Thermal contact model

In 1959, Little [69] extended the acoustic mismatch model to interfaces between solids. The experiments have revealed that in this case, the thermal contact resistance between solids is higher than that evaluated from the model and that data are less reproducible. 

It should be noted that it is difficult to obtain models that can accurately predict thermal contact resistance and rapid solidification parameters, in addition to the difficulties in obtaining thermophysical properties of liquid metals/alloys, especially refractory metals/al-loys. These make the precise numerical modeling of flattening processes of molten metal droplets extremely difficult. Therefore, experimental studies are required. However, the scaling of the experimental results for millimeter-sized droplets to micrometer-sized droplets under rapid solidification conditions seems to be questionable if not impossible,13901 while experimental studies of micrometer-sized droplets under rapid solidification conditions are very difficult, and only inconclusive, sparse and scattered data are available. 

Equation (10) was shown to follow from a thermally activated model of Eyring s type, that is a stress-assisted thermally activated process for viscous flow [154]. For rough surfaces the area of true molecular contact is very small and, hence, the adhesion contribution to the total friction force is usually negligible, as manifested by a zero friction at zero load [148]. Yet in the microscopic limit of the SFM experiment employing a comparatively sharp... 

Fig. 2-15 Joint-roughness model for analysis of thermal contact resistance.

In this work, microscale evaporation heat transfer and capillary phenomena for ultra thin liquid film area are presented. The interface shapes of curved liquid film in rectangular minichannel and in vicinity of liquid-vapor-solid contact line are determined by a numerical solution of simplified models as derived from Navier-Stokes equations. The local heat transfer is analyzed in term of conduction through liquid layer. The data of numerical calculation of local heat transfer in rectangular channel and for rivulet evaporation are presented. The experimental techniques are described which were used to measure the local heat transfer coefficients in rectangular minichannel and thermal contact angle for rivulet evaporation. A satisfactory agreement between the theory and experiments is obtained. 

Direct liquid introduction (DLI) methodology has been described elsewhere (9). A thermospray probe and source (TSP, Model TS 360Q) were acquired from Vestec Corp. (Houston, TX) and later modified to include a probe tip heater incorporated in a copper block. Because of thermal contact, however, there was considerable interaction between the source temperature, the probe tip temperature and the temperature of the capillary. For this reason, attempts to optimize the ion currents by adjusting temperatures had limited success. Typical temperatures of the tip of the interface were 199- 205°C with source temperatures of230-240°C. The two mobile phases used were 0.1M ammonium acetate and 4 1 (v/v) 0.1 M ammonium acetate acetonitrile. The flow rate was 1.0 ml/min 1. Samples were admitted to the TSP probe via a Rheodyne (Model 7125) valve. 

In the classical equilibrium thermodynamics, Stirling and Ericsson cycles have an efficiency that goes to the Carnot efficiency, as it is shown in some textbooks. These three cycles have the common characteristics, including two isothermal processes. The objection to the classical point of view is that reservoirs coupled to the engine modeled by any of these cycles do not have the same temperature as the working fluid because this working fluid is not in direct thermal contact with the reservoir. Thus, an alternative study of these cycles is using finite... 

We will consider the two semi-infinite bodies shown in Fig. 2.24, which have different, but constant, initial temperatures d01 and d02- Their material properties Ax, a1 and A2, a2 are also different. At time t = 0 both bodies are brought into (thermal) contact with each other along the plane indicated by x = 0. After a very short period of time an average temperature is reached along the plane. Heat flows from body 1 with the higher initial temperature to body 2 which has a lower temperature. The transient conduction process described here serves as a model for the description of short-time contact between two (finite) bodies at different temperatures. Examples of this include the touching of different objects with a hand or foot and the short-time interaction of a heated metal body with a cooled object in reforming processes. 

In this expression, is the thermal conductivity of hydrogen, F is the void fraction, 0 is a flattening coefficient which defines contact quality, is the particle thermal conductivity, and is an expression for the thermal conductivity at the particle-gas-particle interface and includes particle diameter Dp. The effective thermal conductivity is highly influenced by Kp p as it describes the contribution of the fluid to the particle thermal contact quality. For a complete description of the model refer to Rodriguez Sanchez et al. [19]. 

Elastoconstriction Resistance of Cylinder-Flat Contacts. The thermal contact resistance model for the contact formed by a smooth circular cylinder of diameter D and thermal conductivity ku and a smooth flat of thermal conductivity k2, was reported by McGee et al. [63] to be... 

Thermal contact, gap, and joint conductance models developed by many researchers over the past five decades are reviewed and summarized in several articles [20,23,50,58,143,147,148] and in the recent text of Madhusudana [59]. The models are, in general, based on the assumption that the contacting surfaces are conforming (or flat) and that the surface asperities have particular height and asperity slope distributions [26, 116, 125]. The models assume either plastic or elastic deformation of the contacting asperities, and require the thermal spreading (constriction) resistance results presented above. 

Elastic Contact Conductance Models of Mikic and Greenwood and Williamson. Sridhar and Yovanovich [106] reviewed the elastic contact models proposed by Greenwood and Williamson [26] and Mikic [66] and compared the correlation equation with data obtained for five different metals. The models were developed for conforming rough surfaces they differ in the description of the surface metrology and the contact mechanics. The thermal model developed by Cooper et al. [14] was used. The details of the development of the models and the correlation equations are reviewed by Sridhar and Yovanovich [106]. The correlation equation derived from the Mikic [66] surface and asperity contact models is... 

M. A. Lambert and L. S. Fletcher, A Review of Models for Thermal Contact Conductance of Metals, AIAA-96-0239, 34th Aerospace Sciences Meeting and Exhibit, Reno, NV, January 15-18,1996. 

G. R. McGee, M. H. Schankula, and M. M. Yovanovich, Thermal Resistance of Cylinder-Flat Contacts Theoretical Analysis and Experimental Verification of a Line-Contact Model, Nuclear Engineering and Design, Vol. 86, pp. 369-381,1985. 

T. H. McWaid and E. Marschall, Applications of the Modified Greenwood and Williamson Contact Model for Prediction of Thermal Contact Resistance, Wear, Vol. 152, pp. 263-277,1992. 

M. R. Sridhar and M. M. Yovanovich, Thermal Contact Conductance of Tool Steel and Comparison with Model, Int. J. of Heat Mass Transfer (39/4) 831-839,1996. 

M. M. Yovanovich and V. W. Antonetti, Application of Thermal Contact Resistance Theory to Electronic Packages, in Advances in Thermal Modeling of Electronic Components and Systems, A. Bar-Cohen and A. D. Kraus eds., Vol. 1, Chap 2, pp. 79-128, Hemisphere Publishing, New York, 1988. 

Dhiman and Chandra [20] developed an analytical model to predict the substrate temperature at which splashing would occur by using a one-dimensional model for solidification of a molten metal droplet in contact with a semi-infinite substrate. They assumed that splashing occurred if the thickness of the solid layer reached that of the splat by the time the droplet had finished spreading. The thermal contact resistance between the droplet and surface was found to play a critical role in... 

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