Three-dimensional driven-cavity flows with a vertical temperature gradient

Numerical studies of three-dimensional flows in a cubical container with a stable vertical temperature stratification are carried out. Flows are driven by the top lid, which slides in its own plane at a constant speed. The top wall is maintained at a higher temperature than the bottom wall. The end walls and the side walls are thermally insulated. Numerical solutions are obtained over a wide range of physical parameters, i.e. 10² ≤ Re ≤ 2 × 10³, 0 ≤ Ri ≤ 10.0 and Pr = 0.71, where the mixed-convection parameter Ri Gr. Re⁻². Systematical comparison of the three-dimensional numerical solutions with the previously reported two-dimensional results illuminates the impact of thermal stratification on the three-dimensional flow characteristics. When Ri < O(1), the effect of the vertical temperature gradient is minor, and the flow structures are similar to those of the non-stratified fluid flows in a conventional lid-driven cavity flow. Fluids in the primary vortex are well mixed, and the temperature is fairly uniform in the main circulating region. When Ri ≥ O(1), the stable temperature distribution tends to suppress the vertical fluid motion. Much of the fluid motion takes place in the vicinity of the top sliding lid and the bulk of the cavity region is nearly stagnant. When Ri > O(1), the fluid motion exhibits vertically layered vortex structures. The Nusselt number is computed at the top and bottom wall, and this also illustrates the varying flow characteristics as Ri encompasses a broad range. Extensive numerical flow visualizations are conducted. Plots demonstrating the primary flows in the (x−y) plane and the secondary flows in the (y−z) plane are presented. These display the influences of Re and Ri on the basic character of the flow and the three-dimensional effects.     

Mass-transfer to a channel wall downstream of a cylinder

The electrochemical method is used to measure the mass-transfer to a channel wall downstream of a cylinder. For Reynolds numbers based on cylinder diameter Re > 50, the flow is unsteady, and the mass-transfer rate is a function of time. When 50 < Re < 200, the mass-transfer rate is periodic with a frequency in the range of 1–3 Hz. When the ratio of cylinder diameter d to channel height h is 0.25, the Strouhal number is measured to be 0.27±0.02, and when d/h = 0.51, the Strouhal number is 0.49±0.01. The average mass-transfer rate at various positions downstream of the cylinder is reported. Experiments are compared to two-dimensional numerical simulations. The simulated and experimental variations of Nusselt number with position and Re contain similar features, but exact agreement is not found.     

Turbulent natural convection in a porous square cavity computed with a macroscopic κ–ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ–ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Computations covered the range 10 < Ra_m < 10⁶ and 10⁻⁷ < Da  < 10⁻¹⁰ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m and for Ra_m less than a certain critical Rayleigh number, Ra_cr. This convergence of results as Ra_m decreases can be seen as a characterization of the laminarization phenomenon. For Ra_m values less than around 10⁴, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra_m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra_m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.     

Experimental study of mixed convection and pressure drop in helically dimpled tubes for laminar and transition flow

This paper presents the experimental results carried out in dimpled tubes for laminar and transition flows and completes a previous work of the authors focused on the turbulent region. It was observed that laminar flow heat transfer through horizontal dimpled tubes is produced in mixed convection, where Nusselt number depends on both the natural convection and the entry region. Employing water and ethylene glycol as test fluids, the following flow range was covered: x^*=10⁻⁴–10⁻² and Ra=10⁶–10⁸.

The experimental results of isothermal pressure drop for laminar flow showed dimpled tube friction factors between 10% and 30% higher than the smooth tube ones. Moreover, it was perceived that roughness accelerates transition to critical Reynolds numbers down to 1400. Correlations for the laminar friction factor f=f(Re,h/d) and for the critical Reynolds Re_crit=Re_crit(h/d) are proposed. The hydraulic behaviour of dimpled tubes was found to depend mainly on dimple height.

In mixed convection, high temperature differences in the cross section were measured and therefore heat transfer was evaluated by a circumferentially averaged Nusselt number. Experimenal correlations for the local and the fully developed Nusselt numbers and are given. Results showed that at low Rayleigh numbers, heat transfer is similar to the smooth tube one whereas at high Rayleigh, enhancement produced by dimpled tubes can be up to 30%.     

Acknowledgment

An experimental and numerical study has been carried out in order to investigate mixed and natural convection heat transfer in a two-dimensional enclosure. A discrete isothermal heat source is located at one of the vertical walls. Also, two ventilation ports are at the bottom and on top of the opposite wall. A forced flow condition was imposed by providing an inlet of air at the bottom port. A Mach–Zehnder interferometer was used to visualize the temperature field within the enclosure and to determine the local and average heat transfer characteristics of the heat source. Five heater positions on the vertical wall and different Rayleigh numbers (4.5 × 10⁵ to 1.15 × 10⁶) and Reynolds numbers (120 to 1600) were considered in the experiments. A finite volume code has been developed based on the SIMPLE algorithm and hybrid discretization scheme for the numerical study. It is observed that the interaction of natural convection with the forced flow leads to various flow fields depending on the Richardson number, Reynolds number and the heater position. Also, results show different trends for variation of the average Nusselt number with the heater position at low and high Reynolds numbers. An optimum position for the heat source, at which the maximum heat transfer is achieved, exists for high Reynolds numbers and has been found to be at the middle of the vertical wall.     

Analysis of mixed convection in a vertical porous layer using non-equilibrium model

The problem of two-dimensional steady mixed convection in a vertical porous layer is investigated numerically in the present paper using the thermally non-equilibrium model. The vertical porous layer is assumed to have a finite isothermally heated segment on one vertical wall which is otherwise adiabatic and the other vertical wall is cooled to a constant temperature. Non-dimensionalization of the governing equations results in four parameters for both aiding and opposing flows: (1) Ra, Rayleigh number (2) Pe, Péclet number (3) K_r, thermal conductivity ratio parameter, and (4) H, heat transfer coefficient parameter. The numerical results are presented for 0.01  H  100, 0.01  K_r  100, 0.01  Pe  100 and Ra = 10, 50 and 100. The results show that, the thermal equilibrium model cannot predict the average Nusselt number correctly for small values of H × K_r. In both the aiding and opposing flows, the total average Nusselt number is decreasing with increasing the heat transfer coefficient parameter at low values of Pe, while for high values of Pe, higher H will enhance the total heat transfer rate. Increasing the thermal conductivity ratio leads to increase in the total average Nusselt number. It is found also that the total average Nusselt number depends strongly on the thermal conductivity ratio parameter and depends slightly on the heat transfer coefficient parameter.     

Cost optimization of a conical electric heater

Electric heaters are used extensively in many industrial applications including air conditioning, water heating, and drying of crop and other materials. There are several interacting parameters that affect heater performance and contribute to its operating and manufacturing costs. The design parameters of interest included coil length, coil diameter, helix diameter, coil pitch, number of turns, coil emissivity, heater wall emissivity, applied voltage, air flow rate, air temperature at the heater outlet, insulation thickness, and the heater dimensions. An objective function for the heater cost was defined in terms of the total annual costs for energy usage and manufacturing. The manufacturing cost included the material cost of the heater, the cost of coating the heater coil, and the cost of insulating the heater. A detailed model describing the performance of a conical heater was utilized to evaluate and minimize the objective function. The optimization problem was completely defined by introducing fourteen inequality constraints, three equality constraints, and ten design variables. The univariate search was used to reduce the number of inequality constraints. The direct search and variable metric methods were used to optimize the objective function at different values of the applied power and air temperature at the heater outlet, leading to the same results. The optimization results indicate that the optimum heater design was found at the minimum values of the coil diameter, conical angle, coil emissivity, and the maximum value of coil temperature. The maximum operating temperature of the optimum heater design (a heater with a silver coated coil) is substantially lower than the maximum normal operating temperature so that longer life for the heating element is expected. The effect of varying the applied power on the objective function showed that as the applied power increases the objective function may increase or decrease, depending on the combined effect of increasing the coil length and heater efficiency and decreasing the insulation thickness. The effect of varying the air temperature at the heater outlet on the objective function indicated that as the air temperature increases the objective function increases. Copyright © 2005 John Wiley & Sons, Ltd.     

Conjugate heat transfer in open cavities with a discrete heater at its optimized position

In this article, we determined optimum position of a discrete heater by maximizing the conductance and then studied heat transfer and volume flow rate with the discrete heater at its optimum position in open cavities. Continuity, Navier–Stokes and energy equations are solved by finite difference-control volume numerical method. The relevant governing parameters were: the Rayleigh numbers from 10⁶ to 10¹², the Prandtl number, Pr = 0.7, the cavity aspect ratio, A = H/L from 0.5 to 2, the wall thickness l/L from 0.05 to 0.15, the heater size h/L from 0.15 to 0.6, and the conductivity ratio k_r from 1 to 50. We found that the global conductance is an increasing function of the Rayleigh number, the conductivity ratio, and a decreasing function of the wall thickness. Best thermal performance is obtained by positioning the discrete heater at off center and slightly closer to the bottom. The Nusselt number and the volume flow rate in and out the open cavity are an increasing function of the Rayleigh number and the wall thickness, and a decreasing function of the conductivity ratio. The Nusselt number is a decreasing function of the cavity aspect ratio and the volume flow rate is an increasing function of it.     

Natural convection in composite wall collectors with porous absorber

Steady natural convection heat transfer has been studied in a modified Trombe wall solar collector with a porous medium used as an absorber. The boundary conditions were: Two isothermal walls at different temperatures, two horizontal bounding adiabatic walls and either uniform or nonuniform heat generating porous layer with orifices. The aspect ratio A was from 5 to 10. The influence of orifice opening and position as well as the nonuniform heat generation within the porous medium have been studied in detail with the Darcy number varying from 10⁻⁸ to 10⁻². The results are presented in terms of practical parameters (θ, θ_max, q) as a function of Ra, Da and other nondimensional geometrical parameters. The isotherms and stream lines within the cavity are also produced. The overall results indicate that Da and geometrical parameters are the most important parameters affecting system performance.     

A theoretical study of laminar mixed convection from a horizontal cylinder in a cross stream

The problem of laminar mixed convection from a horizontal isothermal cylinder is considered. The free stream direction is assumed to be horizontal and perpendicular to the cylinder axis. The study is based on the solution of the full Navier-Stokes and energy equations for 2-dim. flow of a Boussinesq fluid. The free stream is assumed to start impulsively from rest and the velocity and thermal boundary layers are developed in time until reaching steady conditions. The investigation covered the ranges of Reynolds number 1 < Re < 40 and Grashof numbers up to Gr = 5 Re² while keeping Prandtl number at a constant value of 0.7. Comparison of results with previous experimental correlations shows a good agreement. The streamline and isotherm patterns are plotted and different aspects of the phenomenon are discussed.     

Free convection about a rectangular prismatic crystal growing from a solution

Sodium chlorate crystals growing from unstirred aqueous solutions were observed by schlieren techniques. Growth rate data were best correlated by Sh = 0.48 Ra^0.25 with finite interface kinetics and a characteristic length L equal to the crystal height plus the inverse reciprocal sum of the horizontal dimensions. The growth rate was slightly higher when the plume was laminar than when it was irregular. The horizontal growth rate was greater than the vertical growth rate, with the ratio tending to decrease with increasing plume instability. The threshold Grashof number for plume instability was greatly decreased with decreasing height for crystals with the same horizontal dimensions. The frequency of eddy emission was proportional to L⁻²Ra^0.8. The velocity of the eddies approached a constant value with increasing distance above the crystal surface, the terminal value being roughly proportional to Ra^1/2/L.     

Behavioral study of alumina nanoparticles in pool boiling heat transfer on a vertical surface

Experiments were carried out to investigate the pool boiling of alumina‐water nanofluid at 0.1 g/l to 0.5 g/l of distilled water, and the nucleate pool boiling heat transfer of pure water and nanofluid at different mass concentrations were compared at and above the atmospheric pressure. At atmospheric pressure, different concentrations of nanofluids display different degrees of deterioration in boiling heat transfer. The effect of pressure and concentration of nanoparticles revealed significant enhancement in heat flux and deterioration in pool boiling. The heat transfer coefficient of 0.5 g/l alumina‐water nanofluid was compared with pure water and clearly indicates deterioration. At all pressures the heat transfer coefficients of the nanofluid were lower than those of pure water. Experimental observation revealed particles coating over the heater surface and subsequent SEM inspection of the heater surface showed nanoparticles coating on the surface forming a porous layer. To substantiate the nanoparticle deposition and its effect on heat flux, investigation was done by measuring the surface roughness of the heater surface before and after the experiment. While SEM images of the heater surface revealed nanoparticle deposition, surface roughness of the heater surface confirmed it. Based on the experimental investigations it can be concluded that an optimum thickness of nanoparticles coating favors an increase in heat flux. Higher surface temperature due to the presence of nanoparticles coating results in the deterioration of boiling heat transfer. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20365     

Heat-transfer correlations for an immersed finned heat-exchanger coil transferring heat from a hot-water store

Natural-convection heat transfers, to a finned-tube heat-exchanger coil immersed in a hot-water store, have been investigated. Cold water was passed through the pipe of the heat-exchanger in order to extract heat rapidly from the hot water in the store. Natural convection currents in the stored water were created by buoyancy forces, which were induced by the temperature gradients that developed as a result of the heat-extraction process. A heat-transfer correlation in terms of Nusselt and Rayleigh numbers has been deduced in order to predict the natural convection heat-transfer coefficient on the outside surface of the heat exchanger. This correlation, which is valid for heat entering the fins, to within an accuracy of better than 4%, is: Nu=0·280 Ra^0·293 for 100 < Ra < 1500     

Heat transfer from a pulsed laminar impinging jet

A numerical investigation has been performed to study the effect of flow pulsations on time-averaged Nusselt number under a laminar impinging jet. The parameters considered are as follows: time-averaged jet Reynolds number (100 ≤ Re ≤ 1000), frequency of pulsation (1 ≤ f ≤ 20 Hz), and nozzle-to-target spacing (4 ≤ H/d ≤ 9). The combination of Re = 300, f = 5 Hz and H/d = 9 was found to give the best heat transfer performance. Interestingly, it was found that the onset of separation at the wall jet region of pulsating impinging jet is associated with the point of constant Nusselt number during the oscillation cycle. Downstream of the separation point in the wall jet region, the Nusselt number waveform fluctuates out of phase with the inlet velocity. Within one oscillation, large vortices existing during the minimum velocity state are broken into two smaller vortices when the flow is accelerated to reach the maximum velocity, after which the two vortices merge again when the flow decelerates back to the minimum velocity.     

Effects of slip length and hydraulic diameter on hydraulic entrance length of microchannels with superhydrophobic surfaces

This paper investigated effects of slip length and hydraulic diameter on the hydraulic entrance length of laminar flow in superhydrophobic microchannels. Numerical investigations were performed for square microchannels with Re ranging between 0.1 and 1000. It is found that superhydrophobic microchannels have a longer hydraulic entrance length than that of conventional ones by nearly 26.62% at a low Re. The dimensionless hydraulic entrance length slightly increases with the increasing slip length at approximately Re<10, and does not vary with the hydraulic diameter. A new correlation to predict the entrance length in square microchannels with different slip lengths was developed, which has a satisfying predictive performance with a mean absolute relative deviation of 5.69%. The results not only ascertain the flow characteristics of superhydrophobic microchannels, but also suggest that super hydrophobic microchannels have more significant advantages for heat transfer enhancement at a low Re.     

Development of a fan-stirred constant volume combustion chamber and turbulence measurement with PIV

A fan-stirred combustion chamber is deve-loped for spherically expanding flames, with P and T up to 10 bar and 473 K, respectively. Turbulence characteristics are estimated using particle image velocimetry (PIV) at different initial pressures (P = 0.5–5 bar), fan frequencies (ω = 0–2000 r/min), and impeller diameters (D = 100 and 114 mm). The flame propagation of methanol/air is investigated at different turbulence intensities (u′=0–1.77 m/s) and equivalence ratios (φ = 0.7–1.5). The results show that u′ is independent of P and proportional to ω, which can be up to 3.5 m/s at 2000 r/min. L_T is independent of P and performs a power regression with ω approximately. The turbulent field is homogeneous and isotropic in the central region of the chamber while the inertial subrange of spatial energy spectrum is more collapsed to –5/3 law at a high Re_T. Compared to laminar expanding flames, the morpho-logy of turbulent expanding flames is wrinkled and the wrinkles will be finer with the growth of turbulence intensity, consistent with the decline of the Taylor scale and the Kolmogorov scale. The determined S_L in the present study is in good agreement with that of previous literature. The S_L and S_T of methanol/air have a non-monotonic trend with φ while peak S_T is shifted to the richer side compared to S_L. This indicates that the newly built turbulent combustion chamber is reliable for further experimental study.     

Heat transfer enhancement in a tube using circular cross sectional rings separated from wall

A numerical study was undertaken for investigating the heat transfer enhancement in a tube with the circular cross sectional rings. The rings were inserted near the tube wall. Five different spacings between the rings were considered as p = d/2, p = d, p = 3d/2, p = 2d and p = 3d. Uniform heat flux was applied to the external surface of the tube and air was selected as working fluid. Numerical calculations were performed with FLUENT 6.1.22 code, in the range of Reynolds number 4475–43725. The results obtained from a smooth tube were compared with those from the studies in literature in order to validate the numerical method. Consequently, the variation of Nusselt number, friction factor and overall enhancement ratios for the tube with rings were presented and the best overall enhancement of 18% was achieved for Re = 15,600 for which the spacing between the rings is 3d.     

Mixed convection–radiation interaction in a vertical porous channel: Entropy generation

The present work examines analytically the effects of radiation heat transfer on magnetohydrodynamic mixed convection through a vertical channel packed with fluid saturated porous substances. First and Second Laws of thermodynamics are applied to analyze the problem. Special attention is given to entropy generation characteristics and their dependency on the various dimensionless parameters, i.e., Hartmann number (Ha), Plank number (Pl), Richardson number (Ri), group parameter (Br/II), etc. A steady-laminar flow of an incompressible-viscous fluid is assumed flowing through the channel with negligible inertia effect. The fluid is further considered as an optically thin gas and electrically conducting. Governing equations in Cartesian coordinates are solved analytically after reasonable simplifications. Expressions for velocity, temperature, local, and average entropy generation rates are analytically derived and presented graphically.     

Numerical simulation and experimental research on heat transfer and flow resistance characteristics of asymmetric plate heat exchangers

The asymmetric plate heat exchanger (APHE) has the possibility of achieving balanced pressure drops on both hot and cold sides for situations with unbalanced flow, which may in turn enhance the heat transfer. In this paper, the single-phase water flow and heat transfer of an APHE consisted of two types of plates are numerically (400≤Re≤12000) and experimentally (400≤Re≤ 3400) investigated. The numerical model is verified by the experimental results. Simulations are conducted to study the effects of N, an asymmetric index proposed to describe the geometry of APHEs. The correlations of the Nusselt number and friction factor in the APHEs are determined by taking N and working fluids into account. It is found that an optimal N exists where the pressure drops are balanced and the heat transfer area reaches the minimum. The comparison between heat transfer and flow characteristics of the APHEs and the conventional plate heat exchanger (CPHE) is made under various flow rate ratios of the hot side and the cold side and different allowable pressure drops. The situations under which APHE may perform better are identified based on a comprehensive index Nu/f^1/3.     

Test of a small domestic boiler using different pellets

This paper presents results from an experimental study performed on a 13 kW_th commercial domestic boiler using pellets as fuel. Four different types of pellets were used and, for each one, the boiler was tested as a function of its capacity and the fan regulation affecting excess air. Measurements were performed for boiler heat load, pellets consumption rate, flue-gas temperature and composition. Mass balances allowed the calculation of the flue-gas flow rate and associated heat losses. Losses from incomplete combustion have also been quantified. Under boiler steady-state conditions the flue-gas O₂ concentration changes with boiler load and ventilation due to the regulation scheme of the boiler. Flue-gas CO shows a minimum for values of O₂ in the flue-gases of about 13%. NO_x emissions are independent of excess air for low values of nitrogen in the fuel whereas, for larger values, NO_x emissions increase with the O₂ present in the combustion products. The fractional conversion of the pellets nitrogen into NO_x is in line with literature data. The boiler start-up was characterised by the temperature evolution inside and above the bed showing the propagation of combustion in the bed during about 10 min. During boiler start-up, a maximum in CO emissions was observed which is associated with the maximum combustion intensity, as typified by the flue-gas O₂ concentration and temperature, regardless the pellets type.