Heattransfercoefficients for natural water surfaces
Williams, G. P.
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A study was carried out to identify process parameters and modeling features affecting interfacial heattransfercoefficients in the casting of a semi-solid 357 aluminum alloy. A 2-level screening design was created to evaluate the effect of 5 process parameters on these coefficients. The varied parameters were the following: set die temperature, intensification pressure, plunger velocity, lubricant type and lubricant quantity. The interfacial heattransfercoefficients were calculated with an inverse heat conduction method using as inputs the measured die temperatures obtained from the various casting conditions in the screening design. The effects of these process parameters were quantified considering 2 response variables: the peak value of the coefficients and the time the coefficients decreased to 5 % of their peak value. The intensification pressure was found to be dominant for both response variables. It was also observed that features in the finite element model used to solve the inverse heat conduction problem affected the coefficients. The features investigated in the model were: the thermocouple cavity, its depth, its base angle and the presence of the thermocouple inside the cavity. The depth at which the thermocouple cavity was modeled was found to be the prevailing feature affecting the coefficients.
Both the experimental measurements and CFD simulations conducted by Allison focused only on the free delivery point. Since the free delivery point was observed to be the best operating point in the present work, Allison’s results should be consistent. However, they were observed to be substantially lower in thermal resistance. This could have occurred for several reasons. First, the heat losses were only estimated rather than experimentally characterized, which could have led to underestimates of the heat loss (in this scenario, some of the lost energy due to conduction through the insulation, for example,would be counted as part of the reported convective heattransfer). Second, the bottom heated plate appears to extend right up to the impeller shaft, where there is some additional heat trans- fer surface area that was possibly unaccounted for on the bottom plate within the core. The heattransfer in this region could be significant, because the flow entering the eye is likely to impinge upon the bottom plate; impingement zones are known to have thin boundary layers and high heattransfercoefficients. In the present work, this core region had an identical hole in the top and bottom plates, so this difference in the setups could explain why Allison’s reported thermal resistances are lower. The optimal design fron- tiers reported by Allison are compared to Eq. 4.39 in Fig. 4-18. Allison’s CFD-computed frontier shows reasonably good agreement with the present experimental data; however, his experimental-measurement-based correlation for the frontier estimates substantially lower thermal resistances.
The results render it possible to estimate the thermal properties of the materials in question. We are especially interested in the effective thermal diffusivity of porous multiconstituent materials that we estimate as a function of temperature with the help of an inverse method applied to experimental thermograms obtained by the flash method . However, the identification of the diffusivity of porous and/or semitransparent materials is made difficult because of the thermal behavior of these media in which a strong conducto-radiative coupling can quickly occur when the temperature increases. For this reason, we have modeled the coupled conductive and radiative heattransfer as a function of the temperature within porous multiconstituent materials from their morphology discretized into a set of homogeneous voxels. The size of the voxel is larger than the wavelength which is the case in practice because of the studied materials and the high temperature. This modeling rendered it possible, on the one hand, to simulate any kind of numerical thermal experiments, especially the flash method, and on the other hand, to reproduce the thermal behavior of our materials in their using conditions. Our modeling is only accurate in the context we have here presented.
under the winter and summer conditions, respectively, for the curved cavities as compared with the CFD results.. This difference in the heattransfer estimation translates into an error of less than 8% in the overall thermal transmittance of the fenestration system. Therefore, they concluded that the convective heattransfer in curved or trapezoidal cavities can be approximated using the correlations for flat rectangular cavities at the equivalent mean slope of the complex cavity. The conclusion drawn from their study is, however, limited to fairly small Rayleigh numbers (Ra < 7x10 4 ), and therefore, their results cannot be generalised to higher Rayleigh numbers and to other geometry types.
natural and forced convection. 15,18–22
In systems of natural convection with bubble injection, mix- ing is provided by large scale circulations driven by density dif- ferences in the liquid and bubbles. Within such a system, studies have shown that the bubble size has a major effect on the over- all heattransfer. 10 However, there have been only a few studies on forced convective heattransfer in bubbly flows, 15,19,23 where, in addi- tion to buoyancy driven circulation, bubble wakes and their inter- play provide an additional mixing mechanism. In systems of forced convection, experiments and numerical simulations have primar- ily focused on understanding the influence of bubble accumulation and deformability on the global mixing properties. Experimental setups (e.g., Ref. 23 ) are generally limited by the Reynolds number [O(10 2 )]. Industrial systems involving heat and mass transfer with forced convection, i.e., mean liquid velocity (for e.g., heat exchang- ers), reach much higher Reynolds numbers O(10 3 –10 5 ) and beyond. Fundamental studies on the interaction between the turbulence in the carrier fluid, heattransfer, and the dispersed bubbles at such high Reynolds numbers are currently lacking. The objective of our work is to fill this gap. In this paper, we will describe a facility which is built to tackle various unresolved questions related to heattransfer in turbulent bubbly flow. The Twente Mass and HeatTransfer Water Tunnel (TMHT) will be used to (i) quantitatively characterize the global heattransfer of a turbulent flow with and without gas bub- ble injection, (ii) correlate and understand the local heat flux with the local liquid velocity and temperature fluctuations in the bub- bly turbulent flow, and (iii) explore and understand the dependence of the heattransfer on the control parameters, such as the gas con- centration, the bubble size, and the Taylor–Reynolds number of the flow.
across the boundary layer has also been taken into consideration. The Delaware group chose n = 1/3, ie. j is the so-called Colburn
heattransfer factor. ESDU (1973) and Z ukauskas and Ulinskas ( (1988) propose similar but slightly higher values n = 0.34 and 0.36, respectively (over most of the range). Figure 2 shows j and k as a function of Re for Pr = 1. It can be seen that heattransfer is a little higher for staggered than in-line geometries at lower Re.
Let denote Ω the area of the 2D Representative Volume Element (RVE) of the microcracked media, ∂Ω its outer boundary and u the outward unit normal to ∂Ω ( Fig . 1 a). The macroscopic temperature gradient G (respectively heat flux Q) can be defined as the mean temperature (resp. external heat flux) on the boundary ∂Ω. Under sta- tionary thermal conditions, the macroscopic temperature gradient G (resp. heat flux Q) corresponds to the average of the corresponding microscopic quantity g (resp. q):
Nunner (1956) derived a semi-empirical model based on his experimentation of pipes with threads as roughness elements. This can be considered as a case of 2-D roughness and con- sists of a unique relationship between the heattransfer coefficient and skin friction coefficient. Dipprey and Sabersky (1963) remarked that the existence of a unique relationship is funda- mentally wrong and it should depend on the type of roughness. Taking this into account and with the idea of extending Nikuradse’s sand roughened pipe experiments for heattransfer, Dipprey and Sabersky (1963) conducted detailed experiments. They selected similar close- packed sand grain roughness, however, they restricted their study to fully rough regime. They observed that in the fully rough regime, unlike the skin friction coefficient, the heattransfer coefficient decreases monotonically with the Reynolds number. This also indicates different physics of heat and momentum transfer in the presence of roughness. According to them, cavity Stanton number accounts for the heattransfer through the conduction sublayer, which unlike viscous sublayer, exists even for the fully rough regime. Next to the conduction sublayer in roughness cavities, there exist cavity vortices which leads to convective transfer of heat away from the conduction sublayer. Outside the cavity, the Reynolds analogy is as- sumed to be valid. Accounting for the presence of a vortex in roughness cavities or so-called cavity vortex hypothesis, they derived a semi-analytic equation for the cavity Stanton num- ber which accounts for effects of 3-D roughness elements on heattransfer. One of the most important observations from their experimentation is that a certain combination of Reynolds
So far we have assumed that all nanoparticles were at rest in the host fluid. To justify this assumption and verify that our model captures well the main physical mechanims which govern near- field heat exchanges in nanofluids, we now compare the timescales of Brownian motion to that of near field interactions. The time necessary for a particle of mass m to move on a distance equal to the interparticle distance under the action of thermal fluctuations is τ B = πη d a 3 /( 2 k B T ) . On the other hand, the electromagnetic energy is transported through the near-field interactions along a chain of
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Figure 8. –Left: View of the top box containing the 3 actuators
(cover removed). The membrane is glued on the bottom of the actuators. –Right: View of the heat exchanger bottom wall, made of copper. The two grooves constitute the manifolds. Figure 9 shows the configuration of the hydraulic system: adjusting the vertical position of the two constant level tanks imposes the pressure at the inlet and the outlet of the channel. These heights are adjustable and may be changed as required for a given experiment. The mass flow rate is measured thanks to a precision balance, with an uncertainty less than 1% for all experiments. The pump P2 is used to fill the loop prior to each experiment.