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.     

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.     

A mixed convection in a reciprocating $$\Uppi$$ shape channel with opposite direction of gravity and inlet cooling fluids

A numerical study is executed to investigate heat transfer mechanisms of a reciprocating channel cooled by fluids. The problem of the reciprocating piston is a moving boundary problem, and the Finite Element Method and arbitrary Largragian–Eulerian Kinematics method are then utilized. Due to the high temperature of the channel, a mixed convection is taken into consideration for simulating a more realistic situation. Directions of inlet cooling fluids and gravity are opposite. Concerning important parameters of the Reynolds number and Grashof number, reciprocating frequency and amplitude are examined. Thermal stratification layers which are found firmly on the top surface are deeply dependent on the magnitude of Gr/Re ² ratio which directly affects the heat transfer mechanisms.     

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     

Mixed convection cooling of a heated circular cylinder by laminar upward-directed slot jet impingement

An experimental and numerical study has been carried out to investigate the heat transfer characteristics of a horizontal circular cylinder exposed to a slot jet impingement of air. A square-edged nozzle is mounted parallel with the cylinder axis and jet flow impinges on the bottom of the cylinder. The study is focused on low Reynolds numbers ranging from 120 to 1,210, Grashof numbers up to Gr = 10Re ² and slot-to-cylinder spacing from 2 to 8 of the slot width. The flow field is greatly influenced by the slot exit velocity and the buoyancy force due to density change. A Mach–Zehnder Interferometer is used for measurement of local Nusselt number around the cylinder at 10° interval. It is observed that the average Nusselt number decreases with increasing the jet spacing and increases with rising the Reynolds number. A finite volume method utilizing a curvilinear coordinate transformation is used for numerical modeling. The numerical results show good agreement with the experimental results. The flow and thermal field are seen to be stable and symmetric around the cylinder over the range of parameters studied.     

A convective weakly viscoelastic rotating flow with pressure Neumann condition

The objective of this work is to investigate through the numeric simulation, the effects of the weakly viscoelastic flow within a rotating rectangular duct subject to a buoyancy force due to the heating of one of the walls of the duct. A direct velocity–pressure algorithm in primitive variables with a Neumann condition for the pressure is employed. The spatial discretization is made with finite central differences on a staggered grid. The pressure field is directly updated without any iteration. Numerical simulations were done for several Weissemberg numbers (We) and Grashof numbers (Gr) . The numerical results show that for high Weissemberg numbers (We>7.4 × 10^?5) and for ducts with aspect ratio 2:1 and 8:1, the secondary flow is restabilized with a stretched double vortex configuration. It is also observed that when the Grashof number is increased (Gr>17 × 10^?4) , the buoyancy force neutralizes the effects of the Coriolis force for ducts with aspect ratio 8:1. Copyright © 2008 John Wiley & Sons, Ltd.     

Enhanced heat transfer performances of molten salt mixed convection in a vertical annular duct

The mixed convection heat transfer of upward molten salt flow in a vertical annular duct is experimentally and numerically studied. The heat transfer performances of mixed convection are measured under Reynolds number 2,500–12,000 and inlet temperature 300–400 °C, and Nusselt number of molten salt flow with cooled inner wall monotonically increases with buoyancy number. The mixed convection is further simulated by low-Reynolds number k-ε model and variable properties, and the heat transfer tendency from numerical results agrees with that from experiments. At low Reynolds number, the natural convection plays more important role in the mixed convection. As the buoyancy number rises, the thickness of flow boundary layer near the inner wall increases, while the effective thermal conductivity remarkably rises, so the enhanced heat transfer of mixed convection is mainly affected by the effective thermal conductivity due to turbulent diffusion.     

Unsteady natural convection in an enclosure with vertical wavy walls

In this paper, unsteady heat transfer and fluid flow characteristics in an enclosure are investigated. The enclosure consists of two vertical wavy and two horizontal straight walls. The top and the bottom walls are considered adiabatic. Two wavy walls are kept isothermal and their boundaries are approximated by a cosine function. Governing equations including continuity, momentum and energy were discretized using the finite-volume method and solved by SIMPLE method in curvilinear coordinate. Simulation was carried out for a range of Grashof number Gr = 10³–10⁶, Prandtl number Pr = 0.5–4.0, wave ratio A (defined by amplitude/wavelength) 0.0–0.35 and aspect ratio W (defined by average width/wavelength) 0.5–1.0. Streamlines and isothermal lines are presented to corresponding flow and thermal fields. Local and average Nusselt number distributions are presented. The obtained results are in good agreement with available numerical and experimental data.     

Experimental investigation of flow and heat transfer in rectangular cross-sectioned duct with baffles mounted on the bottom surface with different inclination angles

In this study, steady-state forced convection heat transfer and pressure drop characteristics in a horizontal rectangular cross-sectioned duct, baffles mounted on the bottom surface with different inclination angles were investigated experimentally in the Reynolds number range from 1 × 10³ to 1 × 10⁴. The study was performed under turbulent flow conditions. Effects of different baffle inclination angles on flow and heat transfer were studied. Results are also presented in terms of thermal enhancement factor. It is observed that increasing in baffle inclination angle enhances the heat transfer and causes an increase in pressure drop in the duct.     

Combined forced and free convective flow of water at 4°C past a semi-infinite vertical plate

Effects of buoyancy forces on forced and free convective flow of water at 4°C past a semi-infinite vertical plate at constant temperature are studied. Flow is assumed to be vertically upwards. Similarity solutions are derived and the resulting equations are solved numerically on a computer. Velocity and temperature profiles are shown graphically and numerical values of the skin friction and the rate of heat transfer are entered in tables. It is observed that the skin friction and the Nusselt number increase with increasing Gr/Re², where Gr is the Grashof number and Re is the Reynolds number     

Effect of water density inversion on the plane-parallel flow and heat transfer in a channel of constant width

The results of a numerical study of the effect of cold-water density inversion (Prandtl number Pr=11.59) on the flow and heat transfer in a horizontal plane-parallel channel with isothermal top and bottom walls are presented. The calculations were performed for the Grashof number Gr=3·10⁴, the Reynolds number Re=10, and the channel segment length-to-height ratiol/d=40. The wall temperature was so varied that the temperature difference between the top and bottom walls remained constant. Surgut. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 72–78, January–February, 2000.     

An experimental and three-dimensional numerical study on the convective heat transfer inside a trapezoidal duct under constant wall temperature

In this study, steady-state forced convection heat transfer and pressure drop characteristics for hydrodynamically fully developed thermally developing three-dimensional turbulent flow in a horizontal smooth trapezoidal duct with corner angle of 75° and hydraulic diameter of 0.043 m were both experimentally and numerically investigated in the Reynolds number range from 2.6 × 10³ to 67 × 10³ for isothermal conditions. Results have shown that there is a good agreement between the present experimental and numerical results.     

Transient natural convection in horizontal cylinders with constant cooling rate

Transient natural convection in horizontal cylinders with wall temperature decreasing at a constant rate is approached by a numerical method. Numerical solutions are obtained for Pr=0.7, 10, 100 and a range of modified Grashof numbers Gr_a=10³ 10⁹. The time-dependent flow and temperature fields, local and overall heat transfer rates are presented. For quasi-steady state, a generalized correlation equation for Nusselt number valid for Pr 0.7 and GrPr <>⁷ is developed.     

Natural convection from a vertical cylinder in a thermally stratified porous medium

The problem of non-Darcy natural convection adjacent to a vertical cylinder embedded in a thermally stratified porous medium has been analyzed. Nonsimilarity solutions are obtained for the case that the ambient temperature increases linearly with height of the cylinder. A generalized flow model was used in the present study to include the effects of the macroscopic viscous term and the microscopic inertial force. Also, the thermal dispersion effect is considered in the energy equation. Thus, the main aim of this work is to examine the effects of thermal stratification and non-Darcy flow phenomena on the free convection flow and heat transfer characteristics. It was found that the present problem depends on six parameters, namely, the local thermal stratification parameter ξ, the boundary effect parameter Bp, the modified Grashof number Gr^*, wall temperature exponent m, the curvature parameter ω, and the modified Rayleigh number based on pore diameter Ra _d . The impacts of these governing parameters on the local heat transfer parameter are discussed in great detail. Also, representative velocity and temperature profiles are presented at selected values of the thermal stratification parameter. In general, the local heat transfer parameter is increased with increasing the values of m, ω, and Ra _d ; while it is decreased with increasing the values of ξ, Bp, and Gr^*. Received on 19 May 1998     

Direct numerical simulation of turbulent heat transfer in annuli: Effect of heat flux ratio

Fully developed turbulent flow and heat transfer in a concentric annular duct is investigated for the first time by using a direct numerical simulation (DNS) with isoflux conditions imposed at both walls. The Reynolds number based on the half-width between inner and outer walls, δ=(r₂-r₁)/2, and the laminar maximum velocity is Re_δ=3500. A Prandtl number Pr=0.71 and a radius ratio r^*=0.1 were retained. The main objective of this work is to examine the effect of the heat flux density ratio, q^*=q₁/q₂, on different thermal statistics (mean temperature profiles, root mean square (rms) of temperature fluctuations, turbulent heat fluxes, heat transfer, etc.). To validate the present DNS calculations, predictions of the flow and thermal fields with q^*=1 are compared to results recently reported in the archival literature. A good agreement with available DNS data is shown. The effect of heat flux ratio q^* on turbulent thermal statistics in annular duct with arbitrarily prescribed heat flux is discussed then. This investigation highlights that heat flux ratio has a marked influence on the thermal field. When q^* varies from 0 to 0.01, the rms of temperature fluctuations and the turbulent heat fluxes are more intense near the outer wall while changes in q^* from 1 to 100, lead to opposite trends.     

Mixed convection from upward flow of hot air to a cooled vertical pipe

An experimental study had been carried out to investigate the buoyancy-opposed mixed convection from an upward flow of hot air to a vertical pipe with a cooled surface. The investigation covered a wide range of flow regime, ranging from the “free convection significant” to the “forced convection significant” conditions. Reynolds number of the flow extended from 966 to 14780, whereas the Buoyancy parameter, Ω [=Gr_d/(Re_d)²], varied from 0.008 to 2.77. A steady stream of hot air at a moderate pressure and a Prandtl number of 0.707 was arranged to flow upward through a vertical steel pipe, whose external wall was cooled uniformly by ambient air at 20°C. Test section of the vertical pipe was 1625 mm long with an internal diameter of 156 mm and an external diameter of 166 mm. Air temperature at inlet of the test section was varied from 40°C to 70°C. Both radial temperature and velocity profiles of the airflow were measured at inlet and exit of the test section respectively. Temperatures along the pipe wall were also measured. Non-dimensional expression for the prediction of the average heat transfer coefficient of the mixed convection from an upward flow of hot air to a vertical pipe with a cooled surface was developed from the experimental results. Convection heat transfer was found to impair when the flow is laminar and was enhanced for turbulent flow condition. Received on 20 July 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.     

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     

Experimental study on the forced convective flow in a channel with heated blocks in tandem

This study experimentally examines the forced convective flow over two sequentially heated blocks mounted on one principal wall of a channel. The experiments, involving mass transfer, were carried out via the naphthalene sublimation technique (NST). By virtue of the analogy between heat and mass transfer, the results can then be converted to determine the heat transfer. In the experiments, the block spacings were set at 2, 4, 6, 8, 12, 16, and 22 and the Reynolds numbers were set at 1300 and 10⁴ which correspond to the laminar and the turbulent convective flow cases, respectively. Results show that the Sherwood number increases or decreases monotonically along the block surfaces in the laminar convection cases; while the hump and sharp increase in the Sherwood number can be found in the turbulent convection cases. This is attributed to the reattachment of the separating bubble and the flow impingement, respectively. Comparison between the experimental and numerical results is made and the effect of the block spacing on heat transfer is discussed.     

Influence of variable permeability on combined free and forced convection flow past a semi-infinite vertical plate in a saturated porous medium

Combined free and forced convection flow of viscous incompressible fluid past a semi-infinite vertical plate embedded in a porous medium incorporating the variation of permeability and thermal conductivity are studied. Similarity solutions are obtained, for two cases namely uniform permeability (UP) and variable permeability (VP). Velocity and temperature profiles are shown graphically and the numerical values of the skin friction and the rate of heat transfer are entered in tabular form. The effects of the parameters Gr/Re ² (Gr – Grashof number, Re – the Reynolds number), (coefficient of viscositys of the fluid and porous medium), (the Darcy number), * (ratio of thermal conductivity of the solid to the liquid), Pr (the Prandtl number) and E (the Eckert number) on the flow field are discussed.