Effective thermal conductivity variation

Fig. 12 Effective thermal conductivity variations of CNT nanofluid with settling time. CNT volume fraction (4)) was 0.01 %. Plasma conditions and CNT sample designation are given in Table 3...

Some workers have correlated experimental data in terms of k at the arithmetic mean temperature, and some at the temperature of the bulk plasma. Experimental validation of the true effective thermal conductivity is difficult because of the high temperatures, small particle sizes and variations in velocity and temperature in plasma jets. 

There is even more uncertainty in estimating the heat-transfer coefficient at the wall of the tube than in estimating the effective thermal conductivity in the bed of catalyst. The measurement is essentially a difficult one, depending either on an extrapolation of a temperature profile to the wall or on determining the resistance at the wall as the difference between a measured over-all resistance and a calculated resistance within the packed bed. The proper exponent to use on the flow rate to get the variation of the coefficient has been reported as 0.33 (C4), 0.47 (C2), 0.5 and 0.77 (HI), 0.75 (A2), and 1.00 (Ql). 

The two-dimensional method has resulted in better agreement than the simplified approach, but the computed conversions are still less than the experimental results. In view of the problems in estimating the radial heat- and mass-transfer rates, and possible uncertainties in kinetic rate data, the comparison is reasonably good. The net effect of allowing for radial heat and mass transfer is to increase the conversion. The computed results are sensitive to rather small variations in the effective thermal conductivities and diffusivities, which emphasizes the need for the best possible information concerning these quantities. 

C.H. Li and G.P. Peterson, Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nano-paiticle suspensions (nanofluids). Journal of Applied Physics, 99(8), 084314... 

The coefficient Xi is a correlation function that describes the rate of increase of the effective thermal conductivity with flow velocity, Pe is the P6clet number, which describes the contribution of forced convection relative to hydrogen heat conduction, is the velocity at the centerline of the bed, ave is the average velocity, fir) describes the radial variation in dispersion, and... 

Measurements with various temperature differences can be made on a given sample without removing, changing, or altering the sample in any way. This makes possible the determination of the temperature variation of an average effective thermal conductivity over wide ranges of temperature. 

The result is the average effective thermal conductivity of the bed. The reader should be aware, however, that the correlation employed is probably only good to 10 to 20% at best. In using such values in design calculations, one should examine the sensitivity of the resnlts to variations in parameters that are characterized by snch large uncertainties. 

Equations (17) and (19), with the appropriate boundary conditions, were solved numerically to determine the insulation pressure and temperature distributions. The method of solution chosen was essentially the Jacobi method, where all the derivatives of a previous iteration are used in any given iteration. Vertical variation of the effective thermal conductivity was then determined from the temperature distribution. 

Forced vapor circulation through a porous insulation system can cause considerable variation in the effective thermal conductivity over the height of an insulation block. When the total containment system is sensitive to a local degradation in the insulation thermal conductivity, such as an allowable temperature limit of the container material, the insulation system must be designed to prevent degradation. The effects of the insulation thermal conductivity degradation can be determined from the temperature profile distortion caused by the forced vapor circulation. 

Heat conduction into the gas phase causes a modulated expansion of a layer of gas near the sample surface, producing a sound wave that can be detected using a microphone the so-called photoacoustic effect. Thermally induced variations in the gas-phase... 

Annie Paul et al. [36] studied short randomly oriented PP/banana fibre composites. The thermophysical properties of the above composites were studied on the basis of different banana fibre loading and different chemical treatments given to the banana fibres. The incorporation of banana fibres into PP matrix induced a decrease of the effective thermal conductivity of the composite. The use of the theoretical series conduction model allowed to estimate the transverse thermal conductivity of untreated banana fibre composites. As was expected, the series model appears sufficient for the effective thermal conductivity estimation of this kind of composites. All the chemical treatments enhanced both thermal conductivity and diffusivity of the composite considerably in varying degrees. This indicates that the chemical treatment allows a better contact between the fibre and the matrix and reduces considerably the thermal contact resistance. Nevertheless, a significant increase of the thermal conductivity was observed only for benzoylated and 10% NaOH-treated fibre composites. Besides, the variations of density and specific heat upon fibre chemical treatment are small compared to their associated uncertainties. 

Fig.8 Variation of effective thermal conductivity with interface thickness. Based on [42]...

Curves of Figure 19 compare the data published for (a) boron nitride [37,40] (b) aluminium (c) diamond-[37-39] (d) aluminium nitride [37-42] (e) crystalline silica. It can be seen that, at 45 vol.%, the maximum thermal conductivity achieved with diamond powder is 1.5 W m K, while crystalline boron nitride at 35 vol.% affords 2.0Wm K. The thermal conductivity of silver-filled adhesives was studied by using silicon test chips attached to copper and molybdenum substrates [43]. The authors outline the importance of the shape factor A, related to the aspect ratio of the particles, to achieve the highest level of thermal conductivity. Another study reports the variation of the effective thermal resistance, between a test chip and the chip carrier, in relation to the volume fraction of silver and the thickness of the bond layer [44]. The ultimate value of bulk thermal conductivity is 2 W m at 25 vol.% silver. However, the effective thermal conductivity, calculated from the thermal resistance measurements, is only one-fifth of the bulk value when the silicon chip is bonded to a copper substrate. 

First, Eqn. (9-31) will be used directly to estimate (T(0) — Ts)nBx. The approximate effective thermal conductivity, fceff = 5 x 10 cal/s-cm-K, will be used for dus calculation. Then, as a check, Eqn. (9-33) will be applied. Since this calculation is approximate, variation of the heat capacities (cp,i) with temperature will be neglected. 

Powder Insulation A method of reahzing some of the benefits of multiple floating shields without incurring the difficulties of awkward structural complexities is to use evacuated powder insulation. The penalty incurred in the use of this type of insulation, however, is a tenfold reduction in the overall thermal effectiveness of the insulation system over that obtained for multilayer insulation. In applications where this is not a serious factor, such as LNG storage facihties, and investment cost is of major concern, even unevacuated powder-insulation systems have found useful apphcations. The variation in apparent mean thermal conductivity of several powders as a function of interstitial gas pressure is shown in the familiar S-shaped curves of Fig. 11-121. ... 

That some enhancement of local temperature is required for explosive initiation on the time scale of shock-wave compression is obvious. Micromechanical considerations are important in establishing detailed cause-effect relationships. Johnson [51] gives an analysis of how thermal conduction and pressure variation also contribute to thermal explosion times. 

Rolfgaard [2.2] compares the types of trays and heating systems The ribbed trays are said to have an uneven temperature distribution, because the distances between shelf and tray vary between 0.1 mm and 1 mm. The ribs could compensate this only partially. The variation in distances is correct, but Rolfgaard overlooks that the thermal conductivity in the bottom of the tray is so effective that practically no temperature differences are established in the bottom. Even with an evaporation of 3 kg ice/m2 h and the assumption that all heat is Transmitted only in the center of the tray (8 cm from the border of the tray), the temperature difference between border and center is approx. 5 °C. During the drying under actual conditions, no measurable temperature differences can exist. 

Solving the energy equation provides prediction of the temperature distribution and its effect on cell performance in a PEFC. Figure 12 presents a temperature distribution in the middle of the membrane for a single-channel PEFC. The maximum temperature rise in this case is 4 °C, which will only fect cell performance slightly. However, the temperature variation depends strongly on the thermal conductivities of the GDL and flow plate as well as thermal boundary conditions. 

It is also important that the oven not influence the detector temperature. This could happen, not only by thermal conduction, but also by heat transfer through the flowing carrier gas. The second effect is particularly bad because it is one way that variations in gas flow can cause noise or drift in the detector. 

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