Prediction of bubble growth rates and departure volumes in nucleate boiling at isolated sites

A model has been developed to predict heat transfer rates and sizes of bubbles generated during nucleate pool boiling. This model assumes conduction and a natural convective heat transfer mechanism through the liquid layer under the bubble and transient conduction from the bulk liquid. The temperature of the bulk liquid in the vicinity of the bubble is obtained by assuming a turbulent natural convection process from the hot plate to the liquid bulk. The shape of the bubble is obtained by equilibrium analysis. The bubble departure condition is predicted by a force balance equation. Good agreement has been found between the bubble radii predicted by the present theory and the ones obtained experimentally.

Free convection heat transfer from vertical cylinders part I: Power law surface temperature variation

This paper reports on the investigations of laminar free convection heat transfer from vertical cylinders and wires whose surface temperature varies along the height according to the relation TW - T∞ = Nxn. The set of boundary layer partial differential equations and the boundary conditions are transformed to a more amenable form and solved by the process of successive substitution. Numerical solutions of the first approximated equations (two-point nonlinear boundary value type of ordinary differential equations) bring about the major contribution to the problem (about 95%), as seen from the solutions of higher approximations. The results reduce to those for the isothermal case when n=0. Criteria for classifying the cylinders into three broad categories, viz., short cylinders, long cylinders and wires, have been developed. For all values of n the same criteria hold. Heat transfer correlations obtained for short cylinders (which coincide with those of flat plates) are checked with those available in the literature. Heat transfer and fluid flow correlations are developed for all the regimes.

Free convection heat transfer from vertical cylinders part II: Exponential surface temperature variation

Investigation on laminar free convection heat transfer from vertical cylinders and wires having a surface temperature variation of the form TW - T∞ = M emx are presented. As in Part I for power law surface temperature variation, the axisymmetric boundary layer equations of mass, momentum and energy are transformed to more convenient forms and solved numerically. The second approximation refines the results of the first upto a maximum of only 2%. Analysis of the results indicates that cylinders can be classified into the same three categories as in Part I, namely, short cylinders, long cylinders, and wires, heat transfer and fluid flow correlations being developed for each case.

Double diffusive unsteady free convection on two-dimensional and axisymmetric bodies in a porous medium

The unsteady laminar free convection flow of an incompressible electrically conducting fluid over two-dimensional and axisymmetric bodies embedded in a highly porous medium with an applied magnetic field has been studied. The unsteadiness in the flow field is caused by the variation of the wall temperature and concentration with time. The coupled nonlinear partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. It is observed that the skin friction, heat transfer and mass transfer increase with the permeability parameter but decrease with the magnetic parameter. The results are strongly dependent on the variation of wall temperature and concentration with time. The skin friction and heat transfer increase or decrease as the buoyancy forces from species diffusion assist or oppose the thermal buoyancy force. However, the mass transfer is found to be higher for small values of the ratio of the buoyancy parameters than for large values

Unsteady mixed convection with double diffusion over a horizontal cylinder and a sphere within a porous medium

The combined effects of the permeability of the medium, magnetic field, buoyancy forces and dissipation on the unsteady mixed convection flow over a horizontal cylinder and a sphere embedded in a porous medium have been studied. The nonlinear coupled partial differential equations with three independent variables have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The skin friction, heat transfer and mass transfer increase with the permeability of the medium, magnetic field and buoyancy parameter. The heat and mass transfer continuously decrease with the stream-wise distance, whereas the skin friction increases from zero, attains a maximum and then decreases to zero. The skin friction, heat transfer and mass transfer are significantly affected by the free stream velocity distribution. The effect of dissipation parameter is found to be more pronounced on the heat transfer than on the skin friction and mass transfer

Unsteady mixed convection over two-dimensional and axisymmetric bodies

The unsteady laminar incompressible mixed convection flow over a two-dimensional body (cylinder) and an axisymmetric body (sphere) has been studied when the buboyancy forces arise from both thermal and mass diffusion and the unsteadiness in the flow field is introduced by the time dependent free stream velocity. The nonlinear partial differential equations with three independent variables governing the flow have been solved numerically using an implicit finite-difference scheme in combination with the quasilinearization technique. The results indicate that for the thermally assisting flow the local skin friction, heat transfer and mass diffusion are enhanced when the buoyancy force from mass diffusion assists the thermal buoyancy force. But this trend is opposite for the thermally opposing flow. The point of zero skin friction moves upstream due to unsteadiness. No singularity is observed at the point of zero skin friction for unsteady flow unlike steady flow. The flow reversal is observed after a certain instant of time. The velocity overshoot occurs for assisting flows.

Unsteady free convection flow over an infinite vertical porous plate due to the combined effects of thermal and mass diffusion, magnetic field and Hall currents

The unsteady free convection flow over an infinite vertical porous plate, which moves with time-dependent velocity in an ambient fluid, has been studied. The effects of the magnetic field and Hall current are included in the analysis. The buoyancy forces arise due to both the thermal and mass diffusion. The partial differential equations governing the flow have been solved numerically using both the implicit finite difference scheme and the difference-differential method. For the steady case, analytical solutions have also been obtained. The effect of time variation on the skin friction, heat transfer and mass transfer is very significant. Suction increases the skin friction coefficient in the primary flow, and also the Nusselt and Sherwood numbers, but the skin friction coefficient in the secondary flow is reduced. The effect of injection is opposite to that of suction. The buoyancy force, injection and the Hall parameter induce an overshoot in the velocity profiles in the primary flow which changes the velocity gradient from a negative to a positive value, but the magnetic field and suction reduce this velocity overshoot.

Effect of natural convection on oscillating flow in a pipe with cryogenic temperature difference across the ends

The effect of natural convection on the oscillatory flow in an open-ended pipe driven by a timewise sinusoidally varying pressure at one end and subjected to an ambient-to-cryogenic temperature difference across the ends, is numerically studied. Conjugate effects arising out of the interaction of oscillatory flow with heat conduction in the pipe wall are taken into account by considering a finite thickness wall with an insulated exterior surface. Two cases, namely, one with natural convection acting downwards and the other, with natural convection acting upwards, are considered. The full set of compressible flow equations with axissymmetry are solved using a pressure correction algorithm. Parametric studies are conducted with frequencies in the range 5-15 Hz for an end-to-end temperature difference of 200 and 50 K. Results are obtained for the variation of velocity, temperature. Nusselt number and the phase relationship between mass flow rate and temperature. It is found that the Rayleigh number has a minimal effect on the time averaged Nusselt number and phase angle. However, it does influence the local variation of velocity and Nusselt number over one cycle. The natural convection and pressure amplitude have influence on the energy flow through the gas and solid. (C) 2011 Elsevier Ltd. All rights reserved.

Effect of interfacial heat transfer on the onset of oscillatory convection in liquid bridge

In present study, effect of interfacial heat transfer with ambient gas on the onset of oscillatory convection in a liquid bridge of large Prandtl number on the ground is systematically investigated by the method of linear stability analyses. With both the constant and linear ambient air temperature distributions, the numerical results show that the interfacial heat transfer modifies the free-surface temperature distribution directly and then induces a steeper temperature gradient on the middle part of the free surface, which may destabilize the convection. On the other hand, the interfacial heat transfer restrains the temperature disturbances on the free surface, which may stabilize the convection. The two coupling effects result in a complex dependence of the stability property on the Biot number. Effects of melt free-surface deformation on the critical conditions of the oscillatory convection were also investigated. Moreover, to better understand the mechanism of the instabilities, rates of kinetic energy change and "thermal" energy change of the critical disturbances were investigated (C) 2009 Elsevier Ltd. All rights reserved.

The study of flow and temperature fields in conducting droplets suspended in a DC/AC combination field

Electromagnetic Levitation (EML) is a valuable method for measuring the thermo-physical properties of metals - surface tensions, viscosity, thermal/electrical conductivity, specific heat, hemispherical emissivity, etc. – beyond their melting temperature. In EML, a small amount of the test specimen is melted by Joule heating in a suspended AC coil. Once in liquid state, a small perturbation causes the liquid envelope to oscillate and the frequency of oscillation is then used to compute its surface tension by the well know Rayleigh formula. Similarly, the rate at which the oscillation is dampened relates to the viscosity. To measure thermal conductivity, a sinusoidally varying laser source may be used to heat the polar axis of the droplet and the temperature response measured at the polar opposite – the resulting phase shift yields thermal conductivity. All these theoretical methods assume that convective effects due to flow within the droplet are negligible compared to conduction, and similarly that the flow conditions are laminar; a situation that can only be realised under microgravity conditions. Hence the EML experiment is the method favoured for Spacelab experiments (viz. TEMPUS). Under terrestrial conditions, the full gravity force has to be countered by a much larger induced magnetic field. The magnetic field generates strong flow within the droplet, which for droplets of practical size becomes irrotational and turbulent. At the same time the droplet oscillation envelope is no longer ellipsoidal. Both these conditions invalidate simple theoretical models and prevent widespread EML use in terrestrial laboratories. The authors have shown in earlier publications that it is possible to suppress most of the turbulent convection generated in the droplet skin layer, through use of a static magnetic field. Using a pseudo-spectral discretisation method it is possible compute very accurately the dynamic variation in the suspended fluid envelope and simultaneously compute the time-varying electromagnetic, flow and thermal fields. The use of a DC field as a dampening agent was also demonstrated in cold crucible melting, where suppression of turbulence was achieved in a much larger liquid metal volume and led to increased superheat in the melt and reduction of heat losses to the water-cooled walls. In this paper, the authors describe the pseudo-spectral technique as applied to EML to compute the combined effects of AC and DC fields, accounting for all the flow-induced forces acting on the liquid volume (Lorentz, Maragoni, surface tension, gravity) and show example simulations.

Nanofluids development and characterization for heat exchanging intensification

A desmaterialização da economia é um dos caminhos para a promoção do desenvolvimento sustentável na medida em que elimina ou reduz a utilização de recursos naturais, fazendo mais com menos. A intensificação dos processos tecnológicos é uma forma de desmaterializar a economia. Sistemas mais compactos e mais eficientes consomem menos recursos. No caso concreto dos sistemas envolvendo processo de troca de calor, a intensificação resulta na redução da área de permuta e da quantidade de fluido de trabalho, o que para além de outra vantagem que possa apresentar decorrentes da miniaturização, é um contributo inegável para a sustentabilidade da sociedade através do desenvolvimento científico e tecnológico. O desenvolvimento de nanofluidos surge no sentido de dar resposta a estes tipo de desafios da sociedade moderna, contribuindo para a inovação de produtos e sistemas, dando resposta a problemas colocados ao nível das ciências de base. A literatura é unânime na identificação do seu potencial como fluidos de permuta, dada a sua elevada condutividade, no entanto a falta de rigor subjacente às técnicas de preparação dos mesmos, assim como de um conhecimento sistemático das suas propriedades físicas suportado por modelos físico-matemáticos devidamente validados levam a que a operacionalização industrial esteja longe de ser concretizável. Neste trabalho, estudou-se de forma sistemática a condutividade térmica de nanofluidos de base aquosa aditivados com nanotubos de carbono, tendo em vista a identificação dos mecanismos físicos responsáveis pela condução de calor no fluido e o desenvolvimento de um modelo geral que permita com segurança determinar esta propriedade com o rigor requerido ao nível da engenharia. Para o efeito apresentam-se métodos para uma preparação rigorosa e reprodutível deste tipo de nanofluido assim como das metodologias consideradas mais importantes para a aferição da sua estabilidade, assegurando deste modo o rigor da técnica da sua produção. A estabilidade coloidal é estabelecida de forma rigorosa tendo em conta parâmetros quantificáveis como a ausência de aglomeração, a separação de fases e a deterioração da morfologia das nanopartículas. Uma vez assegurado o método de preparação dos nanofluídos, realizou-se uma análise paramétrica conducente a uma base de dados obtidos experimentalmente que inclui a visão central e globalizante da influência relativa dos diferentes fatores de controlo com impacto nas propriedades termofísicas. De entre as propriedades termofísicas, este estudo deu particular ênfase à condutividade térmica, sendo os fatores de controlo selecionados os seguintes: fluido base, temperatura, tamanho da partícula e concentração de nanopartículas. Experimentalmente, verificou-se que de entre os fatores de controlo estudados, os que maior influência detêm sobre a condutividade térmica do nanofluido, são o tamanho e concentração das nanopartículas. Com a segurança conferida por uma base de dados sólida e com o conhecimento acerca da contribuição relativa de cada fator de controlo no processo de transferência de calor, desenvolveu-se e validou-se um modelo físico-matemático com um caracter generalista, que permitirá determinar com segurança a condutividade térmica de nanofluidos.

Separating the influence of projected changes in air temperature and wind on patterns of sea level change and ocean heat content

We present ocean model sensitivity experiments aimed at separating the influence of the projected changes in the “thermal” (near-surface air temperature) and “wind” (near-surface winds) forcing on the patterns of sea level and ocean heat content. In the North Atlantic, the distribution of sea level change is more due to the “thermal” forcing, whereas it is more due to the “wind” forcing in the North Pacific; in the Southern Ocean, the “thermal” and “wind” forcing have a comparable influence. In the ocean adjacent to Antarctica the “thermal” forcing leads to an inflow of warmer waters on the continental shelves, which is somewhat attenuated by the “wind” forcing. The structure of the vertically integrated heat uptake is set by different processes at low and high latitudes: at low latitudes it is dominated by the heat transport convergence, whereas at high latitudes it represents a small residual of changes in the surface flux and advection of heat. The structure of the horizontally integrated heat content tendency is set by the increase of downward heat flux by the mean circulation and comparable decrease of upward heat flux by the subgrid-scale processes; the upward eddy heat flux decreases and increases by almost the same magnitude in response to, respectively, the “thermal” and “wind” forcing. Regionally, the surface heat loss and deep convection weaken in the Labrador Sea, but intensify in the Greenland Sea in the region of sea ice retreat. The enhanced heat flux anomaly in the subpolar Atlantic is mainly caused by the “thermal” forcing.

Experimental investigations of heat transfer coefficients of cutting fluids in metal cutting processes: analysis of workpiece phenomena in a given case study

This paper reports an experimental method to estimate the convective heat transfer of cutting fluids in a laminar flow regime applied on a thin steel plate. The heat source provided by the metal cutting was simulated by electrical heating of the plate. Three different cooling conditions were evaluated: a dry cooling system, a flooded cooling system and a minimum quantity of lubrication cooling system, as well as two different cutting fluids for the last two systems. The results showed considerable enhancement of convective heat transfer using the flooded system. For the dry and minimum quantity of lubrication systems, the heat conduction inside the body was much faster than the heat convection away from its surface. In addition, using the Biot number, the possible models were analyzed for conduction heat problems for each experimental condition tested.

Development of heat sink device by using topology optimization

Small scale fluid flow systems have been studied for various applications, such as chemical reagent dosages and cooling devices of compact electronic components. This work proposes to present the complete cycle development of an optimized heat sink designed by using Topology Optimization Method (TOM) for best performance, including minimization of pressure drop in fluid flow and maximization of heat dissipation effects, aiming small scale applications. The TOM is applied to a domain, to obtain an optimized channel topology, according to a given multi-objective function that combines pressure drop minimization and heat transfer maximization. Stokes flow hypothesis is adopted. Moreover, both conduction and forced convection effects are included in the steady-state heat transfer model. The topology optimization procedure combines the Finite Element Method (to carry out the physical analysis) with Sequential Linear Programming (as the optimization algorithm). Two-dimensional topology optimization results of channel layouts obtained for a heat sink design are presented as example to illustrate the design methodology. 3D computational simulations and prototype manufacturing have been carried out to validate the proposed design methodology.

Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.