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.     

Forced convection from a straight elliptical tube

The paper deals with the problem of two-dimensional laminar forced convection heat transfer from a straight isothermal tube of elliptic cross-section placed in a uniform stream. The study is based on numerical solutions of the conservation equations of mass, momentum, and energy which covers the entire flow domain including the wake region. The parameters influencing the heat transfer process are essentially the Reynolds number, Re, the tube geometry represented by its minor to major axis ratio, Ar, and the angle of inclination, λ. The study focuses on the effect of Re, Ar, and λ on the heat transfer process in the range of Re from 20 to 500. The study reveals that the rate of heat transfer reaches its maximum when λ=0^∘ while the minimum occurs when λ=90^∘. The results also show that smaller axis ratio gives higher heat transfer rate when λ=0^∘. The local Nusselt number and surface vorticity distributions are plotted for a number of cases and the effect of vortex shedding on the overall rate of heat transfer is briefly discussed. Received on 20 September, 1997     

Interaction of turbulent natural convection and surface thermal radiation in inclined square enclosures

Two-dimensional numerical studies of flow and temperature fields for turbulent natural convection and surface radiation in inclined differentially heated enclosures are performed. Investigations are carried out over a wide range of Rayleigh numbers from 10⁸ to 10¹², with the angle of inclination varying between 0° and 90°. Turbulence is modeled with a novel variant of the k–ε closure model. The predicted results are validated against experimental and numerical results reported in literature. The effect of the inclination of the enclosure on pure turbulent natural convection and the latter’s interaction with surface radiation are brought out. Profiles of turbulent kinetic energy and effective viscosity are studied to observe the net effect on the intensity of turbulence caused by the interaction of natural convection and surface radiation. The variations of local Nusselt number and average Nusselt number are presented for various inclination angles. Marked change in the convective Nusselt number is found with the orientation of enclosure. Also analyzed is the influence of change in emissivity on the flow and heat transfer. A correlation relevant to practical applications in the form of average Nusselt number, as a function of Rayleigh number, Ra, radiation convection parameter, N _RC and inclination angle of the enclosure, φ is proposed.     

Experimental investigation of mixed convection heat transfer in a horizontal and inclined rectangular channel

 Mixed convection heat transfer in rectangular channels has been investigated experimentally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Experiments were conducted for Pr=0.7, aspect ratios AR=5 and 10, inclination angles 0° ≤ θ ≤ 30°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr*=7.0 × 10⁵ to 4.0 × 10⁷. From the parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results related to the buoyancy affected secondary flow and the onset of instability have been discussed. Some of the results obtained from the experimental measurements are also compared with the literature, and a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number and increasing aspect ratio. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle. Received on 19 March 2001 / Published online: 29 November 2001     

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     

Heat transfer from a surface fitted with rectangular blocks at different orientation angle

 An experimental investigation was carried out to study the enhancement of the heat transfer from a heated flat plate fitted with rectangular blocks of 1 × 2 × 2 cm³ dimensions in a channel flow as a function of Reynolds number (Re_h), spacing (S _y ) of blocks in the flow direction, and the block orientation angle (α) with respect to the main flow direction. The experiments were performed in a channel of 18 cm width and 10 cm height, with air as the working fluid. For fixed S _x =3.81 cm, which is the space between the blocks in transverse to the flow direction, the experimental ranges of the parameters were S _y =3.33–4.33 cm, α=0–45°, Re_h=7625–31550 based on the hydraulic diameter and the average velocity at the beginning of the test section in the channel. Correlations for Nusselt number were developed, and the ratios of heat transfer with blocks to those with no blocks were given. The results indicated that the heat transfer could be enhanced or reduced depending on the spacing between blocks, and the block orientation angle. The maximum heat transfer rate was obtained at the orientation angle of 45°. Received on 13 December 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 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.     

A correlation for free convection heat transfer from vertical wavy surfaces

Free convection heat transfer along an isothermal vertical wavy surface was studied experimentally and numerically. A Mach-Zehnder Interferometer was used in the experiment to determine the local heat transfer coefficients. Experiments were done for three different amplitude–wavelength ratios of α = 0.05, 0.1, 0.2 and the Rayleigh numbers ranging from Ra _l = 2.9 × 10⁵ to 5.8 × 10⁵. A finite-volume based code was developed to verify the experimental study and obtain the results for all the amplitude–wavelength ratios between α = 0 to 0.2. It is found that the numerical results agree well with the experimental data. Results indicate that the frequency of the local heat transfer rate is the same as that of the wavy surface. The average heat transfer coefficient decreases as the amplitude–wavelength ratio increases and there is a significant difference between the average heat transfer coefficients of the surface with α = 0.2 and those surfaces with α = 0.05 and 0.1. The experimental data are correlated with a single equation which gives the local Nusselt number along the wavy surface as a function of the amplitude–wavelength ratio and the Rayleigh number.     

Numerical simulation of the effects of plate separation and inclination on heat transfer in buoyancy driven open channels

 Effects of plate separation and inclination on free convection between asymmetrically heated vertical and inclined parallel plates have been simulated. The upper isothermally heated plate is facing downwards, the lower plate is passively heated by the upper one. The plate inclinations are chosen to be 0^∘, 30^∘, 45^∘ with respect to vertical position. Three-dimensional laminar numerical simulations are obtained by solving the full elliptic governing equations using a commercial finite volume based computational fluid dynamics (CFD) code. Comparisons of computational results with experiments and data from the literature are made in terms of relevant dimensionless numbers. It was observed that plate spacing and inclination influence the overall heat transfer rate. Received on 3 November 1998     

Numerical investigation of turbulent flow,heat transfer and entropy generation in a helical coiled tube with larger curvature ratio

Three-dimensional turbulent forced convective heat transfer and flow characteristics, and the non-dimensional entropy generation number in a helical coiled tube subjected to uniform wall temperature are simulated using the k–ε standard turbulence model. A finite volume method is employed to solve the governing equations. The effects of Reynolds number, curvature ratio, and coil pitch on the average friction factor and Nusselt number are discussed. The results presented in this paper cover a Reynolds number range of 2 × 10⁴ to 6 × 10⁴, a pitch range of 0.1–0.2 and a curvature ratio range of 0.1–0.3. The results show that the coil pitch, curvature ratio and Reynolds number have different effects on the average friction factor and Nusselt number at different cross-sections. In addition, the flow and heat transfer characteristics in a helical coiled tube with a larger curvature ratio for turbulent flow are different from that of smaller curvature ratio for laminar and turbulent flow in certain ways. Some new features that are not obtained in previous researches are revealed. Moreover, the effects of Reynolds number, curvature ratio, and coil pitch on the non-dimensional entropy generation number of turbulent forced convection in a helical coiled tube are also discussed.     

Numerical simulation of fully developed turbulent flow and heat transfer in annular-sector ducts

 The mixing length theory is employed to simulate the fully developed turbulent heat transfer in annular-sector ducts with five apex angles (θ₀=18,20,24,30,40^∘) and four radius ratios (R _o/R _i=2,3,4,5). The Reynolds number range is 10⁴10⁵. The numerical results agree well with an available correlation which was obtained in following parameter range: θ₀=18,20,24,30,40^∘, R _o/R _i=4 and Re=10⁴5×10⁴. The present work demonstrates that the application range of the correlation can be much extended. Apart from the mixing length theory, the kɛ model with wall function and the Reynolds stress model are also employed. None of the friction factor results predicted by the three models agrees well with the test data. For the heat transfer prediction the mixing length theory seems the best for the cases studied. Received on 17 July 2000 / Published online: 29 November 2001     

Numerical and experimental studies of natural convective heat transfer from vertical and inclined narrow isothermal flat plates

Natural convective heat transfer from an isothermal narrow flat plate embedded in a plane adiabatic surface and inclined at moderate positive and negative angles to the vertical has been numerically and experimentally studied. The solution has the Rayleigh number, the dimensionless plate width, the angle of inclination, and the Prandtl number as parameters. Attention was restricted to a Prandtl number of 0.7. The numerical results have been obtained for Rayleigh numbers between 10³ and 10⁷ for dimensionless plate widths of between 0.3 and 1.2 and for angles of inclination between +45° and −45°. In the experimental study, results have been obtained for Rayleigh numbers between 4 × 10² and 10⁵ for dimensionless plate widths of 0.4 and 2.5 and for angles of inclination between +45° and −45° to the vertical. Empirical equations for the heat transfer rate have been derived.     

Turbulent free convection in a vertical converging channel

This paper presents the results of experimental and numerical investigations of the problem of turbulent natural convection in a converging-plate vertical channel. The channel has two isothermally heated inclined walls and two adiabatic vertical side walls. The parameters involved in this study are the channel geometry represented by the channel width at exit, the inclination of the heated walls and the temperature difference between the heated walls and the ambient. The investigation covered modified Rayleigh numbers up to 10⁸ in the computational study and up to 9.3 × 10⁶ in the experimental work. The experimental measurements focused on the velocity field and were carried out using a PIV system and included measurements of the mean velocity profiles as well as the root-mean-square velocity and shear stress profiles. The experiments were conducted for an inclination angle of 30°, a gap width of 10 mm and two temperature differences (∆T=25.4°C and 49.8°C). The velocity profiles in the lower part of the channel indicated the presence of two distinct layers. The first layer is adjacent to the heated plate and driven by buoyancy forces while the second layer extends from the point of maximum velocity to the channel center plane and driven mainly by shear forces. The velocity profile at the upper portion of the channel has shown the merging of the two boundary layers growing over the two heated walls. The measured values of the Reynolds shear stress and root mean square of the horizontal and vertical velocity fluctuation components have reached their maximum near the wall while having smaller values in the core region. The computational results have shown that the average Nusselt number increases approximately linearly with the increase of the modified Rayleigh number when plotted on log–log scale. The variation of the local Nusselt number indicated infinite values at the channel inlet (leading edge effect) and high values at the channel exit (trailing edge effect). For a fixed value of the top channel opening, the increase of the inclination angle tended to reduce flow velocity at the inlet section while changing the flow structure near the heated plates in such a way to create boundary-layer type flow. The maximum value of the average Nusselt number occurs when θ = 0 and decreases with the increase of the inclination angle. On the other hand, the increase of the channel width at exit for the same inclination angle caused a monotonic increase in the flow velocity at the channel inlet.     

Laminar mixed convection in horizontal concentric annuli with non-uniform circumferential heating

 Steady, laminar, mixed convection in the fully developed region of horizontal concentric annuli has been investigated numerically for the case of non-uniform circumferential heating. Two heating conditions were studied, one in which a 180^∘ arc encompassing the top half of inner surface of the inner cylinder is uniformly heated while the bottom half is kept insulated, and the other in which the heated and the insulated surfaces were reversed. The fluid flow and heat transfer characteristics were found to be affected by the heating conditions. For the investigated range of the governing buoyancy parameter, the modified Grashof number (Gr^*), it was found that bottom heating arrangement gives rise to a vigorous secondary flow, with the result that the average Nusselt numbers are much higher than those for pure forced convection. On the other hand, the local Nusselt numbers are nearly circumferentially uniform. In the case of top heating arrangement, a less vigorous secondary flow is induced because of temperature stratification, with average Nusselt numbers that are substantially lower than those for bottom heating and with large circumferential variation of the local Nusselt number. Received on 15 March 2000     

Experimental and numerical study of developing turbulent flow and heat transfer in convergent/divergent square ducts

 The work reported in this paper is a systematic experimental and numerical study of friction and heat transfer characteristics of divergent/convergent square ducts with an inclination angle of 1^∘ in the two direction at cross section. The ratio of duct length to average hydraulic diameter is 10. For the comparison purpose, measurement and simulation are also conducted for a square duct with constant cross section area, which equals to the average cross section area of the convergent/divergent duct. In the numerical simulation the flow is modeled as being three-dimensional and fully elliptic by using the body-fitted finite volume method and the kɛ turbulence model. The uniform heat flux boundary condition is specified to simulate the electrical heating used in the experiments. The heat transfer performance of the divergent/convergent ducts is compared with the duct with uniform cross section under three constraints (identical mass flow rate, pumping power and pressure drop). The agreement of the experimental and numerical results is quite good except at the duct inlet. Results show that for the three ducts studied there is a weak secondary flow at the cross section, and the circumference distribution of the local heat transfer coefficient is not uniform, with an appreciable reduction in the four corner regions. In addition, the acceleration/deceleration caused by the cross section variation has a profound effect on the turbulent heat transfer: compared with the duct of constant cross section area, the divergent duct generally shows enhanced heat transfer behavior, while the convergent duct has an appreciable reduction in heat transfer performance. Received on 18 September 2000 / Published online: 29 November 2001     

Fluid flow and heat transfer characteristics for a square prism (blockage ratio = 0.1) placed inside a wind tunnel

Experimental investigations in fluid flow and heat transfer have been carried out to study the effect of wall proximity due to flow separation around a square prism at Reynolds number 2.6 × 10⁴, blockage ratio 0.1, different height-ratios and various angles of attack. The static pressure distribution has been measured on all faces of the square prism. The results have been presented in the form of pressure coefficient, drag coefficient for various height-ratios. The pressure distribution shows positive values on the front face whereas on the rear face negative values of the pressure coefficient have been observed. The positive pressure coefficient for different height-ratios does not vary too much but the negative values of pressure coefficient are higher for all points on the surface as the bluff body approaches towards the upper wall of the wind tunnel. The drag coefficient decreases with the increase in angle of attack as the height-ratio decreases. The maximum value of drag coefficient has been observed at an angle of attack nearly 50° for the square prism at all height-ratios. The heat transfer experiments have been carried out under constant heat flux condition. Heat transfer coefficient are determined from the measured wall temperature and ambient temperature and presented in the form of Nusselt number. Both local and average Nusselt numbers have been presented for various height-ratios. The variation of local Nusselt number has been shown with non-dimensional distance for different angles of attack. The variation of average Nusselt number has also been shown with different angles of attack. The local as well as average Nusselt number decreases as the height-ratio decreases for all non-dimensional distance and angle of attack, respectively, for the square prism. The average Nusselt number for the square prism varies with the angle of attack. But there is no definite angle of attack at which the value of average Nusselt number is either maximum or minimum.     

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.     

Natural Convection in a Cavity Filled with Porous Layers on the Top and Bottom Walls

Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10⁻¹ to 10⁻⁶, porosity values from 0.2 to 0.8, Rayleigh numbers from 10³ to 10⁷, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged. The interfacial stress jump coefficients β ₁ and β ₂ were varied from  −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles in the mid-width of the cavity are investigated.