Film boiling heat transfer from a horizontal circular plate facing downward

The two‐dimensional, steady, pool film boiling heat transfer from a horizontal circular plate facing downward to a stagnant saturated liquid is studied theoretically. It is assumed that the vapor‐liquid interface is smooth and that radiation can be disregarded. The relevant governing equations for the vapor film are solved for saturated water at atmospheric pressure using an improved two‐equation boundary‐layer integral method. It is shown that the dimensionless temperature profile is affected by the wall superheat ΔT_sat and that the ratio of Nu to X^0.2 is an increasing function of ΔT_sat. Here, Nu represents the mean Nusselt number and X the film‐boiling Rayleigh number. In addition, it is revealed that the one‐equation boundary‐layer integral method developed by Nishio and colleagues is fairly accurate in predicting the film thickness, the representative radial velocity, and the mean Nusselt number. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 72–84, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10071     

Vapor bubble dynamics and heat transfer characteristics over the spherical surface during saturated pool boiling

The present study deals with numerical investigations of the boiling phenomena over a spherical surface at different degrees of superheat (ΔT), varying from 10 to 500 K. Various phenomena like vapor sliding, bubble formation, pinch-off, induced vorticity have been illustrated for a deep understanding of the boiling process over a spherical surface. The effect of the degree of superheat on the bubble pinch-off time and volume is also investigated. Further, reported the spatial observation of vapor sliding and retention over the surface with time scale, overall and average characteristics. The fast Fourier transform of a spaced average void fraction of liquid and Nusselt number showed the dominance of film boiling with respect to the degree of superheat. As the degree of superheat increases, the vapor generation rate also increases, which produces a more vapor–liquid interface. Further, with an increase in the degree of superheat, the vapor generation progression shifted from linear to nonlinear patterns. A sphere with ΔT = 500 K generated 32.59 times more vapor than a sphere with ΔT = 10 K. It is found that the vapor generation is dependent on the degree of superheating and exposed time for heating. Thus, a correlation and artificial neural network model have been developed to predict vapor generation during boiling over the spherical surface as a function of time and degree of superheat.     

Effect of thermal boundary condition on forced convection from circular cylinders

Researchers commonly assume that the effect of constant temperature and constant heat flux thermal boundary condition on forced convection from a circular cylinder is negligible. Such claim was assessed using Computational Fluid Dynamics for Reynolds number, Re, ≤ 3,000. The flow was directly solved without modeling for Re?≤?300, and Large Eddy Simulation was used for Re?=?1,000 and Re?=?3,000. Constant property simulations were done for Prandtl number of 0.7. Fluid dynamics parameters: drag coefficient, Strouhal number, separation angle and recirculation length, were used to assess the accuracy of the simulations. The main parameter of interest, the Nusselt number, is higher locally for constant heat flux than constant temperature for 60?≤?Re?≤?3,000. In addition, the ratio of overall Nusselt number for constant heat flux to that for constant temperature increases for Re < 30 and is ～1.15 between 30?≤?Re?≤?3,000, showing that thermal boundary condition has significant effect on heat transfer from circular cylinder. Finally, the study developed empirical correlations relating overall Nusselt number to studied Reynolds number range.     

Bubble growth and transient heat transfer at the onset of boiling

An experimental study was conducted to investigate transient local heat transfer around a bubble at onset of boiling on a thin glass heating plate immersed in saturated n-hexane at low pressure. Eight rapid response Cu-Ni thermocouples consisting of a vacuum deposited thin film were used to measure the temperature change of the heating surface. Simultaneous high-speed video photographs were also obtained. The surface temperatures near a nucleation site decreased rapidly owing to the evaporation of a thin layer (microlayer) of liquid formed beneath the bubble in the early period and the rate of bubble growth increased with increasing incipient boiling superheat (ΔT_IB). The thickness of the microlayer decreased markedly with increasing ΔT_IB. © 1998 Scripta Technica, Heat Trans Jpn Res, 26(7): 484–492, 1997     

Numerical modeling of heat and mass transfer characteristics during the forced convection drying of a square cylinder under strong blockage

Two-dimensional analysis of heat and mass transfer during drying of a square cylinder (SC) for confined flow with a strong blockage ratio (β?=?0.8) was performed using the alternating direction implicit (ADI)-based software. The influence of Reynolds number (Re?=?10–50) and moisture diffusivity number (D?=?1?×?10^?5???1?×?10^?8?m²/s) on the heat and mass transfer mechanisms was investigated. The convective heat transfer coefficients on SC surfaces were obtained using a commercial software package. The moisture content distributions inside a SC under transient conditions were calculated using the ADI method. The calculations showed that a higher Reynolds number enhances the overall mean Nusselt number and heat transfer coefficient value. The largest mean Nusselt number and heat transfer coefficient values were obtained at the front face of the SC, which makes the greatest contribution to the overall mean Nusselt number and heat transfer coefficient values for all surfaces of the SC. The effect of Reynolds number on the overall drying time was also investigated. Low Reynolds number and moisture diffusivity values lead to an increase in the overall drying time (Δt_od). For Re?=?10, the Δt_od values are 502.19?→?220288?s and for Re?=?50, the Δt_od values are 126.14?→?70353.21?s for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-Re?=?10/Δt_od-Re?=?50 ratios are 3.98–3.89 and 3.13 for a moisture diffusivity range of D?=?1?×?10^?5???1?×?10^?8?m²/s. Δt_od-D2/Δt_od-D1 is 7.47 for Re?=?10, and Δt_od-D3/Δt_od-D2 is 7.63 for Re?=?50, whereas Δt_od-D3/Δt_od-D1 is 438.66 for Re?=?10, and Δt_od-D3/Δt_od-D1 is 557.74 for Re?=?50. Additionally, iso-moisture contours of SC were presented and relations for Nusselt number and mass transfer coefficient values were derived.     

Natural convection heat transfer from a hollow horizontal cylinder with external longitudinal fins: A numerical approach

Abstract

The continuity, momentum, and the energy equations have been solved in 3D to predict the thermal plume and flow field around an isothermal horizontal longitudinally finned hollow cylinder in air. Effect of Rayleigh number (Ra), L/D, H/D, and s/D on heat transfer from the finned cylinder have been investigated where the input parameters are varied in a wide range of 10⁴ ≤ Ra ≤10⁷, 0.5?≤?L/D?≤?5, 0.0833?≤?H/D?≤?2, and 0.0785?≤?s/D?≤?0.785. Average surface Nusselt number (Nu) increases with increase in Ra and decreases with increase in cylinder length and fin number for all H/D. Nu for a finned solid cylinder is found to be marginally higher than that of the hollow cylinder except at low H/D of 0.0833 and high Ra of 10⁷ when s/D is less than 0.2617 for all L/D. Fin effectiveness is found to be increased with addition of taller fins for both the solid and hollow cylinder with longitudinal fins. Efficiency of the finned cylinder decreases with increase in fin height and Ra for all L/D and s/D. A general correlation of Nu as a function of all the pertinent input parameters (Ra, L/D, H/D, and s/D) has been proposed separately for the hollow isothermal cylinder having longitudinal fins, which can be used for industrial and academic purposes.     

Explosive boiling of liquid argon films on flat and nanostructured surfaces

Abstract

Because of the effects of the nanostructure, phase change behaviors on flat and nanostructured surfaces display distinct features. In this work, the molecular dynamics simulation method is employed to investigate the onset temperature of explosive boiling (T_s) with various film thicknesses, pillar heights, and wettability. The simulation results show that T_s decreases with the film thickness on both wettability flat surfaces. However, the decreasing rates have the significant distinctions, where the difference between two surfaces of T_s with the identical film thickness decreases. In addition, the simulation results demonstrate that all the values of T_s on nanostructured surfaces are lower than those on flat surfaces with the same film thickness. With the increase of the film thickness, T_s presents a decreasing trend on both wettability and nanostructured surfaces, especially with the liquid film with the thickness over 6?nm, where a completely opposite conclusion compared to the flat surface is represented.     

Numerical study of mixed convection in a ventilated square enclosure with the lattice Boltzmann method

In this article, numerical study of heat transfer by convection in a square cavity was investigated. The vertical walls of the cavity are differentially heated and the horizontal walls are considered adiabatic. A ventilation jet is created by a fan placed in the cavity. A lattice Boltzmann model for incompressible flow equation is used to simulate the problem. A parametric study was performed presenting the influence of Reynolds number (20 ≤ Re?≤?500), Rayleigh number (10≤Ra?≤?10⁺⁶), and fan position (0.2?≤?L_F≤0.8). It has been observed that heat transfer rate increases with the Reynolds number increasing and it is maximal for the L_F=0.2.     

Free convection enhancement in an annulus between horizontal confocal elliptical cylinders using hybrid nanofluids

ABSTRACT

In the present paper, natural convection in an annulus between two confocal elliptic cylinders filled with a Cu-Al₂O₃/water hybrid nanofluid is investigated numerically. The inner cylinder is heated at a constant surface temperature while the outer wall is isothermally cooled. The basic equations are formulated in elliptic coordinates and developed in terms of the vorticity-stream function formulation using the dimensionless form for 2D, laminar and incompressible flow under steady-state condition. The governing equations are discretized using the finite volume method and solved by an in-house FORTRAN code. Numerical simulations are performed for various volume fractions of nanoparticles (0?≤???≤?0.12) and Rayleigh numbers (10³?≤?Ra?≤?3?×?10⁵). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at e₁?=?0.9, e₂?=?0.6 and γ?=?0° respectively. It is found that employing a Cu-Al₂O₃/water hybrid nanofluid is more efficient in heat transfer rate compared to the similar Al₂O₃/water nanofluid.     

Computations of film boiling. Part II: multi-mode film boiling

Film boiling on horizontal periodic surfaces is investigated by direct numerical simulations. A front tracking/finite difference technique is used to solve the momentum and the energy equations in both phases and to account for inertia, viscosity, and surface deformation. Effect of the unit cell size W on the interface dynamics, heat transfer, and fluid flow is studied for different wall superheats. The simulations are carried out over sufficiently long times to capture several bubble release cycles and to evaluate the quasi steady-state Nusselt number . While instantaneous Nusselt number will change as result of a change in the system size, statistically steady-state Nusselt number remains almost the same. Simulations of two-dimensional systems in large unit cells, 5λ_d2 < W < 10λ_d2, show a distribution of bubble spacing in the range of 0.61λ_d2-1.46λ_d2. At relatively low superheats (Ja ? 0.064) the bubbles are released periodically from the vapor film, but at intermediate superheats (0.064 < Ja < 2.13) permanent vapor jets are formed with no bubble break off. At sufficiently high superheats, the vapor jets start to interact. It is shown that the average bubble spacing does not change with changes in the wall superheat.     

Momentum and heat transfer characteristics of a thin circular disk in Bingham plastic fluids

The laminar forced convection momentum and heat transfer aspects of a circular disk oriented normal to the flow and maintained at a constant flux or a constant temperature condition in a stream of a Bingham plastic fluid are studied over wide ranges of parameters as follows: Reynolds number, Re?≤?150; Prandtl number, 1 ≤Pr?≤?100; Bingham number, Bn?≤?100, and thickness-to-diameter ratio, 0.01?≤?(t/d)?≤?0.075. The new results on hydrodynamics are analyzed in terms of streamline plots, recirculation length, morphology of yielded/unyielded regions, and drag coefficient, and on heat transfer aspects in terms of isotherm contours, local and average Nusselt number. The flow domain is spanned by the simultaneous existence of the yielded and unyielded sub-regions, depending upon the relative strengths of the fluid inertia (Re) and yield stress (Bn). All else being equal, the rate of heat transfer is higher for an isothermal disk than that for the isoflux condition. Both the drag and average Nusselt number bear a positive dependence on the Bingham number. The drag is influenced only slightly (～5%) by thickness (t/d); however, the heat transfer can increase on this count by up to 15% under appropriate conditions. Finally, the present numerical results on drag and Nusselt number (in terms of j_H-factor) have been correlated via simple empirical equations using the modified definitions of the Reynolds (Re^*) and Prandtl number (Pr^*), thereby enabling a priori estimation of drag and heat transfer in a new application.     

Natural Convection Heat Transfer of Liquid Metal Gallium Nanofluids in a Rectangular Enclosure

A new mixed nanofluid (Cu/diamond–gallium [Cu/diamond–Ga] nanofluid) is proposed, and the mass ratio of Cu nanoparticles and diamond nanoparticles in the new mixed nanofluid is 10:1. The natural convection heat transfer of Cu/diamond–Ga nanofluid, Cu–gallium (Cu–Ga) nanofluid, and liquid metal gallium with different volume fractions in a rectangular enclosure is investigated by a single‐phase model in this paper. The effects of temperature difference, nanoparticle volume fraction and the kinds of nanofluid on the natural convection heat transfer are discussed. The natural convection heat transfer of the three kinds of fluids is compared. It is found that Nusselt numbers of the Cu/diamond–Ga nanofluid along with X direction increases with the nanoparticle volume fraction and temperature difference. Cu/diamond–Ga nanofluid can enhance the heat transfer by 73.0% and 9.7% at low‐temperature difference (ΔT = 1 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively. It also can enhance the heat transfer by 85.9% and 5.2% at high‐temperature difference (ΔT = 11 K) compared with liquid metal gallium and Cu–Ga nanofluid, respectively.     

Dissipative model of film boiling crisis

A dissipative model of the film boiling crisis based on the variational hypothesis of nonequilibrium phase change is presented. Transfer systems—characteristic for film and transition boiling of a liquid droplet on a plane horizontal and isothermal heating surface—were constructed. The value of the minimum film boiling temperature T_p,min was calculated from the criterion of equality of local potentials for two competitive transfer systems. The curves p = p(T_p,min) for hydrodynamic and thermodynamic models of the film boiling crisis for water have been determined and compared with the results achieved for the dissipative model.     

Evaporation of an oil‐in‐water type emulsion droplet on a hot surface

Evaporation characteristics of an Oil‐in‐Water (O/W) emulsion droplet were examined experimentally. The evaporation time per unit of initial surface area of a droplet τ^* was used to estimate the evaporation characteristics of droplets with different diameters and to compare a water droplet and an emulsion droplet. Results show that τ^* of an O/W emulsion droplet is shorter than a water droplet in the Leidenfrost film boiling regime. The four evaporation modes of O/W type emulsion droplets were observed. These depended on the mixing ratio of water and oil, G_S, and hot surface temperature, T_W. Increasing G_S increases the emulsion droplet's Leidenfrost temperature when the droplet is used as a die‐cast releasing agent. Microexplosions were observed during Leidenfrost film boiling when T_W was greater than 250^°C. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 527–537, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20081     

Three-dimensional numerical investigation of film boiling by the lattice Boltzmann method

A three-dimensional lattice Boltzmann model is presented to simulate the film-boiling phenomenon. Single- and multimode film boilings are investigated. The flow and temperature fields around the vapor phase are obtained for various Jakob numbers. Furthermore, the effects of Jakob number on the Nusselt number and vapor tip velocity are investigated. The results show that on increasing the Jakob number, the bubble tip velocity increases while the Nusselt number decreases. Furthermore, it is found that in multimode film boiling, the peak and trough values of the local Nusselt number happen at the bubble position and the gap valleys between adjacent bubbles, respectively.     

CFD analysis on heat transfer through different extended surfaces

The present study includes computational fluid dynamics analysis and comparison of heat enhancement through different extended surfaces, especially in rectangular and square conductive and nonconductive fins. Computational and numerical analysis of heat transfer from a rectangular extended surface and a pin-finned plate studied to calculate the average Nusselt number in parallel, vertical direction placed along the sidewall. The total rise of the mean Nusselt number is noticed around 36% in pin-finned plate with respect to a plain plate. This is examined with optimal fin spacing of S_v with L ratio equals to 0.2 and S_h with W ratio equals to 0.25, height of extended surfaces 24 mm with 45° angle of inclination. The mean Nusselt number reduces with a rise in the angle of inclination and also increases with a rise in aspect ratio. The present study reveals that inline and staggered arrangements do not yield appreciably different results. The maximum average Nusselt number difference between conductive and nonconductive fins is around 5% for S_h per W ratio 0.33 and S_v per L ratio 0.2 at an angle of inclination 45°, fin height of 6 mm (height to thickness ratio 2).     

Effect of surfactant addition on boiling heat transfer in a liquid film flowing in a diverging open channel

An experimental study was conducted to investigate how the addition of small amounts of a surfactant influences the heat transfer characteristics in a thin boiling liquid film flowing in a diverging open channel. Heat transfer experiments were conducted with fluid inlet temperatures from 40 °C to 92 °C. The flow field on the plate included thin film supercritical flow upstream of a hydraulic jump and thick film subcritical flow downstream of a hydraulic jump. Nusselt numbers for the non-boiling heat transfer without surfactant addition scaled linearly with the film Reynolds number. The boiling heat transfer produced higher Nusselt numbers with a weaker dependence on the Reynolds number. Experimental results showed that a boiling surfactant solution created a thick foam layer with high heat transfer rates and Nusselt numbers that are very weakly dependent on the inlet flow rate or the inlet Reynolds number.     

Thermo-Solutal Buoyancy Induced Mixed Convection in a Backward Facing Step Channel using Velocity-Vorticity Formulation

Double diffusive mixed convection in a horizontal channel with backward facing step is analyzed using velocity-vorticity formulation with a focus on the effect of recirculatory flow pattern on convective heat and mass transfer. The governing equations consist of vorticity transport equation with thermal and solutal buoyancy force terms, velocity Poisson equations, energy equation, and solutal concentration equation. Galerkin's weighted residual finite-element method has been employed to solve the equations for vorticity, velocity, temperature, and concentration fields in the computational domain. Test results are obtained to study the effect of thermal Grashof number (Gr _T ), solutal Grashof number (Gr _S ), and expansion ratio on the average Nusselt and Sherwood numbers. Results indicate that the convective heat transfer increased with increase in Gr _T only when the Gr _S number is in the aiding mode. The maximum local Nusselt number is always observed to be located adjacent to the downstream of the fluid reattachment point. Using the matched method of asymptotic expansions, correlations have also been developed for average Nusselt and Sherwood numbers for both cases of aiding and opposing buoyancy forces.     

Numerical and Experimental Investigation of Crystal Growth Rate Dependence on Facet Undercooling for Dielectric Crystal Growth from the Melt

Combined experimental and numerical tools are developed and used to define more exactly the growth kinetic relations for (211) crystallographic orientation of Bi₄Ge₃O₁₂ (BGO) crystal growth—namely, the dependence of crystal growth rate V on supercooling, ΔT of the melt/crystal interface. A new apparatus for in situ measurements of the time dependence of the supercooling, ΔT(t), was used, and a new, two-dimensional numerical model was applied to analyze the effect of temperature boundary conditions and faceting phenomena on the character of the observed V(ΔT) dependence. The measurements of the ΔT(t) dependence show that there is a large enough undercooling and a novel effect of the appearance of the local maximum on ΔT(t) dependence at the finish of crystallization. Results on V(ΔT) dependence show that, for the variant of the crystal growth technique used (melt cooling during axial heating process method [AHP]), the type of the V(ΔT) dependence does not depend on boundary conditions. The new investigations illustrate the superlinear behavior for V(ΔT) dependence for (211) BGO crystallographic orientation and show that previous data on sublinear behavior of V(ΔT) dependence for this crystallographic orientation of BGO have not been justified.