The Falkner–Skan Wedge Flows of Power-Law Fluids Embedded in a Porous Medium

The non-Darcy flow characteristics of power-law non-Newtonian fluids past a wedge embedded in a porous medium have been studied. The governing equations are converted to a system of first-order ordinary differential equations by means of a local similarity transformation and have been solved numerically, for a number of parameter combinations of wedge angle parameter m, power-law index of the non-Newtonian fluids n, first-order resistance A and second-order resistance B, using a fourth-order Runge–Kutta integration scheme with the Newton–Raphson shooting method. Velocity and shear stress at the body surface are presented for a range of the above parameters. These results are also compared with the corresponding flow problems for a Newtonian fluid. Numerical results show that for the case of the constant wedge angle and material parameter A, the local skin friction coefficient is lower for a dilatant fluid as compared with the pseudo-plastic or Newtonian fluids.     

Unsteady air–water flow measurements in sudden open channel flows

Measurements of air–water flow properties are reasonably simple in steady flows, but not so in unsteady flows. Some studies investigated periodic flows in which instantaneous data were averaged over several cycles. During the present work, new unsteady air–water flow measurements were performed in sudden open channel flow surges. Unsteady air–water flow measurements were performed in the wave front with an array of resistivity probes. The results demonstrated quantitatively strong aeration of the leading edge in terms of void fractions, bubble count rates and specific interface areas. Experimental results highlighted that this strongly aerated region was relatively short: i.e. typically 0.3 to 0.5 m long. Measurements of air and water chord sizes highlighted a wide range of bubble and droplet sizes. Time-variations of air–water flow structure were observed.

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The characteristics of gas–solid flow and wall heat transfer in a fluidized bed reactor

Numerical study using computational fluid dynamics has been carried out to investigate the heat transfer characteristics of a laboratory fluidized bed reactor. The fluidized bed reactor of vTI (Johann Heinrich von Thünen-Institute)-Institute of Wood Technology and Wood Biology is modeled. For the simulation of multiphase flow and thermal fields, an Eulerian–Eulerian approach is applied. The flow and thermal characteristics of the reactor are fully investigated for the wide range of superficial gas velocities and two different particle diameters. In particular, the contributions of the gas bubble and emulsion phase flows on the wall heat transfer are scrutinized. From the predicted results, it is fully elucidated that particular near-wall bubble motions mainly govern the wall heat transfer.     

Stiffness problem in modeling wave flows of heterogeneous media with a three‐temperature scheme of interphase heat and mass transfer

The numerical modeling of wave flows of heterogeneous media with a threetemperature scheme of interphase heat and mass transfer involves the problem of equation stiffness. A discrete model of improved stability was developed to describe these processes. Test calculations of the interaction of a shock wave with a bounded layer of a mixture of a gas and droplets assuming a discrete model over a wide range of initial data showed that the stability conditions do not depend on the rate of interphase interaction (Cstability).     

Average and extremal properties of heat transfer and shear stress on a wall surface in Rayleigh–Bénard convection

In this study surface-averaged and extremal properties of heat transfer and shear stress on the upper wall surface of Rayleigh–Bénard convection are numerically examined. The Prandtl number was raised up to 10³, and the Rayleigh number was changed between 10⁴ and 10⁷. As a result, average Nusselt number Nu and shear rate τ/Pr depends on Pr, Ra, and the entire numerical results are distributed between two correlation equations corresponding to small and large Pr. The small and large Pr equations are closely related to steady and unsteady flow regimes, respectively. Nevertheless, a single relation τ/Pr ~ Nu ^3.0 exists to explain the entire results. Similarly the change of local maximal properties Nu _max and τ _max/Pr depends on Pr, Ra, and these values are also distributed between two correlation equations corresponding to small and large Pr cases. Despite such complicated dependence we can obtain a correlation equation as a form of τ _max/Pr ~ Nu _max^2.6, which has not been obtained theoretically.     

An application of the k-ɛ model with variable Prandtl number to heat transfer computations in air flows

The two-equation `low Reynolds number' k-? model of turbulence with a set of universal constants suggested by Launder and Sharma is modified in the present paper. The variability of the turbulent Prandtl number Pr_t in the energy equation is assumed along with a change of a constant in the dissipation term of the turbulent kinetic energy equation. The turbulent heat transfer is computed for an air flow in a circular pipe for the Reynolds number within the range of 10⁴?4. The modification considerably improves the agreement between the numerical results and the experiment data published in the available literature.     

Particle shape effect on hydrodynamics and heat transfer in spouted bed: A CFD–DEM study

Spouted bed has drawn much attention due to its good heat and mass transfer efficiency in many chemical units. Investigating the flow patterns and heat and mass transfer inside a spouted bed can help optimize the spouting process. Therefore, in this study, the effects of particle shape on the hydrodynamics and heat transfer in a spouted bed are investigated. This is done by using a validated computational fluid dynamics–discrete element method (CFD–DEM) model, considering volume–equivalent spheres and oblate and prolate spheroids. The results are analysed in detail in terms of the flow pattern, microstructure, and heat transfer characteristics. The numerical results show that the prolate spheroids (Ar = 2.4) form the largest bubble from the beginning of the spouting process and rise the highest because the fluid drag forces can overcome the interlocking and particle–particle frictional forces. Compared with spherical particles, ellipsoidal spheroids have better mobility because of the stronger rotational kinetic energy resulting from the rough surfaces and nonuniform torques. In addition, the oblate spheroid system exhibits better heat transfer performance benefiting from the larger surface area, while prolate spheroids have poor heat transfer efficiency because of their orientation distribution. These findings can serve as a reference for optimizing the design and operation of complex spouted beds.     

Hysteretic heat transfer study of liquid–liquid two-phase flow in a T-junction microchannel

Liquid–liquid two-phase flow in microchannels is capable of boosting the heat removal rate in cooling processes. Formation of different two-phase flow patterns which affect the heat transfer rate is numerically investigated here in a T-junction containing water-oil flow. For this purpose, the finite element method (FEM) is applied to solve the unsteady two-phase Navier–Stokes equations along with the level set (LS) equation in order to capture the interface between phases. It is shown that the two-phase flow pattern in microchannels depends on the flow initial condition which causes hysteresis effect in two-phase flow. In this study, the hysteresis is observed in flow pattern and consequently in the heat transfer rate. The effect of wall contact angle on the hydrodynamics and heat transfer in the microchannel is investigated to gain useful insight into the hysteresis phenomenon. It is observed that the hysteresis is significant in super-hydrophilic microchannels, while it disappears at the contact angle of 75^°. The effect of water to oil flow rate ratio (Q_wat/Q_oil) on the heat transfer is also studied. The flow rate ratio has a negligible effect on the Nusselt number (Nu) in the dripping regime, while the Nu decreases with an increase of Q_wat/Q_oil in the co-flow regime. The thickness of the oil film, velocity, and temperature distribution are studied in the co-flow regime. It is revealed that the normalized slip velocity reduces at higher values of Q_wat/Q_oil, which causes a reduction in the averaged Nu. In dripping regimes, higher flow rate ratios lead to a more frequent generation of droplet/slugs at a smaller size. The passage of the slugs or droplets increases the local Nu. Larger droplets generated at lower flow rate ratios cause a larger increase in the local Nu than smaller droplets. The temperature and velocity field around the droplets are also illustrated to investigate the heat transfer improvement. The generated vortex at the tip of the oil jet causes an increase in the velocity and Nu on the water side.     

Dependence of interfacial heat transfer coefficient on casting surface temperature during solidification of Al–Si alloy castings cast in CO2 sand mold

Interfacial heat transfer coefficient at the metal–mold interface (IHTC) was estimated by an iterative algorithm based on the function specification method. An Al–9 wt% Si alloy plate casting was made in a sand mold prepared by CO₂ process. Thermal history obtained from the experiment was used to solve an inverse heat conduction problem. Acquired transient IHTC values are then given in function of the casting surface temperature at the interface. By comparing the obtained results with previous findings, the influence of grain fineness number and consequently of mold roughness on maximum IHTC values is revealed.     

Detection of liquid–vapor–solid triple contact line in two-phase heat transfer phenomena using high-speed infrared thermometry

Heat transfer in complex physical situations such as nucleate boiling, quenching and dropwise condensation is strongly affected by the presence of a liquid–vapor–solid triple contact line, where intense energy transfer and phase change occur. A novel experimental technique for the detection of the liquid–vapor–solid line in these situations is presented. The technique is based on high-speed infrared (IR) thermometry through an IR-transparent silicon wafer heater; hence the name DEPIcT, or DEtection of Phase by Infrared Thermometry. Where the heater surface is wet, the IR camera measures the temperature of the hot water in contact with the heater. On the other hand, where vapor (whose IR absorptivity is very low) is in contact with the heater, the IR light comes from the cooler water beyond the vapor. The resulting IR image appears dark (cold) in dry spots and bright (hot) in wetted area. Using the contrast between the dark and bright areas, we can visualize the distribution of the liquid and gas phases in contact with the heater surface, and thus identify the liquid–vapor–solid contact line. In other words, we measure temperature beyond the surface to detect phases on the surface. It was shown that even small temperature differences (∼1 °C) can yield a sharp identification of the contact line, within about 100 μm resolution. DEPIcT was also shown to be able to detect thin liquid layers, through the analysis of interference patterns.     

Prediction of the boiling temperature and heat flux in sugar–water solutions under pool-boiling conditions

Condensing of a sugar–water solution is a widely used production process, especially in food industry. In this study, boiling temperature and heat transfer of different concentration levels of sugar/water solution is experimentally studied. In the experiment, the pool boiling with constant temperature difference between surface and boiling temperature is investigated. Boiling point of sugar/water solution depends on sugar mass concentration and on vapor phase pressure. A function is suggested to calculation the boiling temperature. The experimental data and the calculated values of boiling temperature are compared. The results are verified with previous investigations. It is determined that the heat flux between surface and sugar/water solution while pool boiling displays a linear relation with water mass concentration in the solution. Heat transfer coefficient could be determined in dependency of surface temperature and sugar mass concentration. Furthermore a function is suggested to predict the heat flux for engineering purpose, which is already used in similar form for pure substances.     

An adaptive finite element method for viscoplastic flows in a square pipe with stick–slip at the wall

This paper presents the numerical solution of non-linear yield stress phenomena by using a new mixed anisotropic auto-adaptive finite element method. The Poiseuille flow of a Bingham fluid with slip yield boundary condition at the wall is considered. Despite its practical interest, for instance for pipeline flows of yield-stress fluids such as concrete and cements, this problem has not been addressed yet to our knowledge. The case of a pipe with a square section has been investigated in detail. The computations cover the full range of the two main dimensionless numbers and exhibit complex flow patterns: all the different flow regimes are completely identified.     

Study of heat transfer of a helium–xenon mixture in heated channels with different cross-sectional shapes

This paper describes the results of an experimental study of heat transfer in the case of the flow of a helium–xenon mixture with a Prandtl number approximately equal to 0.23 and the flows of pure helium and air in heated tubes of circular or triangular cross sections with a constant density of the heat flow. The region of thermal stability is studied. The law of heat transfer on the stabilized region is compared with known relationships. The approach that helps obtaining an expression for the calculation of heat transfer in heat transfer devices with circular and triangular cross sections, which operate in a mixture heating mode on the initial region, is developed.     

Roll waves structure in two-layer Hele–Shaw flows

The mathematical model of inhomogeneous fluid motion in a Hele–Shaw cell is proposed. Based on this model the equations for describing two-layer flows and development of roll waves at the interface are derived. Conditions of roll waves existence are formulated in terms of Whitham criterion. Numerical calculations of the interface position are provided. It is shown that small perturbations of the interface in the inlet section of the channel lead to the roll waves for certain parameters of the flow. Two-parametric class of exact solutions corresponding to the roll waves regime is obtained. Diagrams of critical depths of roll waves development are constructed.     

Gas–liquid two-phase flows in rectangular polymer micro-channels

This study addresses gas–liquid two-phase flows in polymer (PMMA) micro-channels with non-molecularly smooth and poorly wetting walls (typical contact angle of 65°) unlike previous studies conducted on highly wetting molecularly smooth materials (e.g., glass/silicon). Four fundamentally different topological flow regimes (Capillary Bubbly, Segmented, Annular, Dry) were identified along with two transitory ones (Segmented/Annular, Annular/Dry) and regime boundaries were identified from the two different test chips. The regime transition boundaries were influenced by the geometry of the two-phase injection, the aspect ratio of the test micro-channels, and potentially the chip material as evidenced from comparisons with the results of previous studies. Three principal Segmented flow sub-regimes (1, 2, and 3) were identified on the basis of quantified topological characteristics, each closely correlated with two-phase flow pressure drop trends. Irregularity of the Segmented regimes and related influencing factors were addressed and discussed. The average bubble length associated with the Segmented flows scaled approximately with a power law of the liquid volumetric flow ratio, which depends on aspect ratio, liquid superficial velocity, and the injection system. A simplified semi-empirical geometric model of gas bubble and liquid plug volumes provided good estimates of liquid plug length for most of the segmented regime cases and for all test-channel aspect ratios. The two-phase flow pressure drop was measured for the square test channels. Each Segmented flow sub-regime was associated with different trends in the pressure drop scaled by the viscous scale. These trends were explained in terms of the quantified flow topology (measured gas bubble and liquid plug lengths) and the number of bubble/plug pairs. Significant quantitative differences were found between the two-phase pressure drop in the polymer micro-channels of this study and those obtained from previous glass/silicon micro-channel studies, indicating that the effect of wall surface properties is important. Pressure drop trends on the capillary scale along gas bubbles extracted from the measurements in square micro-channels indicated a linear dependence on the Capillary number and did not agree with those predicted by highly idealized theory primarily because explicit and implicit assumptions in the theory were not relevant to practical conditions in this study.