Numerical simulation of condensation for R410A at varying saturation temperatures in mini/micro tubes

ABSTRACT

Heat transfer and pressure drop characteristics of condensation for R410A inside horizontal tubes (d_h = 0.25, 1, and 2 mm) at saturation temperatures Tsat = 310, 320, and 330 K are investigated numerically. The results indicate that local heat transfer coefficients and pressure drop gradients increase with increasing mass flux and vapor quality and with decreasing tube diameter and saturation temperature. Liquid film thickness also increases with increasing saturation temperature because of the lower surface tension at higher saturation temperature. When gravity dominates the condensation process, a vortex with its core lying at the bottom of the tube is found in the vapor phase region. For the annular flow regime, stream traces point from the symmetry plan to the liquid–vapor interface, where the vapor phase becomes the liquid phase. Numerical heat transfer coefficients and pressure drop gradients are compared to available empirical correlations. Two new models for heat transfer coefficients and frictional pressure drop gradients are developed based on the numerical work.     

The Second Law of Thermodynamics for a Two-Temperature Model of Heat Transport in Metal Films

ABSTRACT

The second law of thermodynamics asserts that heat will always flow “downhill”, i.e., from an object having a higher temperature to one having a lower temperature. For a parabolic rigid heat conductor with a single temperature T and a single heat-flux q this amounts to the statement that the inner product of q and ?T must be non-positive for every point x of the conductor and for every non-negative time t. For a homogeneous and isotropic body in which classical Fourier law with a heat conductivity coefficient k is postulated, the second law is satisfied if k is a positive parameter. For ultra-fast pulse-laser heating on metal films, a parabolic two-temperature model coupling an electron temperature T_e with a metal lattice temperature T_l has been proposed by several authors. For such a model, at a given point of space x and a given time t there are two different temperatures T_e and T_l as well as two different heat-fluxes q _e and q _l related to the gradients of T_e and T_l, respectively, through classical Fourier law. As a result, for a homogeneous and isotropic model the positive definiteness of the heat conductivity coefficients k_e and k_l corresponding to T_e and T_l, respectively, implies that the second law of thermodynamics is satisfied for each of the pairs (T_e, q _e) and (T_l, q _l), separately. Also, the positive definiteness of k_e and k_l, and of the corresponding heat capacities c_e and c_l as well as of a coupling factor G imply that a temperature initial-boundary value problem for the two-temperature model has unique solution. In the present paper, an alternative form of the second law of thermodynamics for the two-temperature model with k_l = 0 and q _l =  0 is obtained from which it follows that in a one-dimensional case the electron heat-flux q_e(x, t) has direction that is opposite not only to that of ?T_e(x, t)/?x but also to that of ?T_l(x, t + τ_T)/?x, where τ_T is an intrinsic small time of the model. Also, for a general two-temperature rigid heat conductor in which k_e, k_l, c_e, c_l, and G are positive, an inequality of the second law of thermodynamics type involving a pair (T_e ? T_l, q _e ?  q _l) is postulated to prove that a two-heat-flux initial-boundary value problem of the two-temperature model has a unique solution. For a one-dimensional case, the semi-infinite sectors of the plane ( q _l, q _e) over which uniqueness does not hold true are also revealed.     

R1234yf Flow Boiling Heat Transfer Inside a 2.4-mm Microfin Tube

ABSTRACT

This paper presents an experimental study on R1234yf flow boiling inside a mini microfin tube with an inner diameter at the fin tip of 2.4 mm. R1234yf is a new refrigerant with an extremely low global warming potential (GWP <1), proposed as a possible substitute for the common R134a, whose GWP is about 1300. The mass flux was varied between 375 and 940 kg m^?2 s^?1, heat flux from 10 to 50 kW m^?2, and vapor quality from 0.1 to 1. The saturation temperature at the inlet of the test section was kept constant and equal to 30°C. The wide range of operative test conditions permitted highlighting the effects of mass flux, heat flux, and vapor quality on the thermal and hydraulic behavior during the flow boiling mechanism inside such a mini microfin tube. The results show that at low heat flux the phase-change process is mainly controlled by two-phase forced convection, and at high heat flux by nucleate boiling. The two-phase frictional pressure drop increases with increasing both mass velocity and vapor quality. Dry-out was observed only at the highest heat flux, at vapor qualities of around 0.94–0.95.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.     

High-pressure Condensing Refrigerant Flows Through Microchannels,Part II: Heat Transfer Models

ABSTRACT

Condensation of high-pressure refrigerants in small-diameter channels over a wide range of reduced pressures approaching the critical point is investigated in this two-part study. Part I presented pressure drop measurements and a two-phase pressure drop model. In this paper, Part II of the study, a condensation heat transfer model is presented. Heat transfer coefficients were measured during condensation of R404A in circular channels (inner diameter = 0.86, 1.55, 3.05 mm) over the entire quality range. The saturation temperature was varied from 30 to 60°C, and mass flux from 200 to 800 kg m^-2 s^-1, to evaluate their effects on condensation heat transfer coefficient. The heat transfer model is developed using a microchannel flow regime map and the void fraction model previously developed by the authors. The resulting model predicts 93.6% of the data within ±25%. The model exhibited good agreement with data from condensing ammonia and carbon dioxide, predicting 84.8% and 97% of their data within ±25%, respectively.     

NATURAL-CONVECTIVE HEAT TRANSFER IN A SQUARE CAVITY WITH TIME-VARYING SIDE-WALL TEMPERATURE

ABSTRACT

The natural-convective heat transfer in an inclined square enclosure is studied numerically. The top and bottom horizontal walls are adiabatic, and the right side wall is maintained at a constant temperature T ₀. The temperature of the opposing vertical wall varies by sine law with time about a mean value T ₀. The system of Navier–Stokes Equations in Boussinesq approximation is solved numerically by the control-volume method with SIMPLER algorithm. The enclosure is filled with air (Pr = 1) and results are obtained in the range of inclination angle 0° ≤ α ≤ 90° for two values of Grashof number (2 × 10⁵ and 3 × 10⁵). It can be noted that there is a nonzero time-averaged heat flux through the enclosure at α ≠ 0°. The dependencies of time-averaged heat flux on oscillation frequency and inclination angle are depicted. It is found that the maximal heat transfer corresponds to the values of inclination angle α = 54^○ and dimensionless frequency f = 20π for both Grashof numbers studied (2 × 10⁵ and 3 × 10⁵).     

Multi-Objective Optimization of Micro Pin-Fin Arrays for Cooling of High Heat Flux Electronics with a Hot Spot

ABSTRACT

This article presents fully three-dimensional conjugate heat transfer analysis and a multi-objective, constrained optimization to find sizes of pin-fins, inlet water pressure, and average speed for arrays of micro pin-fins used in the forced convection cooling of an integrated circuit with a uniformly heated 4 × 3 mm footprint and a centrally located 0.5 × 0.5 mm hot spot. Sizes of micro pin-fins having cross sections shaped as circles, symmetric airfoils, and symmetric convex lenses are optimized to completely remove heat due to a steady, uniform heat flux of 500 W cm^?2 imposed over the entire footprint (background heat flux) and a steady, uniform heat flux of 2000 W cm^?2 imposed on the hot spot area only (hot spot heat flux). The two simultaneous objectives are to minimize maximum substrate temperature and minimize pumping power, while keeping the maximum temperature constrained below 85°C and removing all of input thermal energy by convection. The design variables are the inlet average velocity and size of the pin-fins. A response surface is generated for each of the objectives and coupled with a genetic algorithm to arrive at a Pareto frontier of the best trade-off solutions. Numerical results show that, for a specified maximum temperature, optimized arrays with pin-fins having symmetric convex lens shapes create the lowest pressure drop, followed by the symmetric airfoil and circular cross-section pin-fins. An a posteriori three-dimensional stress–deformation analysis incorporating hydrodynamic and thermal loads shows that Von-Mises stress for each pin-fin array is significantly below the yield strength of silicon, thus, confirming structural integrity of such arrays of micro pin-fins.     

Thermal Control of Protruding Electronic Components with PCM: A Parametric Study

This work deals with the melting and natural convection in a rectangular enclosure heated from three discrete protruding electronic components (heat sources) mounted on a conducting vertical plate (substrate). The heat sources generate heat at a constant and uniform volumetric rate. A part of the power generated in the heat sources is dissipated to the phase change material (PCM, n-eicosane with a melting temperature T _m  = 36°C) that filled the enclosure. To investigate the thermal behavior of the proposed heat sink, a mathematical model, based on the mass, momentum, and energy conservation equations was developed. The model has been verified and then validated comparing the melting front with available experimental results. Numerical investigations have been conducted in order to examine the effects of the electronic components thickness and the plate thermal diffusivity on the maximum temperature of electronic components. The percentage contribution of plate heat conduction on the total removed heat and temperature profile in the plate have also been analyzed. Correlations for the nondimensional secured working time (time to reach the threshold temperature, T _cr  = 75°C) and its corresponding melt fraction were derived.     

Numerical investigation on heat transfer of supercritical water in a roughened tube

ABSTRACT

The turbulent mixed convection heat transfer of supercritical water flowing in a vertical tube roughened by V-shaped grooves has been numerically investigated in this paper. The turbulent supercritical water flow characteristics within different grooves are obtained using a validated low-Reynolds number κ-ε turbulence model. The effects of groove angle, groove depth, groove pitch-to-depth ratio, and thermophysical properties on turbulent flow and heat transfer of supercritical water are discussed. The results show that a groove angle γ = 120° presents the best heat transfer performance among the three groove angles. The lower groove depth and higher groove pitch-to-depth ratio suppress the enhancement of heat transfer. Heat transfer performance is significantly decreased due to the strong buoyancy force at T_b = 650.6 K, and heat transfer deterioration occurs in the roughened tube with γ = 120°, e = 0.5 mm, and p/e = 8 in the present simulation. The results also show that the rapid variation in the supercritical water property in the region near the pseudo-critical temperature results in a significant enhancement of heat transfer performance.     

Thermal protection with liquid film in turbulent mixed convection channel flows

In this numerical study, a channel flow of turbulent mixed convection of heat and mass transfer with film evaporation has been conducted. The turbulent hot air flows downward of the vertical channel and is cooled by the laminar liquid film on both sides of the channel with thermally insulated walls. The effect of gas–liquid phase coupling, variable thermophysical properties and film vaporization are considered in the analysis. In the air stream, the k–ε turbulent model has been utilized to formulate the turbulent flow. Parameters used in this study are the mass flow rate of the liquid film B, Reynolds number Re, and the free stream temperature of the hot air T_o. Results show that the heat flux was dramatically increases due to the evaporation of liquid water film. The heat transfer increases as the mass flow rate of the liquid film decreases, while the Reynolds number and inlet temperature increase, and the influences of the Re and T_o are more significant than that of the liquid flow rate. It is also found that liquid film helps lowering the heat and mass transfer rate from the hot gas in the turbulent channel, especially at the downstream.     

Buoyancy-induced flow and heat transfer in a porous annulus between concentric horizontal circular and square cylinders

ABSTRACT

This paper reports on natural convection heat transfer in a porous annulus between concentric horizontal circular and square cylinders. The heated inner circular cylinder is maintained at the uniform hot temperature T_h, whereas the cooled outer square duct is held at the uniform cold temperature T_c. A pressure-based collocated finite-volume method is used to numerically investigate the effects on the total heat transfer of Rayleigh number (Ra), Prandtl number (Pr), Darcy number (Da), porosity (?), and annulus aspect ratio (R/L). Results demonstrate that at low Ra values, conduction is the dominant heat transfer mode. Convection contribution to total heat transfer becomes more important beyond a critical Ra value, which decreases with an increase in Da and/or ?. Furthermore, an increase in the enclosure aspect ratio (R/L) leads to an increase in total heat transfer. A similar behavior is obtained with Prandtl number, where predictions indicate higher heat transfer rates at higher Pr values with its effect increasing as Ra increases. Streamlines and isotherms reveal flow separation for some of the reported cases. Limited computations are also performed for natural convection in a porous annulus between two horizontal concentric circular cylinders having the same inner and outer perimeters as the investigated enclosure. Comparison of the predicted average Nusselt number estimates with similar ones obtained in the original enclosure reveals a large percentage difference in values, demonstrating the strong influence of geometry on natural convection in enclosures.     

Numerical study of nanofluids condensation heat transfer in a square microchannel

ABSTRACT

This paper presents a numerical study of nanofluids condensation heat transfer inside a single horizontal smooth square tube. The numerical results are compared with the previous experimental predictions. The numerical results show that the heat transfer coefficient could be improved within 20% by increasing the volume fraction of Cu nanoparticle by 5% or by increasing the mass flux from 80 to 110 kg/m² s. Reducing the hydraulic diameter of the microchannel from 200 to 160 µm leads to an increase in the condensation average heat transfer coefficient by 10%. A new correlation estimating the Nusselt number for the condensation of nanofluids or pure vapor is proposed. It predicts average condensation heat transfer with a good agreement with those computed.     

Experimental Study on Subcooled Flow Boiling in Horizontal Microtubes and Effect of Heated Length

ABSTRACT

In this study, subcooled flow boiling was investigated in horizontal microtubes. Experiments were conducted using deionized water as the working fluid over a mass flux range of 4000–7000 kg m^?2s^?1 in microtubes with inner and outer diameters of ～600 and ～900 μm, respectively. Microtubes with lengths of 3, 6, and 12 cm were tested to clarify the effect of heated length on flow boiling heat transfer and pressure drop characteristics. A force analysis related to two-phase flow was conducted to understand the effect of forces on bubble dynamics. Pressure drop and heat transfer data in flow boiling were acquired. Experimental heat flux data were compared with partial boiling heat flux correlations, and good agreements were obtained. Pressure drop was larger in longer microtubes in comparison to shorter ones, while higher heat fluxes were obtained in shorter microtubes at the same wall superheat. Two-phase heat transfer coefficient increased with the microtube length due to lower temperature difference between wall temperature and bulk fluid temperature in longer microtubes. Higher heat fluxes achieved in shorter microtubes at the same wall superheat imply higher critical heat fluxes in shorter microtubes.     

Anisotropy Effects on Heat and Fluid Flow by Unsteady Natural Convection and Radiation in Saturated Porous Media

ABSTRACT

This article deals with a numerical study of fluid flow and heat transfer by unsteady natural convection and thermal radiation in a vertical channel opened at both ends and filled with anisotropic, in both thermal conductivity and permeability, fluid-saturated porous medium. The bounding walls of the channel are gray and kept at a constant hot temperature.

In the present study we suppose the validity of the Darcy law for motion and of the local thermal equilibrium assumption. The radiative transfer equation (RTE) is solved by the finite-volume method (FVM). The numerical results allow us to represent the time–space variations of the different state variables. The sensitivity of the fluid flow and the heat transfer to different controlling parameters, namely, the single scattering albedo ω, the temperature ratio R, the anisotropic thermal conductivity ratio R_c, and the anisotropic permeability ratio R_k, are addressed. Numerical results indicate that the controlling parameters of the problem, namely, ω, R, R_c, and R_k, have significant effects on the flow and thermal field behavior and also on the transient process of heating or cooling of the medium. Effects of such parameters on time variations of the volumetric flow rate q_v and the convected heat flux Q at the channel's outlet are also studied.     

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.     

MIXED CONVECTION OVER NONISOTHERMAL HORIZONTAL SURFACES IN A POROUS MEDIUM: THE ENTIRE REGIME”“

ABSTRACT

Flow and heat transfer characteristics of mixed convection from horizontal surfaces in a saturated porous medium are investigated. Two conditions of surface heating were considered, a variable wall temperature (VWT) in the form T_w(x) — T_∞ = axⁿ and a variable surface heat flux (VHF) in the form q_w(x) = bx^m. Two different nonsimilarity parameters for VWT and VHF cases, respectively, due to the nonuniform heating conditions, are found by nondimensionalizing the governing equations. The nonsimilarity parameters cover the entire regime of mixed convection from the pure forced convection limit at X = 1 (or X^* = 1) to the pure free convection limit at X = 0 (or X^* = 0). The resulting transformed governing equations are solved by a finite difference scheme. Numerical results for both VWT and VHT boundary conditions, including velocity and temperature profiles and local Nusselt numbers, are presented for selected values of the exponents n and m. Simple and accurate correlation equations valid for the entire mixed convection regime are also presented for the local and average Nusselt numbers.     

On the Validity of the Isothermal Model for Natural Convection Flow around Blocks Submitted to Volumetric Heat Generation in a Horizontal Channel

This work presents numerical results of natural convection in a horizontal channel provided with heating blocks periodically mounted on its lower adiabatic surface. The upper surface of the channel is maintained cold at a constant temperature. The parameters of the study are the ratio of solid blocks to fluid thermal conductivities (0.1 ≤ k* = k _s /k _a ≤ 200), the Rayleigh number (10⁴ ≤ Ra ≤ 10⁷), and the relative blocks height (1/8 ≤ B ≤ 1/2). Two models are considered in this study depending on whether the blocks are submitted to uniform heat generation (model 1), or maintained isothermal (model 2) at the average temperature calculated using model 1. The effect of the thermal conductivities ratio and the other controlling parameters on the validity of the isothermal model is examined. It is found that when multiple steady solutions are possible, some of the solutions obtained with the isothermal model may not reproduce the results of the model with blocks submitted to volumetric heat generation, even at very large conductivities ratio.     

Heat transfer and pressure drop during HFC refrigerant saturated vapour condensation inside a brazed plate heat exchanger

This paper presents the heat transfer coefficients and the pressure drop measured during HFC refrigerants 236fa, 134a and 410A saturated vapour condensation inside a brazed plate heat exchanger: the effects of saturation temperature (pressure), refrigerant mass flux and fluid properties are investigated. The heat transfer coefficients show weak sensitivity to saturation temperature (pressure) and great sensitivity to refrigerant mass flux and fluid properties. A transition point between gravity controlled and forced convection condensation has been found for a refrigerant mass flux around 20 kg/m²s that corresponds to an equivalent Reynolds number around 1600–1700. At low refrigerant mass flux (G_r < 20 kg/m²s) the heat transfer coefficients are not dependent on mass flux and are well predicted by the Nusselt [20] analysis for vertical surface: the condensation process is gravity controlled. For higher refrigerant mass flux (G_r > 20 kg/m²s) the heat transfer coefficients depend on mass flux and are well predicted by Akers et al. [21] equation: forced convection condensation occurs. In the forced convection condensation region the heat transfer coefficients show a 25–30% increase for a doubling of the refrigerant mass flux.The frictional pressure drop shows a linear dependence on the kinetic energy per unit volume of the refrigerant flow and therefore a quadratic dependence on mass flux.HFC-410A shows heat transfer coefficients similar to HFC-134a and 10% higher than HFC-236fa together with frictional pressure drops 40-50% lower than HFC-134a and 50–60% lower than HFC-236fa.     

Wind Effect on Combined Convection and Surface Radiation Heat Losses of a Fully Open Cylindrical Cavity With Insulation

Wind effect, of both the wind incidence angle and the wind speed, on convection and surface radiation heat losses of a fully open cylindrical cavity with constant bottom wall temperature was numerically investigated. The impacts of cavity tilt angle and wall temperature were also considered. Temperature contours, velocity contours, and vectors inside and around the cavity were presented. The variations of average convection and radiation heat loss Nusselt numbers Nu_c and Nu_r and percentages of heat losses with related parameters (wind speed, wind incidence angle, tilt angle, and bottom wall temperature) were also shown. In the end, correlations about Nu_c and Nu_r for practical applications were proposed. Results show that compared with no-wind condition, Nu_c under a wind condition is almost always higher except for head-on wind with velocity of 1.5 m/s, while Nu_r is always lower. Nu_c varies slightly, while Nu_r increases rapidly as the bottom wall temperature increases. With the existence of wind, the effect of tilt angle on heat transfer becomes more complex. A critical wind direction close to 30° is detected, which maximizes Nu_c and percentage of convective heat loss. The results also demonstrate that wind speed, wind incidence angle, and tilt angle should be considered simultaneously when analyzing heat transfer inside the cavity under a wind condition.     

Laminar free convection from a vertical plate with uniform surface heat flux in chemically reacting systems

Two-dimensional steady laminar free convection from a vertical plate with uniform surface heat flux rate is studied in a gas where a reversible very fast reaction of dissociation A↔2B takes place at atmospheric pressure. The effective thermophysical properties of the gas in the interval of dissociation are evaluated and the governing boundary-layer equations are solved numerically by a finite-difference method with control volume formulation for a wide range of values of the independent variables which have a significant influence on the phenomenon. In the case of undisturbed fluid temperature T_∞ smaller than T_0.5, corresponding to a rate of dissociation α=0.5, three different heat transfer regimes, marked by two critical heat fluxes, may be distinguished as the surface heat flux rate increases. The theoretical results obtained for the critical heat fluxes as well as the coefficient of convection are expressed in terms of correlations among dimensionless parameters defined through the mixture effective properties.