Non-thermal equilibrium melting of granular packed bed in horizontal forced convection. Part I: experiment

A series of experiments are conducted to investigate the non-thermal equilibrium characteristics of melting of a packed bed under horizontal forced and mixed convections. This configuration imposes a complex treatment in phase change heat transfer that involves not only the coupled heat, mass and momentum exchanges but also the local geometric change of the packed bed (packing effect). Using visualization observations and measurements, we determine experimentally the volumes and packing patterns of the melting granular packed beds and the time variation of average melting rate per unit bed volume and average heat transfer coefficient for Re=71–2291, Gr/Re²=1.48×10⁻⁵–17.32, and Ste=0.0444–0.385. The effects of water velocity and water temperature on the melting and heat transfer in the melting process are analyzed. The effects of packing patterns on Nusselt number correlations are presented. Using the definition of a terminal velocity, a Reynolds number ratio is developed as the criterion defining the floating, non-floating or transitional packing pattern.     

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.     

Cooling strategy by mixed convection of a discrete heater at its optimum position in a square cavity with ventilation ports

We studied cooling strategy in a square enclosure with ventilation ports and a discrete heat source at its optimum position. We searched the optimum heater position by maximizing the global conductance at different Rayleigh and Reynolds numbers and considered three different ventilation ports arrangements. We solved the conservation equations of mass, momentum and energy for mixed convection. We found that the heater position is at off center in all cases, its optimum position is insensitive to the variation of Ra and Re; it solely depends on the ventilation ports arrangement. The Nusselt number is dependent on Ri = Ra/Re²: at its low values, Nu is a decreasing function of Ri and at its high values, it is an increasing function of it.     

Chimney effect in a “T” form cavity with heated isothermal blocks: The blocks height effect

In this paper, a numerical study of natural convection from a two dimensional “T” form cavity with rectangular heated blocks is conducted. The blocks are identical, and the domain presents a symmetry with respect to a vertical axis passing through the middle of the opening. The governing equations are solved using a control volume method, and the SIMPLER algorithm for the velocity–pressure coupling is employed. Special emphasis is given to detail the effect of Rayleigh number and block height on the heat transfer and the flow rate generated by the chimney effect. The results are given for the parameters of control as, 10⁴Ra3×10⁶, Pr=0.71, opening diameter (C=l^′/H^′=0.15), blocks gap (D=d^′/H^′=0.5) and blocks height (1/8B=h^′/H^′1/2). These results show that the heat transfer variation with Ra is in the same manner as those met in the case of the vertical smooth or ribbed channels.     

A correlation for heat transfer by natural convection from horizontal cylinders that accounts for viscous dissipation

Eight previously published correlation equations plus one new correlation for heat transfer by natural convection from horizontal isothermal cylinders are tested against a fairly extensive body of experimental data culled from the literature for 10⁻⁸ < Ra < 10⁸ and 0.7 < Pr < 4 × 10⁴. The new equation, which represents the Nusselt number as a function of the Prandtl and Rayleigh numbers plus an additional dimensionless parameter that accounts for viscous dissipation, is shown to correlate the experimental data more accurately than does any one of the eight previously published equations. It is concluded that viscous dissipation may not be neglected in all cases of natural convection from horizontal cylinders, and further, that the inclusion of a viscous dissipation term in certain related problems, such as natural convection in porous media, may lead to more accurate correlation equations.     

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.     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

Measurements of convective heat transfer from a horizontal cylinder rotating in a tank of water

The present paper deals with measurements of heat transfer from a horizontal cylinder rotating in water. The experimental results have been correlated by the equation Nu = 0.133Re^2/3 · Pr^1/3 for a range of rotating Reynolds numbers from 1000 to 46 000, and Prandtl numbers from 2.2 to 6.4. This equation compares very well with the experimental and theoretical information available for air, water and oil in published works.

The analogy suggested by Anderson and Saunders between natural convection from a horizontal plate and the present type of flow has been used to predict the Nusselt numbers. The analogy solution and the present experimental results have been found to compare very well with each other.     

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 studies of laminar flow and heat transfer in a one-porous-wall square duct with wall injection

Experiments were conducted to investigate the effect of fluid injection on laminar flow and heat transfer characteristics in a one-porous-wall square duct. Uniform air flow at Re₀ = 400−2000 entered the duct with a cross section of 20 × 20 mm² and a ratio of the active injection length to the hydraulic diameter of 40. Pressurized air was injected through a thick layer of porous material for flow uniformity and a heated porous duct wall at injection rates Re_w = 5−20. All of the measured and deduced data, including the axial velocity profiles, the pressure drops, the friction factors, the porous wall temperatures, the outlet fluid temperatures and the Nusselt numbers, were presented and compared with the previous theoretical results. The deduced friction factors and Nusselt numbers from the experimental data were correlated within differences of ±10% and ±15% respectively.     

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.     

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     

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.     

Total and local heat transfer from a smooth circular cylinder in cross-flow at high reynolds number

The total and local heat transfer from a smooth circular cylinder to the cross flow of air has been measured over the Reynolds number range 3 × 10⁴ < Re < 4 × 10⁶. The interaction between flow and heat transfer is discussed. In particular, the boundary-layer effects on the heat transfer, such as transition from laminar to turbulent flow or boundary-layer separation, are considered in conjunction with the distributions of local static pressure and skin friction.     

The development of laminar natural-convective flow in a vertical uniform heat flux duct

An account of a theoretical and experimental study of laminar natural-convective flow in heated vertical ducts is presented. The ducts are open-ended and circular in cross-section and their internal surfaces dissipate heat uniformly.

Temperature and velocity fields and the relationship between Nusselt and Rayleigh numbers were obtained by solving the governing equations by a step-by-step numerical technique. Two Rayleigh numbers are introduced, one expressed in terms of the uniform heat flux and the other in terms of the mean wall temperature. The influence that the Prandtl number has on the relationship between the Nusselt and Rayleigh numbers is discussed. Three inlet conditions were examined; they all gave the same Nusselt relationship at small Rayleigh numbers and the differences between the Nusselt relationships obtained at large Rayleigh numbers were only small.

Experimentally determined Nusselt numbers, with air as the convected fluid, agreed satisfactorily with the theoretical relationship.     

Effect of tube inclination on laminar convection in uniformly heated tubes for flat-plate solar collectors

A numerical study using a combination of boundary vorticity method and line iterative relaxation method is carried out to determine the free convection effects on fully developed upward laminar forced flow in uniformly heated inclined tubes. The combined free and forced laminar convection for water with the inclined tube configuration in the low Reynolds number flow regime has practical application in flat-plate solar collectors for water heating. The tube inclination or gravitational force orientation effects on flow and heat transfer characteristics are clarified and show that in high Rayleigh number regime the tube orientation effect has considerable influence on the results, particularly in the neighborhood of horizontal direction. The numerical results show that the perturbation analysis in terms of power series of Rayleigh number is invalid for the present problem and reveal further that a maximum value for Nusselt number does not exist for any tube inclination angle with given values of the dimensionless parameters which is clearly contrary to the result from perturbation solution.     

Improving thermal performance of the roof enclosure of heavy construction buildings

High heat flux through the enclosures of heavy building constructions during summer and winter seasons is of great concern with respect to energy-related economics and environmental issues. This paper demonstrates the importance of quantitative evaluation of enclosure design and proves the potential for substantial energy savings by minor alterations of conventional roof designs. These modifications include adding insulation layer(s), removing construction details and obstructing fluid flow within the attic cavity by partial or full vertical partition within the cavity. The CFD approach adopted for this purpose is based on a numerical study of steady, conjugate natural convection in the cavity of an attic of heavy construction buildings. Because of the flow characteristics, laminar and turbulent models were employed for summer and winter day boundary conditions, respectively. Steady state results based on the finite-volume method were obtained for Rayleigh number in the range 10⁸–10¹⁰. Representative results illustrating the effects of the proposed design modifications on the local and total Nusselt numbers at the indoor surfaces are presented and discussed for summer and winter day boundary conditions. The results show that considerable energy saving may be achieved via relatively simple design changes. It is also shown that adding an insulation layer does not necessarily translate into energy conservation, and that eliminating a minor design detail might have significant rewards in terms of energy savings.     

Numerical Simulation of Buoyancy-Induced Turbulent Flow Between Two Concentric Isothermal Spheres

Buoyancy-induced turbulent flow and natural convection heat transfer between two differentially heated concentric isothermal spheres is studied numerically. The low-Reynolds-number k–ω model is used for turbulence modeling. The two-dimensional governing equations are discretized using control volume method and solved by employing the alternating direction implicit scheme. Results are presented in the form of streamline and temperature patterns, and local and average Nusselt numbers, over the heated and cooled boundaries for a wide range of Rayleigh numbers (10²–10¹⁰), extending the previous studies to the turbulent flow regime and for the radius ratio of 2. The results of the flow pattern and average Nusselt numbers were compared with the previously published experimental and numerical investigations and very good agreements were observed. For low values of Rayleigh numbers, regions with conduction-dominated flow pattern accompanied with low values of Nusselt numbers were observed, while for higher Rayleigh numbers, the flow pattern was changed to the convection dominated boundary layer type flow, resulting in an increase in the rate of heat transfer and flow velocities adjacent to both inner and outer boundaries. The average Nusselt numbers were correlated against Rayleigh number and a 1/4 power dependence of Ra in both laminar and turbulent regimes is obtained.     

The optimal spacing of parallel plates cooled by forced convection

This paper reports the optimal board-to-board spacing and maximum total heat transfer rate from a stack of parallel boards cooled by laminar forced convection. The optimal spacing is proportional to the board length raised to the power 1/2, the property group (μ)^1/4, and (ΔP)^−1/4, where ΔP is the pressure head maintained across the stack. The maximum total heat transfer rate is proportional to (ΔP)^1/2, the total thickness of the stack (H), and the maximum allowable temperature difference between the board and the coolant inlet. Board surfaces with uniform temperature and uniform heat flux are considered. It is shown that the surface thermal condition (uniform temperature vs uniform heat flux) has a minor effect on the optimal spacing and the maximum total heat transfer rate.     

The liquid flow in multi-stage flash evaporators

In an attempt to reach a quantitative understanding of the interaction between the fluid mechanics and flash evaporation in a stage of a multi-stage flash (MSF) evaporator, and in horizontal free-surface streams in general, a numerical analysis is performed, as a first step, of two-dimensional turbulent isothermal flow of a liquid in a flash chamber (stage) with and without a baffle (sill) placed downstream of the inlet orifice. Experiments are also performed, and validate the model successfully in the range of flows of 4.3 × 10⁵−8.7 × 10⁵ kg h⁻¹ (m width)⁻¹ and liquid level of 0.4 m, conditions typical to MSF evaporators. The baffle plate is found to serve well in propelling the entering liquid to the free surface and in generating low-pressure regions, primarily near the stream line rising from the top edge of the baffle, both effects promoting evaporation rates. The interstage orifice coefficient is found to be practically independent of the liquid superheat, temperature, and mass flow rate.