Effect of Kapitza resistance on standing surface waves in superfluid helium

We analyze theoretically the resonant frequencies of standing surface waves produced by second sound in⁴He. In particular, we show that an empirical heat transfer coefficient involved in a recently proposed boundary condition can be related to Kapitza resistance. We also calculate the heat flux within the helium and deduce that the height of the surface waves is strongly frequency dependent.     

Coupling of rayleigh-like waves with zero-sound modes in normal3He

The Landau kinetic equation is solved in the collisionless regime for a sample of normal³He excited by a surface perturbation of arbitrary ω andk. The boundary condition for the nonequilibrium particle distribution is determined for the case of specular reflection of the elementary excitations at the interface. Using the above solution, the energy flux through the boundary is obtained as a function of the surface wave velocity ω/k. The absorption spectrum and its frequency derivative are calculated numerically for typical values of temperature and pressure. The spectrum displays a sharp, resonant-like maximum concentrated at the longitudinal sound velocity and a sharp maximum of the derivative concentrated at the transverse sound velocity. The energy transfer is cut off discontinuously below the Fermi velocity. An experimental measurement of the energy transfer spectrum would permit a determination of both zero-sound velocities and the Fermi velocity with spectroscopic precision.     

Cylindrical standing surface waves in superfluid helium

A theoretical analysis is given of the resonant frequencies of standing surface waves produced in a cylinder filled with superfluid⁴He. In particular, it is shown that a heat transfer coefficient involved in a recently proposed empirical boundary condition can be related to the Kapitza resistance.     

Effect of boundary conditions on the heat transfer law for a turbulent boundary layer

The heat transfer at an impermeable plate has been experimentally investigated under various boundary conditions. The conservativeness of the heat transfer law St₀=f(Re _T ^** ) is demonstrated for a monotonic increase of temperature and heat flux along the surface.     

Kapitza conductance model using loaded acoustic surface waves

An investigation is presented of the heat transfer between liquid helium and solids associated with surface impurities or faults. The solid is described as a linear chain which is terminated by a matched dissipating element, formed by an impurity, which excites loaded acoustic surface waves (loaded Rayleigh waves). Using established theoretical and experimental results on the behavior of acoustic surface waves on a solid-to-helium interface, a heat transfer coefficient is calculated. Suggestions are made on the interpretation of some outstanding problems in Kapitza work in the light of the present model.Supported by the SRC in the form of research grants.     

Effects of flow and colony morphology on the thermal boundary layer of corals

The thermal microenvironment of corals and the thermal effects of changing flow and radiation are critical to understanding heat-induced coral bleaching, a stress response resulting from the destruction of the symbiosis between corals and their photosynthetic microalgae. Temperature microsensor measurements at the surface of illuminated stony corals with uneven surface topography (Leptastrea purpurea and Platygyra sinensis) revealed millimetre-scale variations in surface temperature and thermal boundary layer (TBL) that may help understand the patchy nature of coral bleaching within single colonies. The effect of water flow on the thermal microenvironment was investigated in hemispherical and branching corals (Porites lobata and Stylophora pistillata, respectively) in a flow chamber experiment. For both coral types, the thickness of the TBL decreased exponentially from 2.5 mm at quasi-stagnant flow (0.3 cm s⁻¹), to 1 mm at 5 cm s⁻¹, with an exponent approximately 0.5 consistent with predictions from the heat transfer theory for simple geometrical objects and typical of laminar boundary layer processes. Measurements of mass transfer across the diffusive boundary layer using O₂ microelectrodes revealed a greater exponent for mass transfer when compared with heat transfer, indicating that heat and mass transfer at the surface of corals are not exactly analogous processes.     

Laminar forced convection in wedge flow with separation

Abstract

A perturbation method is used to study the steady and unsteady laminar boundary layer heat transfer from a wedge with separation for a step‐discontinuity in the surface temperature. The analytic solutions obtained can be used to calculate the steady and unsteady heat transfer rate with arbitrary surface temperature. The effects of the Prandtl number on the temperature distribution and the heat transfer rate are discussed in detail. The solution is valid for large or moderate Prandtl number.     

Calculation of radiative-convective heat transfer in the combustor of diesel engine

An integral method is suggested for the calculation of local heat transfer in the cylinder of diesel engine in view of radiation-convection interaction. The turbulent boundary layer is investigated on the combustor surface of arbitrary curvature subjected to the flow of a working medium which radiates and absorbs thermal energy. The thermal radiation transfer is described within the Schwarzschild model. Integral relations of boundary layer are used for solving equations of complex heat transfer. The integral characteristics of radiative heat transfer in the combustor of a diesel engine are determined (emissivity factor of the working medium, Bouguer and Boltzmann numbers, attenuation factor, and coefficient allowing for the diffuseness of radiation). The calculated values of local radiative-convective heat flux on the combustor surface are in good agreement with the experimental data obtained in a high-speed diesel engine under conditions of bench tests.     

Heat transfer and icing of a rough cylinder

Heat transfer from a rough ice surface to air is a fundamental factor determining the icing rate and ice shape on an object under conditions where the impinging water flux exceeds the icing rate. In order to examine the effect of the roughness characteristics on icing, a boundary-layer model of heat transfer from a front half of a rough circular cylinder is proposed. The model is based on the integral equations of the boundary layer, and predicts the local heat transfer coefficient along the cylinder surface and, subsequently, the overall heat transfer rate. Comparison between the results of the model and the available experimental data for three different roughnesses in the cylinder Reynolds number range 5 × 10⁴ < Re < 4 × 10⁶ show that the model simulates the heat transfer more precisely than the previous formulations used in icing models.     

Buoyancy effects on the laminar boundary layer heat transfer along vertically moving cylinders

Abstract

The effects of buoyancy forces on the laminar boundary layer flow and heat transfer along vertically moving cylinders are analyzed for the cases of prescribed surface temperature and prescribed wall heat flux in power of streamwise distance. Local similarity solutions are obtained to show the effects of buoyancy parameters and the transverse curvature of the cylinder on the surface friction and heat transfer rate.     

Conjugate problem of heat transfer in a laminar boundary layer with injection

The author examines two conjugate problems of heat transfer in the laminar boundary layer at the boundary of a semi-infinite porous medium on the assumption that fluid filters continuously through the porous surface and that the injection velocity varies as x^–1/2, where x is the distance in the direction of flow.     

Non-axial-symmetric thermal stresses in circular discs or cylinders

A solution is presented for the computation of the transient thermoelastic stresses in a hollow cylinder with temperature boundary conditions given as a circumferential variation of surface heat transfer coefficient. The temperature distribution is solved explicitly. The problem is set up using the Airy stress function which leads to the biharmonic equation. This approach requires the satisfaction of three Michell integrals at the inner boundary in order to ensure single-valued displacements and rotation. An iterative method is described in which these integrals are all simultaneously satisfied and thus provide the necessary non-zero boundary conditions for the solution of the biharmonic equation which is rapidly solved by Gaussian elimination. Results are presented for the general case where the temperature is a function of r and θ. The computer program is checked by assuming a constant value of the surface heat transfer coefficients. In this case a closed form solution is obtained.     

Heat exchange processes near the boundary of a film boiling nucleus

Results are presented of an experimental investigation of the change in temperature, heat flux to the liquid, and rate of displacement of the isotherms near a film boiling nucleus propagating over a plane surface. The experiment was carried out in a liquid nitrogen bath at atmospheric pressure on the saturation line. The heater was a sapphire plate 1.2 mm thick having a heat transfer surface area of 77×22 mm². The following facts were established: 1) near the boundary of the film boiling nucleus a new heat exchange mechanism takes place caused by the instability of the liquid microlayer; 2) the maximum heat flux to the liquid is considerably greater than the critical heat flux; 3) the vapor film in the film boiling region grows gradually with increasing distance from the boundary, i.e., there is a smooth transition in terms of heat exchange intensity before the equilibrium film boiling level is reached. Pis’ma Zh. Tekh. Fiz. 25, 39–46 (November 12, 1999)     

Free convection of a heat generating fluid in a hemispherical closed volume

From a theoretical analysis and results of previous studies, a model of the free convection of a heat-generating fluid in a hemispherical closed volume with a completely isothermal boundary is developed. By applying analytical estimates, we establish that at values of modified Rayleigh numbers Ra₁ > 10¹³, the flow in the entire volume is turbulent, which substantially simplifies the problem. Integrated relations for heat emission through the upper and lower parts of the boundary of the hemispherical capacity are obtained as a result. Results of numerical calculations have shown that the majority of heat is removed through the spherical surface downwards. The ratio of the heat flux through the upper horizontal boundary to heat flux through the lower boundary decreases from 0.5 to 0.3 in the range of modified Rayleigh numbers Ra_I from 10⁹ to 10¹⁷.     

Some problems of heat conduction with phase transitions

An approximation of the problem of heating of a body by a surface heat flux of density 10⁷–10¹⁴ W/m₂ is presented. Expressions are obtained for calculating the movement of the melting boundary and external destruction boundary and temperature conditions on the surface.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 3, pp. 497–504, March, 1971.     

Magnetic coupling contributions to the thermal boundary resistance between3He and metals

In a recent experiment, Perry, DeConde, Sauls, and Stein found a thermal boundary resistance between³He and platinum that was inversely proportional to temperature and decreased with application of a magnetic field. These authors suggested an explanation of the experimental observations in terms of a hyperfine contact interaction between the helium nuclear spins in the first surface monolayer and the conduction electrons of the metal. In the present work the magnetic coupling between the electron-nuclear spin systems is investigated for the contact interaction using a realistic representation of the metallic spin susceptibility at the helium site. The longer range dipole interaction is also considered and results for copper, silver, gold, and platinum indicate that both magnetic coupling mechanisms are orders of magnitude too weak to account for experimentally observed heat transfer rates. The much larger heat transfer rate obtained by Perryet al. is traced to their overestimation of the conduction electron local density of states at the helium site.     

Air-side heat transfer enhancement of a refrigerator evaporator using vortex generation

In most domestic and commercial refrigeration systems, frost forms on the air-side surface of the air-to-refrigerant heat exchanger. Frost-tolerant designs typically employ a large fin spacing in order to delay the need for a defrost cycle. Unfortunately, this approach does not allow for a very high air-side heat transfer coefficient, and the performance of these heat exchangers is often air-side limited. Longitudinal vortex generation is a proven and effective technique for thinning the thermal boundary layer and enhancing heat transfer, but its efficacy in a frosting environment is essentially unknown. In this study, an array of delta-wing vortex generators is applied to a plain-fin-and-tube heat exchanger with a fin spacing of 8.5 mm. Heat transfer and pressure drop performance are measured to determine the effectiveness of the vortex generator under frosting conditions. For air-side Reynolds numbers between 500 and 1300, the air-side thermal resistance is reduced by 35–42% when vortex generation is used. Correspondingly, the heat transfer coefficient is observed to range from 33 to 53 W m⁻² K⁻¹ for the enhanced heat exchanger and from 18 to 26 W m⁻² K⁻¹ for the baseline heat exchanger.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.     

Forced convection heat transfer to liquid helium I in the nucleate boiling region

Heat transfer and critical heat fluxes to helium boiling in a 2 mm id copper tube (100 mm long) were measured in the pressure range 1.1–1.5 atm and at mass velocities 18–96 kg m^?2s^?1. Corresponding Reynolds numbers are (1.2–6.2) × 10⁴. Experimentally obtained heat transfer coefficients show satisfactory agreement with those calculated according to the Kutateladze equation but with less pronounced pressure dependence. It was found that in the boiling region developed quality did not influence the heat transfer coefficient. An expression was obtained, which describes with ±10% error, the dependence of critical heat flux on mass flow rate in the pressure range 1.1–1.5 atm and mass quality 0.33–0.6.     

Three-dimensional fundamental solutions for transient heat transfer by conduction in an unbounded medium,half-space,slab and layered media

This paper presents analytical Green's functions for the transient heat transfer phenomena by conduction, for an unbounded medium, half-space, slab and layered formation when subjected to a point heat source. The transient heat responses generated by a spherical heat source are computed as Bessel integrals, following the transformations proposed by Sommerfeld [Sommerfeld A. Mechanics of deformable bodies. New York: Academic Press; 1950; Ewing WM, Jardetzky WS, Press F. Elastic waves in layered media. New York: McGraw-Hill; 1957]. The integrals can be modelled as discrete summations, assuming a set of sources equally spaced along the vertical direction. The expressions presented here allow the heat field inside a layered formation to be computed without fully discretizing the interior domain or boundary interfaces.The final Green's functions describe the conduction phenomenon throughout the domain, for a half-space and a slab. They can be expressed as the sum of the heat source and the surface terms. The surface terms need to satisfy the boundary conditions at the surfaces, which can be of two types: null normal fluxes or null temperatures. The Green's functions for a layered formation are obtained by adding the heat source terms and a set of surface terms, generated within each solid layer and at each interface. These surface terms are defined so as to guarantee the required boundary conditions, which are: continuity of temperatures and normal heat fluxes between layers.This formulation is verified by comparing the frequency responses obtained from the proposed approach with those where a double-space Fourier transformation along the horizontal directions [Tadeu A, António J, Simões N. 2.5D Green's functions in the frequency domain for heat conduction problems in unbounded, half-space, slab and layered media. CMES: Computer Model Eng Sci 2004;6(1):43–58] is used. In addition, time domain solutions were compared with the analytical solutions that are known for the case of an unbounded medium, a half-space and a slab.