Experimental and numerical investigation of dynamic heat transfer parameters in packed bed

Dynamic experiments in a nonadiabatic packed bed were carried out to evaluate the response to disturbances in wall temperature and inlet airflow rate and temperature. A two-dimensional, pseudo-homogeneous, axially dispersed plug-flow model was numerically solved and used to interpret the results. The model parameters were fitted in distinct stages: effective radial thermal conductivity (K (r)) and wall heat transfer coefficient (h (w)) were estimated from steady-state data and the characteristic packed bed time constant (tau) from transient data. A new correlation for the K (r) in packed beds of cylindrical particles was proposed. It was experimentally proved that temperature measurements using radially inserted thermocouples and a ring-shaped sensor were not distorted by heat conduction across the thermocouple or by the thermal inertia effect of the temperature sensors.

Effect of vehicle pretreatment on the flux, retention, and diffusion of topically applied penetrants in vitro

Purpose. The flux of a topically applied drug depends on the activity in the skin and the interaction between the vehicle and skin. Permeation of vehicle into the skin can alter the activity of drug and the properties of the skin barrier. The aim of this in vitro study was to separate and quantify these effects. Methods. The flux of four radiolabeled permeants (water, phenol, diflunisal, and diazepam) with log K-oct/water values from 1.4 to 4.3 was measured over 4 h through heat-separated human epidermis pretreated for 30 min with vehicles having Hildebrand solubility parameters from 7.9 to 23.4 (cal/cm(3))(1/2). Results. Enhancement was greatest after pretreatment with the more lipophilic vehicles. A synergistic enhancement was observed using binary mixtures. The flux of diazepam was not enhanced to the same extent as the other permeants, possibly because its partitioning into the epidermis is close to optimal (log K-oct 2.96). Conclusion. An analysis of the permeant remaining in the epidermis revealed that the enhancement can be the result of either increased partitioning of permeant into the epidermis or an increasing diffusivity of permeants through the epidermis.

Numerical 3D modeling of heat transfer in human tissues for microwave radiometry monitoring of Brown fat metabolismo

Background: Brown adipose tissue (BAT) plays an important role in whole body metabolism and could potentially mediate weight gain and insulin sensitivity. Although some imaging techniques allow BAT detection, there are currently no viable methods for continuous acquisition of BAT energy expenditure. We present a non-invasive technique for long term monitoring of BAT metabolism using microwave radiometry. Methods: A multilayer 3D computational model was created in HFSS™ with 1.5 mm skin, 3-10 mm subcutaneous fat, 200 mm muscle and a BAT region (2-6 cm3) located between fat and muscle. Based on this model, a log-spiral antenna was designed and optimized to maximize reception of thermal emissions from the target (BAT). The power absorption patterns calculated in HFSS™ were combined with simulated thermal distributions computed in COMSOL® to predict radiometric signal measured from an ultra-low-noise microwave radiometer. The power received by the antenna was characterized as a function of different levels of BAT metabolism under cold and noradrenergic stimulation. Results: The optimized frequency band was 1.5-2.2 GHz, with averaged antenna efficiency of 19%. The simulated power received by the radiometric antenna increased 2-9 mdBm (noradrenergic stimulus) and 4-15 mdBm (cold stimulus) corresponding to increased 15-fold BAT metabolism. Conclusions: Results demonstrated the ability to detect thermal radiation from small volumes (2-6 cm3) of BAT located up to 12 mm deep and to monitor small changes (0.5°C) in BAT metabolism. As such, the developed miniature radiometric antenna sensor appears suitable for non-invasive long term monitoring of BAT metabolism.

Optimal exponent heat balance and refined integral methods applied to Stefan problems

When using a polynomial approximating function the most contentious aspect of the Heat Balance Integral Method is the choice of power of the highest order term. In this paper we employ a method recently developed for thermal problems, where the exponent is determined during the solution process, to analyse Stefan problems. This is achieved by minimising an error function. The solution requires no knowledge of an exact solution and generally produces significantly better results than all previous HBI models. The method is illustrated by first applying it to standard thermal problems. A Stefan problem with an analytical solution is then discussed and results compared to the approximate solution. An ablation problem is also analysed and results compared against a numerical solution. In both examples the agreement is excellent. A Stefan problem where the boundary temperature increases exponentially is analysed. This highlights the difficulties that can be encountered with a time dependent boundary condition. Finally, melting with a time-dependent flux is briefly analysed without applying analytical or numerical results to assess the accuracy.

Improving the accuracy of heat balance integral methods applied to thermal problems with time dependent boundary conditions

In this paper the two main drawbacks of the heat balance integral methods are examined. Firstly we investigate the choice of approximating function. For a standard polynomial form it is shown that combining the Heat Balance and Refined Integral methods to determine the power of the highest order term will either lead to the same, or more often, greatly improved accuracy on standard methods. Secondly we examine thermal problems with a time-dependent boundary condition. In doing so we develop a logarithmic approximating function. This new function allows us to model moving peaks in the temperature profile, a feature that previous heat balance methods cannot capture. If the boundary temperature varies so that at some time t & 0 it equals the far-field temperature, then standard methods predict that the temperature is everywhere at this constant value. The new method predicts the correct behaviour. It is also shown that this function provides even more accurate results, when coupled with the new CIM, than the polynomial profile. Analysis primarily focuses on a specified constant boundary temperature and is then extended to constant flux, Newton cooling and time dependent boundary conditions.

Activation of the heat shock response in plants by chlorophenols: transgenic Physcomitrella patens as a sensitive biosensor for organic pollutants.

The ability to detect early molecular responses to various chemicals is central to the understanding of biological impact of pollutants in a context of varying environmental cues. To monitor stress responses in a model plant, we used transgenic moss Physcomitrella patens expressing the beta-glucuronidase reporter (GUS) under the control of the stress-inducible promoter hsp17.3B. Following exposure to pollutants from the dye and paper industry, GUS activity was measured by monitoring a fluorescent product. Chlorophenols, heavy metals and sulphonated anthraquinones were found to specifically activate the hsp17.3B promoter (within hours) in correlation with long-term toxicity effects (within days). At mildly elevated physiological temperatures, the chemical activation of this promoter was strongly amplified, which considerably increased the sensitivity of the bioassay. Together with the activation of hsp17.3B promoter, chlorophenols induced endogenous chaperones that transiently protected a recombinant thermolabile luciferase (LUC) from severe heat denaturation. This sensitive bioassay provides an early warning molecular sensor to industrial pollutants under varying environments, in anticipation to long-term toxic effects in plants. Because of the strong cross-talk between abiotic and chemical stresses that we find, this P. patens line is more likely to serve as a direct toxicity bioassay for pollutants combined with environmental cues, than as an indicator of absolute toxicity thresholds for various pollutants. It is also a powerful tool to study the role of heat shock proteins (HSPs) in plants exposed to combined chemical and environmental stresses.

Heat shock response in photosynthetic organisms: membrane and lipid connections.

The ability of photosynthetic organisms to adapt to increases in environmental temperatures is becoming more important with climate change. Heat stress is known to induce heat-shock proteins (HSPs) many of which act as chaperones. Traditionally, it has been thought that protein denaturation acts as a trigger for HSP induction. However, increasing evidence has shown that many stress events cause HSP induction without commensurate protein denaturation. This has led to the membrane sensor hypothesis where the membrane's physical and structural properties play an initiating role in the heat shock response. In this review, we discuss heat-induced modulation of the membrane's physical state and changes to these properties which can be brought about by interaction with HSPs. Heat stress also leads to changes in lipid-based signaling cascades and alterations in calcium transport and availability. Such observations emphasize the importance of membranes and their lipids in the heat shock response and provide a new perspective for guiding further studies into the mechanisms that mediate cellular and organismal responses to heat stress.

Numerical and ExperimentalModelling of Gas Flow and Heat Transfer in the Air Gap of An Electric Machine

This work deals with the cooling of high-speed electric machines, such as motors and generators, through an air gap. It consists of numerical and experimental modelling of gas flow and heat transfer in an annular channel. Velocity and temperature profiles are modelled in the air gap of a high-speed testmachine. Local and mean heat transfer coefficients and total friction coefficients are attained for a smooth rotor-stator combination at a large velocity range. The aim is to solve the heat transfer numerically and experimentally. The FINFLO software, developed at Helsinki University of Technology, has been used in the flow solution, and the commercial IGG and Field view programs for the grid generation and post processing. The annular channel is discretized as a sector mesh. Calculation is performed with constant mass flow rate on six rotational speeds. The effect of turbulence is calculated using three turbulence models. The friction coefficient and velocity factor are attained via total friction power. The first part of experimental section consists of finding the proper sensors and calibrating them in a straight pipe. After preliminary tests, a RdF-sensor is glued on the walls of stator and rotor surfaces. Telemetry is needed to be able to measure the heat transfer coefficients at the rotor. The mean heat transfer coefficients are measured in a test machine on four cooling air mass flow rates at a wide Couette Reynolds number range. The calculated values concerning the friction and heat transfer coefficients are compared with measured and semi-empirical data. Heat is transferred from the hotter stator and rotor surfaces to the coolerair flow in the air gap, not from the rotor to the stator via the air gap, althought the stator temperature is lower than the rotor temperature. The calculatedfriction coefficients fits well with the semi-empirical equations and precedingmeasurements. On constant mass flow rate the rotor heat transfer coefficient attains a saturation point at a higher rotational speed, while the heat transfer coefficient of the stator grows uniformly. The magnitudes of the heat transfer coefficients are almost constant with different turbulence models. The calibrationof sensors in a straight pipe is only an advisory step in the selection process. Telemetry is tested in the pipe conditions and compared to the same measurements with a plain sensor. The magnitudes of the measured data and the data from the semi-empirical equation are higher for the heat transfer coefficients than thenumerical data considered on the velocity range. Friction and heat transfer coefficients are presented in a large velocity range in the report. The goals are reached acceptably using numerical and experimental research. The next challenge is to achieve results for grooved stator-rotor combinations. The work contains also results for an air gap with a grooved stator with 36 slots. The velocity field by the numerical method does not match in every respect the estimated flow mode. The absence of secondary Taylor vortices is evident when using time averagednumerical simulation.

Converter-flux-based current control of voltage source PWM rectifiers - analysis and implementation

Pulsewidth-modulated (PWM) rectifier technology is increasingly used in industrial applications like variable-speed motor drives, since it offers several desired features such as sinusoidal input currents, controllable power factor, bidirectional power flow and high quality DC output voltage. To achieve these features,however, an effective control system with fast and accurate current and DC voltage responses is required. From various control strategies proposed to meet these control objectives, in most cases the commonly known principle of the synchronous-frame current vector control along with some space-vector PWM scheme have been applied. Recently, however, new control approaches analogous to the well-established direct torque control (DTC) method for electrical machines have also emerged to implement a high-performance PWM rectifier. In this thesis the concepts of classical synchronous-frame current control and DTC-based PWM rectifier control are combined and a new converter-flux-based current control (CFCC) scheme is introduced. To achieve sufficient dynamic performance and to ensure a stable operation, the proposed control system is thoroughly analysed and simple rules for the controller design are suggested. Special attention is paid to the estimationof the converter flux, which is the key element of converter-flux-based control. Discrete-time implementation is also discussed. Line-voltage-sensorless reactive reactive power control methods for the L- and LCL-type line filters are presented. For the L-filter an open-loop control law for the d-axis current referenceis proposed. In the case of the LCL-filter the combined open-loop control and feedback control is proposed. The influence of the erroneous filter parameter estimates on the accuracy of the developed control schemes is also discussed. A newzero vector selection rule for suppressing the zero-sequence current in parallel-connected PWM rectifiers is proposed. With this method a truly standalone and independent control of the converter units is allowed and traditional transformer isolation and synchronised-control-based solutions are avoided. The implementation requires only one additional current sensor. The proposed schemes are evaluated by the simulations and laboratory experiments. A satisfactory performance and good agreement between the theory and practice are demonstrated.

Position sensorless electrically excited synchronous motor drive for industrial use based on direct flux linkage and torque control

Synchronous machines with an AC converter are used mainly in large drives, for example in ship propulsion drives as well as in rolling mill drives in steel industry. These motors are used because of their high efficiency, high overload capacity and good performance in the field weakening area. Present day drives for electrically excited synchronous motors are equipped with position sensors. Most drives for electrically excited synchronous motors will be equipped with position sensors also in future. This kind of drives with good dynamics are mainly used in metal industry. Drives without a position sensor can be used e.g. in ship propulsion and in large pump and blower drives. Nowadays, these drives are equipped with a position sensor, too. The tendency is to avoid a position sensor if possible, since a sensor reduces the reliability of the drive and increases costs (latter is not very significant for large drives). A new control technique for a synchronous motor drive is a combination of the Direct Flux Linkage Control (DFLC) based on a voltage model and a supervising method (e.g. current model). This combination is called Direct Torque Control method (DTC). In the case of the position sensorless drive, the DTC can be implemented by using other supervising methods that keep the stator flux linkage origin centered. In this thesis, a method for the observation of the drift of the real stator flux linkage in the DTC drive is introduced. It is also shown how this method can be used as a supervising method that keeps the stator flux linkage origin centered in the case of the DTC. In the position sensorless case, a synchronous motor can be started up with the DTC control, when a method for the determination of the initial rotor position presented in this thesis is used. The load characteristics of such a drive are not very good at low rotational speeds. Furthermore, continuous operation at a zero speed and at a low rotational speed is not possible, which is partly due to the problems related to the flux linkage estimate. For operation in a low speed area, a stator current control method based on the DFLC modulator (DMCQ is presented. With the DMCC, it is possible to start up and operate a synchronous motor at a zero speed and at low rotational speeds in general. The DMCC is necessary in situations where high torque (e.g. nominal torque) is required at the starting moment, or if the motor runs several seconds at a zero speed or at a low speed range (up to 2 Hz). The behaviour of the described methods is shown with test results. The test results are presented for the direct flux linkage and torque controlled test drive system with a 14.5 kVA, four pole salient pole synchronous motor with a damper winding and electric excitation. The static accuracy of the drive is verified by measuring the torque in a static load operation, and the dynamics of the drive is proven in load transient tests. The performance of the drive concept presented in this work is sufficient e.g. for ship propulsion and for large pump drives. Furthermore, the developed methods are almost independent of the machine parameters.

Heat storage rate and acute fatigue in rats

Thermal environmental stress can anticipate acute fatigue during exercise at a fixed intensity (%VO2max). Controversy exists about whether this anticipation is caused by the absolute internal temperature (Tint, ºC), by the heat storage rate (HSR, cal/min) or by both mechanisms. The aim of the present study was to study acute fatigue (total exercise time, TET) during thermal stress by determining Tint and HSR from abdominal temperature. Thermal environmental stress was controlled in an environmental chamber and determined as wet bulb globe temperature (ºC), with three environmental temperatures being studied: cold (18ºC), thermoneutral (23.1ºC) or hot (29.4ºC). Six untrained male Wistar rats weighing 260-360 g were used. The animals were submitted to exercise at the same time of day in the three environments and at two treadmill velocities (21 and 24 m/min) until exhaustion. After implantation of a temperature sensor and treadmill adaptation, the animals were submitted to a Latin square experimental design using a 2 x 3 factorial scheme (velocity and environment), with the level of significance set at P<0.05. The results showed that the higher the velocity and the ambient temperature, the lower was the TET, with these two factors being independent. This result indicated that fatigue was independently affected by both the increase in exercise intensity and the thermal environmental stress. Fatigue developed at different Tint and HSR showed the best inverse relationship with TET. We conclude that HSR was the main anticipating factor of fatigue.

Hydrogen Sensor Application of Anodic Titanium Oxide Nanostructures

Hydrogen (H2) fuel cells have been considered a promising renewable energy source. The recent growth of H2 economy has required highly sensitive, micro-sized and cost-effective H2 sensor for monitoring concentrations and alerting to leakages due to the flammability and explosiveness of H2 Titanium dioxide (TiO2) made by electrochemical anodic oxidation has shown great potential as a H2 sensing material. The aim of this thesis is to develop highly sensitive H2 sensor using anodized TiO2. The sensor enables mass production and integration with microelectronics by preparing the oxide layer on suitable substrate. Morphology, elemental composition, crystal phase, electrical properties and H2 sensing properties of TiO2 nanostructures prepared on Ti foil, Si and SiO2/Si substrates were characterized. Initially, vertically oriented TiO2 nanotubes as the sensing material were obtained by anodizing Ti foil. The morphological properties of tubes could be tailored by varying the applied voltages of the anodization. The transparent oxide layer creates an interference color phenomena with white light illumination on the oxide surface. This coloration effect can be used to predict the morphological properties of the TiO2 nanostructures. The crystal phase transition from amorphous to anatase or rutile, or the mixture of anatase and rutile was observed with varying heat treatment temperatures. However, the H2 sensing properties of TiO2 nanotubes at room temperature were insufficient. H2 sensors using TiO2 nanostructures formed on Si and SiO2/Si substrates were demonstrated. In both cases, a Ti layer deposited on the substrates by a DC magnetron sputtering method was successfully anodized. A mesoporous TiO2 layer obtained on Si by anodization in an aqueous electrolyte at 5°C showed diode behavior, which was influenced by the work function difference of Pt metal electrodes and the oxide layer. The sensor enabled the detection of H2 (20-1000 ppm) at low operating temperatures (50–140°C) in ambient air. A Pd decorated tubular TiO2 layer was prepared on metal electrodes patterned SiO2/Si wafer by anodization in an organic electrolyte at 5°C. The sensor showed significantly enhanced H2 sensing properties, and detected hydrogen in the range of a few ppm with fast response/recovery time. The metal electrodes placed under the oxide layer also enhanced the mechanical tolerance of the sensor. The concept of TiO2 nanostructures on alternative substrates could be a prospect for microelectronic applications and mass production of gas sensors. The gas sensor properties can be further improved by modifying material morphologies and decorating it with catalytic materials.

Étude de l'influence de la réassociation en surface des atomes N et O sur l'inactivation des spores bactériennes dans une post-décharge N2-O2 basse pression en flux

Le recours au plasma pour stériliser des dispositifs médicaux (DM) est un domaine de recherche ne datant véritablement que de la fin des années 1990. Les plasmas permettent, dans les conditions adéquates, de réaliser la stérilisation à basse température (≤ 65°C), tel qu’exigé par la présence de polymères dans les DM et ce contrairement aux procédés par chaleur, et aussi de façon non toxique, contrairement aux procédés chimiques comme, par exemple, l’oxyde d’éthylène (OEt). Les laboratoires du Groupe de physique des plasmas à l’Université de Montréal travaillent à l’élaboration d’un stérilisateur consistant plus particulièrement à employer les effluents d’une décharge N2-%O2 basse pression (2-8 Torrs) en flux, formant ce que l’on appelle une post-décharge en flux. Ce sont les atomes N et O de cette décharge qui viendront, dans les conditions appropriées, entrer en collisions dans la chambre de stérilisation pour y créer des molécules excitées NO*, engendrant ainsi l’émission d’une quantité appréciable de photons UV. Ceux-ci constituent, dans le cas présent, l’agent biocide qui va s’attaquer directement au bagage génétique du micro-organisme (bactéries, virus) que l’on souhaite inactiver. L’utilisation d’une lointaine post-décharge évite du même coup la présence des agents érosifs de la décharge, comme les ions et les métastables. L’un des problèmes de cette méthode de stérilisation est la réduction du nombre de molécules NO* créées par suite de la perte des atomes N et O, qui sont des radicaux connus pour interagir avec les surfaces, sur les parois des matériaux des DM que l’on souhaite stériliser. L’objectif principal de notre travail est de déterminer l’influence d’une telle perte en surface, dite aussi réassociation en surface, par l’introduction de matériaux comme le Téflon, l’acier inoxydable, l’aluminium et le cuivre sur le taux d’inactivation des spores bactériennes. Nous nous attendons à ce que la réassociation en surface de ces atomes occasionne ainsi une diminution de l’intensité UV et subséquemment, une réduction du taux d’inactivation. Par spectroscopie optique d’émission (SOE), nous avons déterminé les concentrations perdues de N et de O par la présence des matériaux dans le stérilisateur, ainsi que la diminution de l’émission UV en découlant. Nous avons observé que cette diminution des concentrations atomiques est d’autant plus importante que les surfaces sont catalytiques. Au cours de l’étude du phénomène de pertes sur les parois pour un mélange N2-%O2 nous avons constaté l’existence d’une compétition en surface entre les atomes N et O, dans laquelle les atomes d’oxygènes semblent dominer largement. Cela implique qu’au-delà d’un certain %O2 ajouté à la décharge N2, seuls les atomes O se réassocient en surface. Par ailleurs, l’analyse des courbes de survie bi-phasiques des micro-organismes a permis d’établir une étroite corrélation, par lien de cause à effet, entre la consommation des atomes N et O en surface et la diminution du taux d’inactivation des spores dans la première phase. En revanche, nous avons constaté que notre principal agent biocide (le rayonnement ultraviolet) est moins efficace dans la deuxième phase et, par conséquent, il n’a pas été possible d’établir un lien entre la diminution des concentrations et le taux d’inactivation de cette phase-là.

Development of thermo-analytical prediction and classification models for food in thermal devices using a multi sensor system and artificial neural networks

Die thermische Verarbeitung von Lebensmitteln beeinflusst deren Qualität und ernährungsphysiologischen Eigenschaften. Im Haushalt ist die Überwachung der Temperatur innerhalb des Lebensmittels sehr schwierig. Zudem ist das Wissen über optimale Temperatur- und Zeitparameter für die verschiedenen Speisen oft unzureichend. Die optimale Steuerung der thermischen Zubereitung ist maßgeblich abhängig von der Art des Lebensmittels und der äußeren und inneren Temperatureinwirkung während des Garvorgangs. Das Ziel der Arbeiten war die Entwicklung eines automatischen Backofens, der in der Lage ist, die Art des Lebensmittels zu erkennen und die Temperatur im Inneren des Lebensmittels während des Backens zu errechnen. Die für die Temperaturberechnung benötigten Daten wurden mit mehreren Sensoren erfasst. Hierzu kam ein Infrarotthermometer, ein Infrarotabstandssensor, eine Kamera, ein Temperatursensor und ein Lambdasonde innerhalb des Ofens zum Einsatz. Ferner wurden eine Wägezelle, ein Strom- sowie Spannungs-Sensor und ein Temperatursensor außerhalb des Ofens genutzt. Die während der Aufheizphase aufgenommen Datensätze ermöglichten das Training mehrerer künstlicher neuronaler Netze, die die verschiedenen Lebensmittel in die entsprechenden Kategorien einordnen konnten, um so das optimale Backprogram auszuwählen. Zur Abschätzung der thermische Diffusivität der Nahrung, die von der Zusammensetzung (Kohlenhydrate, Fett, Protein, Wasser) abhängt, wurden mehrere künstliche neuronale Netze trainiert. Mit Ausnahme des Fettanteils der Lebensmittel konnten alle Komponenten durch verschiedene KNNs mit einem Maximum von 8 versteckten Neuronen ausreichend genau abgeschätzt werden um auf deren Grundlage die Temperatur im inneren des Lebensmittels zu berechnen. Die durchgeführte Arbeit zeigt, dass mit Hilfe verschiedenster Sensoren zur direkten beziehungsweise indirekten Messung der äußeren Eigenschaften der Lebensmittel sowie KNNs für die Kategorisierung und Abschätzung der Lebensmittelzusammensetzung die automatische Erkennung und Berechnung der inneren Temperatur von verschiedensten Lebensmitteln möglich ist.

On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat engine controversy

In this paper, the available potential energy (APE) framework of Winters et al. (J. Fluid Mech., vol. 289, 1995, p. 115) is extended to the fully compressible Navier– Stokes equations, with the aims of clarifying (i) the nature of the energy conversions taking place in turbulent thermally stratified fluids; and (ii) the role of surface buoyancy fluxes in the Munk & Wunsch (Deep-Sea Res., vol. 45, 1998, p. 1977) constraint on the mechanical energy sources of stirring required to maintain diapycnal mixing in the oceans. The new framework reveals that the observed turbulent rate of increase in the background gravitational potential energy GPEr , commonly thought to occur at the expense of the diffusively dissipated APE, actually occurs at the expense of internal energy, as in the laminar case. The APE dissipated by molecular diffusion, on the other hand, is found to be converted into internal energy (IE), similar to the viscously dissipated kinetic energy KE. Turbulent stirring, therefore, does not introduce a new APE/GPEr mechanical-to-mechanical energy conversion, but simply enhances the existing IE/GPEr conversion rate, in addition to enhancing the viscous dissipation and the entropy production rates. This, in turn, implies that molecular diffusion contributes to the dissipation of the available mechanical energy ME =APE +KE, along with viscous dissipation. This result has important implications for the interpretation of the concepts of mixing efficiency γmixing and flux Richardson number Rf , for which new physically based definitions are proposed and contrasted with previous definitions. The new framework allows for a more rigorous and general re-derivation from the first principles of Munk & Wunsch (1998, hereafter MW98)’s constraint, also valid for a non-Boussinesq ocean: G(KE) ≈ 1 − ξ Rf ξ Rf Wr, forcing = 1 + (1 − ξ )γmixing ξ γmixing Wr, forcing , where G(KE) is the work rate done by the mechanical forcing, Wr, forcing is the rate of loss of GPEr due to high-latitude cooling and ξ is a nonlinearity parameter such that ξ =1 for a linear equation of state (as considered by MW98), but ξ <1 otherwise. The most important result is that G(APE), the work rate done by the surface buoyancy fluxes, must be numerically as large as Wr, forcing and, therefore, as important as the mechanical forcing in stirring and driving the oceans. As a consequence, the overall mixing efficiency of the oceans is likely to be larger than the value γmixing =0.2 presently used, thereby possibly eliminating the apparent shortfall in mechanical stirring energy that results from using γmixing =0.2 in the above formula.