PPI, aspect ratio of 0.5 offered the highest average Nu number among the studied samples. An empirical correlation for modified Nusselt number at isoflux boundary condition considering the foam morphology parameter and inclination angle was proposed within deviation ±15% between the correlation and the experimental data.     

Buoyancy and cross flow effects on heat transfer of multiple impinging slot air jets cooling a flat plate at different orientations

The present article reports on heat transfer characteristics associated with multiple laminar impinging air jet cooling a hot flat plat at different orientations. The work aims to study the interactions of the effects of cross flow, buoyancy induced flow, orientation of the hot surface with respect to gravity, Reynolds numbers and Rayleigh numbers on heat transfer characteristics. Experiments have been carried out for different values of jet Reynolds number, Rayleigh number and cross flow strength and at different orientations of the air jet with respect to the target hot plate. In general, the effective cooling of the plate has been observed to be increased with increasing Reynolds number and Rayleigh number. The results concluded that the hot surface orientation is important for optimum performance in practical applications. It was found that for Re ≥ 400 and Ra ≥ 10,000 (these ranges give 0.0142 ≤ Ri ≤ 1.59 the Nusselt number is independent on the hot surface orientation. However, for Re ≤ 300 and Ra ≥ 100,000 (these ranges give 1.59 ≤ Ri ≤ 42.85): (i) the Nusselt number for horizontal orientation with hot surface facing down is less that that of vertical orientation and that of horizontal orientation with hot surface facing up, and (ii) the Nusselt number of vertical orientation is approximately the same as that of horizontal orientation with hot surface facing up. For all surfaces orientations and for the entire ranges of Re and Ra, it was found that increasing the cross flow strength decreases the effective cooling of the surface.     

Convective heat transfer characteristics of laminar pulsating pipe air flow

 Heat transfer characteristics to laminar pulsating pipe flow under different conditions of Reynolds number and pulsation frequency were experimentally investigated. The tube wall of uniform heat flux condition was considered. Reynolds number was varied from 780 to 1987 while the frequency of pulsation ranged from 1 to 29.5 Hz. The results showed that the relative mean Nusselt number is strongly affected by pulsation frequency while it is slightly affected by Reynolds number. The results showed enhancements in the relative mean Nusselt number. In the frequency range of 1–4 Hz, an enhancement up to 30% (at Reynolds number of 1366 and pulsation frequency of 1.4 Hz) was obtained. In the frequency range of 17–25 Hz, an enhancement up to 9% (at Reynolds number of 1366 and pulsation frequency of 17.5 Hz) was indicated. The rate of enhancement of the relative mean Nusselt number decreased as pulsation frequency increased or as Reynolds number increased. A reduction in relative mean Nusselt number occurred outside these ranges of pulsation frequencies. A reduction in relative mean Nusselt number up to 40% for pulsation frequency range of 4.1–17 Hz and a reduction up to 20% for pulsation frequency range of 25–29.5 Hz for Reynolds numbers range of 780–1987 were considered. This reduction is directly proportional to the pulsation frequency. Empirical dimensionless equations have been developed for the relative mean Nusselt number that related to Reynolds number (750 < Re < 2000) and the dimensionless frequency (3<Ω<18) with about 10% rms. Received on 16 May 2000 / Published online: 29 November 2001     

Heat transfer studies of the oblique impingement of round jets upon a curved surface

 The effect of jet inclination of the local heat transfer under an obliquely impinging round air jet striking on isothermal circular cylinder is experimentally investigated. The circumferential heat transfer distribution as well as axial Nusselt number is measured. The considered parameters are jet Reynolds number in range of 3800–40,000, and jet inclination angle, ranging from 90 to 20. The experiments are carried out for nozzle sizes, d=3, 5 and 7 mm, and separation distance from 7 to 30 of the nozzle diameter. The output results indicated that the point of maximum heat transfer along the x-axis is shifted upstream and the local heat transfer distribution changed as a function of jet inclination. The magnitude of the shift was found to be significantly higher than that observe for a flat plate. The increasing inclination caused increasing asymmetry around the point of maximum heat transfer, with the upstream side of heat transfer profile dropping off more rapidly than the downstream side. Correlations of both the magnitude and shift of maximum heat transfer point are presented. The surface average heat transfer rate is calculated and compared with the normal impingement. Received on 5 June 2000 / Published online: 29 November 2001     

Experimental investigation of natural convection heat transfer in horizontal and inclined annular fluid layers

In the present study, an experimental investigation of heat transfer and fluid flow characteristics of buoyancy-driven flow in horizontal and inclined annuli bounded by concentric tubes has been carried out. The annulus inner surface is maintained at high temperature by applying heat flux to the inner tube while the annulus outer surface is maintained at low temperature by circulating cooling water at high mass flow rate around the outer tube. The experiments were carried out at a wide range of Rayleigh number (5 × 10⁴ < Ra < 5 × 10⁵) for different annulus gap widths (L/D _o = 0.23, 0.3, and 0.37) and different inclination of the annulus (α = 0°, 30° and 60°). The results showed that: (1) increasing the annulus gap width strongly increases the heat transfer rate, (2) the heat transfer rate slightly decreases with increasing the inclination of the annulus from the horizontal, and (3) increasing Ra increases the heat transfer rate for any L/D _o and at any inclination. Correlations of the heat transfer enhancement due to buoyancy driven flow in an annulus has been developed in terms of Ra, L/D _o and α. The prediction of the correlation has been compared with the present and previous data and fair agreement was found.     

Investigation of the different base fluid effects on the nanofluids heat transfer and pressure drop

A numerical study of laminar forced convective flows of three different nanofluids through a horizontal circular tube with a constant heat flux condition has been performed. The effect of Al₂O₃ volume concentration 0 ≤ φ ≤ 0.09 in the pure water, water-ethylene glycol mixture and pure ethylene glycol as base fluids, and Reynolds number of 100 ≤ Re ≤ 2,000 for different power inputs in the range of 10 ≤ Q(W) ≤ 400 have been investigated. In this study, all of the nanofluid properties are temperature and nanoparticle volume concentration dependent. The governing equations have been solved using finite volume approach with the SIMPLER algorithm. The results indicate an increase in the averaged heat transfer coefficient with increasing the mass of ethylene glycol in the water base fluid, solid concentration and Reynolds number. From the investigations it can be inferred that, the pressure drop and pumping power in the nanofluids at low solid volumetric concentration (φ < 3%) is approximately the same as in the pure base fluid in the various Reynolds numbers, but the higher solid nanoparticle volume concentration causes a penalty drop in the pressure. Moreover, this study shows it is possible to achieve a higher heat transfer rate with lower wall shear stress with the use of proper nanofluids.     

Numerical study of simultaneous natural convection heat transfer from both surfaces of a uniformly heated thin plate with arbitrary inclination

 Numerical studies were conducted to investigate the natural convection heat transfer around a uniformly heated thin plate with arbitrary inclination in an infinite space. The numerical approach was based on the finite volume technique with a nonstaggered grid arrangement. For handling the pressure–velocity coupling the SIMPLE-algorithm was used. QUICK scheme and first order upwind scheme were employed for discretization of the momentum and energy convective terms respectively. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 4.8×10⁶ to 1.87×10⁸. Local and average heat transfer characteristics were compared with regarding to the inclination angle. The empirical expressions for local and average Nusselt number were correlated. It has been found that for inclination angle less than 10^∘, the flow and heat transfer characteristics are complicated and the average Nusselt number can not be correlated by one equation while for inclination angle larger than 10^∘, the average Nusselt number can be correlated into an elegant correlation. Received on 18 April 2001 / Published online: 29 November 2001