Numerical modeling of pin–fin micro heat exchangers

A micro heat exchanger (MHE) can effectively control the temperature of surfaces in high heat flux applications. In this study, several turbulence models are analyzed using a 3D finite element model of a MHE. The MHE consists of a narrow planar flow passage between flat parallel plates with small cylindrical pin fins spanning these walls. The pin fin array geometry investigated is staggered, with pin diameters of 0.5, 5.1 and 8.5 mm, height to diameter ratio of 1.0 and streamwise (longitudinal) and spanwise (transverse) to diameter ratios of 1.5 and 2.5, respectively. Pressure loss and heat transfer simulated results for 4,000 ≤ Re ≤ 50,000 are reported and compared with previously published numerical and experimental results. It was found that the flat micro pin fin overall thermal performance always exceeds that of the parallel plate counterpart (smooth channel) by a factor of as much as 2.2 for the 8.5 mm diameter pins, and by 4 for the 0.5 mm diameter pins in the investigated Reynolds number range. Further, among the six turbulence models investigated, the RNG model tends to be the best model to predict both the Nusselt number and the friction factor and capture the main feature of the flow field in MHE.     

Third heat‐transfer crisis with stepwise heat supply

The paper reports experimental results on heattransfer crises with stepwise heat supply to a heater, in which the metastable liquid decomposes in the form of vaporization fronts. Data on the dynamics of heattransfer crises under saturation and underheating conditions are given. It is shown that below the vapor formed during propagation of vaporization fronts, a liquid microlayer is absent.     

Effect of heat flow on heat‐transfer characteristics for a supersonic spatial flow around a spherically blunted cone

Heattransfer processes for a supersonic spatial flow around a spherically blunted cone were studied by solving direct and inverse threedimensional problems taking into account heat flow along the longitudinal and circumferential coordinates. It is shown that highly heatconducting materials can be used to advantage to decrease the maximum temperatures on the windward side of streamline bodies.     

Wiener–Hopf solution of rewetting of an infinite cylinder with internal heat generation

The two-dimensional quasi-steady conduction equation governing conduction controlled rewetting of an infinite cylinder with heat generation has been solved by Wiener–Hopf technique. The analytical solution yields the quench front temperature as a function of various model parameters such as Peclet number, Biot number and dimensionless heat generation rate. Also, the dry out heat generation rate is obtained by setting the Peclet number equal to zero, which gives the maximum permissible heat generation so as to prevent the dry out of the coolant.     

Effects of heat flux on λ-transition in liquid 4He

This paper is concerned with the derivation of a phase field model for λ-transition in ⁴He, when the liquid is subject to pressure and heat flux. As parameter that controls the transition, a field f that is the geometrical mean between the density of the fluid and that of the superfluid is used. The resulting model, that is a generalization of previous papers on the same subject, chooses as field variables the density, the velocity, the temperature and the heat flux, in addition to this field f. The restrictions on the constitutive quantities are obtained by using the Liu method of Lagrange multipliers. New results with respect to previous models are the presence of non-local terms to describe inhomogeneities in the field variables and dissipative effects of mechanical and thermal origin, and the fact that the model describes the behaviour of the liquid also far from the λ-transition region.     

Experimental study on the heat transfer and pressure drop of a cross-flow heat exchanger with different pin–fin arrays

In this study, convective heat transfer and pressure drop in a cross-flow heat exchanger with hexagonal, square and circular (HSC) pin–fin arrays were studied experimentally. The pin–fins were arranged in an in-line manner. For the applied conditions, the optimal spacing of the pin–fin in the span-wise and stream-wise directions has been determined. The variable parameters are the relative longitudinal pitch (S _L /D = 2, 2.8, 3.5), and the relative transverse pitch was kept constant at S _T /D = 2. The performances of all pin–fins were compared with each other. The experimental results showed that the use of hexagonal pin–fins, compared to the square and circular pin–fins, can lead to an advantage in terms of heat transfer enhancement. The optimal inter-fin pitches are provided based on the largest Nusselt number under the same pumping power, while the optimal inter-fin pitches of hexagonal pin–fins are S _T /D = 2 and S _L /D = 2.8. Empirical equations are derived to correlate the mean Nusselt number and friction coefficient as a function of the Reynolds number, pin–fin frontal surface area, total surface area, and total number. Consequently, the general empirical formula is given in the present form.

Effects of heat and mass transfer peristaltic flow of?Williamson fluid in a vertical annulus

In the present investigation, we have studied the effects of mixed convection heat and mass transfer on peristaltic flow of Williamson fluid model in a vertical annulus. The governing equations of Williamson fluid model are simplified using the assumptions of long wavelength and low Reynold’s number. An approximated analytical and numerical solutions are found for the velocity field using (i) Perturbation method (ii) Shooting method. The comparisons of analytical and numerical solutions have been presented. The expressions for pressure rise, velocity against various physical parameter are discussed through graphs.     

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation （absorption）

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.     

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.     

Hydrodynamics and heat transfer characteristics of G–S magnetically stabilized beds consisting of admixtures of shale oil and magnetic particles

The hydrodynamic and heat transfer behavior of a bed consisting of magnetic and shale oil particle admixtures under the effect of a transverse magnetic field is investigated. The phase diagram, bed void fraction are studied under wide range of the operating conditions i.e., gas velocity, magnetic field intensity and fraction of the magnetic particles. It is found that the range of the stabilized regime is reduced as the magnetic fraction decreases. In addition, the bed voidage at the onset of fluidization decreases as the magnetic fraction decreases. On the other hand, Nusselt number and consequently the heat transfer coefficient is found to increase as the magnetic fraction decreases. An empirical equation is investigated to relate the effect of the gas velocity, magnetic field intensity and fraction of the magnetic particles on the heat transfer behavior in the bed.     

Forced convective heat transfer from premixed flames —Part 2: Impingement heat transfer

A study of convective heat transfer from impinging flames is completed with the presentation of heat transfer rates measured in premixed methane-air flames. Unburnt gas equivalence ratios from 0.8 to 1.2 have been examined, with burner exit Reynolds numbers ranging from 2000 to 12 000. Heat fluxes measured at the stagnation point of a body of revolution and a circular cylinder demonstrate that the trends observed in measured heat flux profiles are mainly determined by variations in the mean velocity and temperature within a flame, with peak heat transfer rates occuring within or close to the flame reaction zone. Increases in Reynolds number lead to an increase in the peak heat flux attained within a flame and to a decrease in the axial extent of the flame equilibrium region. Variations in equivalence ratio away from approximately stoichiometric conditions lead to a decrease in the maximum rate of heat transfer from a flame and to a shifting of the position of maximum flux downstream. Theoretical predictions applicable to the equilibrium region of the flames are in reasonable accord with experimental data.     

Lattice Boltzmann simulation of the effects of cavity structures and heater thermal conductivity on nucleate boiling heat transfer

The boiling heat transfer technology with cavity surfaces can provide higher heat flux under lower wall superheat, which is of great significance for the cooling of electronic chips and microelectromechanical devices. In this paper, the boiling characteristics of the cavity surfaces are investigated based on the lattice Boltzmann(LB) method, focusing on the effects of cavity shapes, sizes, and heater thermal conductivity on the heat transfer performance. The results show that the triangular cavi...     

Determination of thermal conductivities of Sn–Zn lead-free solder alloys with radial heat flow and Bridgman-type apparatus

The variations of thermal conductivities of solid phases versus temperature for pure Sn, pure Zn and Sn–9 wt.% Zn, Sn–14 wt.% Zn, Sn–50 wt.% Zn, Sn–80 wt.% Zn binary alloys were measured with a radial heat flow apparatus. The thermal conductivity ratios of liquid phase to solid phase for the pure Sn, pure Zn and eutectic Sn–9 wt.% Zn alloy at their melting temperature are found with a Bridgman-type directional solidification apparatus. Thus, the thermal conductivities of liquid phases for pure Sn, pure Zn and eutectic Sn–9 wt.% Zn binary alloy at their melting temperature were evaluated by using the values of solid phase thermal conductivities and the thermal conductivity ratios of liquid phase to solid phase.     

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.     

The pressure drop characteristics of air–water bubbling flow for evaporative heat transfer

This paper presents a study on a novel water bubbling layer pressure drop and heat transfer experiment that was conducted to investigate the characteristics of pressure drop of air flow across the water bubbling layer. The attempt was to reduce the pressure drop while maintaining a higher value of the heat transfer coefficient. This type of heat transfer between water and merged tubes has potential application in evaporative cooling. To achieve the goal the pressure drop should be reduced by decreasing the bubble layer thickness through the water pump circulation. Pressure drops of air passing through the perforated plate and the water bubbling layer were measured for different heights of water bubbling layer, hole-plate area ratio of the perforated plate and the air velocity through the holes. Experimental data show that the increase of water bubbling layer height and air velocity both increase the pressure drop while the effect of the hole-plate area ratio of the perforated plate on the heat transfer coefficient is relatively complex. The measurements showed that even at a considerably lower height of water bubbling layer the heat transfer coefficient can exceed 5,000 W/m²-K. The heat transfer coefficients of 30 mm high water bubbling layer are higher than that of other higher water bubbling layers tested in the experiments     

Effect of periodic heat transfer on the transient thermal behavior of a convective-radiative fully wet porous moving trapezoidal fin

A moving trapezoidal profiled convective-radiative porous longitudinal fin wetted in a single-phase fluid is considered in the current article. The periodic variation in the fin base temperature is taken into account along with the temperature sensitive thermal conductivity and convective heat transfer coefficients. The modeled problem, which is resolved into a non-linear partial differential equation(PDE), is made dimensionless and solved by employing the finite difference method(FDM). The resu...     

Experimental investigation on heat transfer of forced convection condensation of ethanol–water vapor mixtures on a vertical mini-tube

In this paper, condensation heat transfer characteristics of ethanol–water vapor mixtures on a vertical mini-vertical tube with 1.221 mm outside diameter were investigated experimentally. The experiments were performed at different velocities and pressures over a wide range of ethanol mass fractions in vapor. The test results indicated that, with respect to the change of the vapor-to-surface temperature difference, the condensation curves of the heat transfer coefficients revealed nonlinear characteristics, and had peak values. At 2 % ethanol mass fraction in vapor, the condensation heat transfer coefficient value of the ethanol–water vapor mixture was found to have a maximum heat transfer coefficient of 50 kW m^?2 K^?1, which was 3–4 times than that of pure steam. The condensation heat transfer coefficients decreased with increased ethanol mass fraction in vapor. The vapor pressure and vapor velocity had a positive effect on the condensation heat transfer coefficients of ethanol–water vapor mixtures.     

Experimental study of the condensation heat transfer characteristics of CO2 in a horizontal microfin tube with a diameter of 4.95?mm

The condensation heat transfer characteristics for CO₂ flowing in a horizontal microfin tube were investigated by experiment with respect to condensation temperature and mass flux. The test section consists of a 2,400?mm long horizontal copper tube of 4.6?mm inner diameter. The experiments were conducted at refrigerant mass flux of 400–800?kg/m²s, and saturation temperature of 20–30?°C. The main experimental results showed that annular flow was highly dominated the majority of condensation flow in the horizontal microfin tube. The condensation heat transfer coefficient increases with decreasing saturation temperature and increasing mass flux. The experimental data were compared against previous heat transfer correlations. Most correlations failed to predict the experimental data. However, the correlation by Cavallini et al. showed relatively good agreement with experimental data in the microfin tube. Therefore, a new condensation heat transfer correlation is proposed with mean and average deviations of 3.14 and ?7.6?%, respectively.     

Flow and heat transfer of a slightly rarefied gas over a stretching surface

This work deals with the study of the boundary layer flow and mass transfer of a visco-elastic fluid immersed in a porous medium over a stretching surface in the presence of surface slip, chemical reaction and variable viscosity. The partial differential equations governing the flow have been transformed by similarity transformation into a system of coupled nonlinear ordinary differential equations which is solved numerically by means of the fourth order Runge-Kutta integration scheme coupled with the shooting technique. The effects of various involved interesting parameters on the velocity fields and concentration fields are shown graphically and investigated. In addition, tabulated results for the local skin-friction coefficient and the local Sherwood number are presented and discussed.