Conduction, axial

This model v/as used by Atwood et al (1989) to compare the performance of 12 m and 1.2 m long tubular reactors using the UCKRON test problem. Although it was obvious that axial conduction of matter and heat can be expected in the short tube and not in the long tube, the second derivative conduction terms were included in the model so that no difference can be blamed on differences in the models. The continuity equations for the compounds was presented as ... 

Now, the heat conducted from the cell will be considered to be controlled by the radial conductivity of the total cell contents and not by the cell walls alone. Furthermore, the axial conductivity of the cell will be ignored as its contribution to heat loss will be several orders of magnitude less than that lost by radial convection. 

Chapter 4 is devoted to single-phase heat transfer. Data on heat transfer in circular micro-tubes and in rectangular, trapezoidal and triangular ducts are presented. Attention is drawn to the effect of energy dissipation, axial conduction and wall roughness on the thermal characteristics of flow. Specific problems connected with electro-osmotic heat transfer in micro-channels, three-dimensional heat transfer in micro-channel heat sinks and optimization of micro-heat exchangers are also discussed. 

The IR technique also yielded temperature distributions (Fig. 2.17) in the symmetry plane at Re = 30 and g = 19 x lO W/m. The wall temperature decreases by axial conduction through the solid walls in the last part of the micro-channel (x/L > 0.75) since this part is not heated. Neither the wall nor the fluid bulk temperature distribution can be approximated as linear. 

Part 1. Presentation of the model. Int J Heat Mass Transfer 47 3375-3385 Tiselj I, Hetsroni G, Mavko B, Mosyak A, Pogrebnyak E, Segal Z (2004) Effect of axial conduction on the heat transfer in micro-channels Int J Heat Mass Transfer 47 2551-2565 Triplett KA, Ghiaasiaan SM, Abdel-Khalik SI, Sadowski DL (1999) Gas-liquid two-phase flow in microchannels. Part I. Two-phase flow patterns. Int J Multiphase Flow 25 377-394 Tsai J-H, Lin L (2002) Transient thermal bubble formation on polysihcon micro-resisters. J Heat Transfer 124 375-382... 

The effect of axial conduction on heat transfer in the fluid in the micro-channel can be characterized by a dimensionless parameter... 

It shows that close to the micro-channel inlet, heat losses to the cooling inlet due to axial conduction in the fluid are dominant. In the second case parameter M is ... 

The existence of heat transfer due to axial conduction in the fluid leads to increasing difference between wall and fluid temperatures and decreasing value of the Nus-... 

The problem of axial conduction in the wall was considered by Petukhov (1967). The parameter used to characterize the effect of axial conduction is P = (l - dyd k2/k ). The numerical calculations performed for q = const, and neglecting the wall thermal resistance in radial direction, showed that axial thermal conduction in the wall does not affect the Nusselt number Nuco. Davis and Gill (1970) considered the problem of axial conduction in the wall with reference to laminar flow between parallel plates with finite conductivity. It was found that the Peclet number, the ratio of thickness of the plates to their length are important dimensionless groups that determine the process of heat transfer. 

Fig. 4.15 Effect of axial conduction, channel between two parallel plates (Maranzana et al. 2004) (schematic view) 1 cover plate, 2 micro-channel, 3 silicon block 1,...

Fig. 4.16a-c Effect of axial conduction. Numerical simulation, (a) Interface temperature. (b) Interface heat flux, (c) The Nusselt numbers. Reprinted from Maranzana et al. (2004) with permission... 

Heat transfer in micro-channels occurs under superposition of hydrodynamic and thermal effects, determining the main characteristics of this process. Experimental study of the heat transfer in micro-channels is problematic because of their small size, which makes a direct diagnostics of temperature field in the fluid and the wall difficult. Certain information on mechanisms of this phenomenon can be obtained by analysis of the experimental data, in particular, by comparison of measurements with predictions that are based on several models of heat transfer in circular, rectangular and trapezoidal micro-channels. This approach makes it possible to estimate the applicability of the conventional theory, and the correctness of several hypotheses related to the mechanism of heat transfer. It is possible to reveal the effects of the Reynolds number, axial conduction, energy dissipation, heat losses to the environment, etc., on the heat transfer. 

Davis EJ, Gill WN (1970) The effect of axial conduction in the waU on heat transfer with laminar flow. Int J Heat Mass Transfer 23 459 70... 

Mala GM, Li D, Werner C (1997b) Flow characteristics of water through a micro-channel between two parallel plates with electro kinetic effects. Int J Heat Fluid Flow 18 491 96 Male van P, Croon de MHJM, Tiggelaar RM, Derg van den A, Schouten JC (2004) Heat and mass transfer in a square micro-channel with asymmetric heating. Int J Heat Mass Transfer 47 87-99 Maranzana G, Perry I, Maillet D (2004) Mini- and micro-channels influence of axial conduction in the walls. Int J Heat Mass Transfer 47 3993 004 Maynes D, Webb BW (2003) Full developed electro-osmotic heat transfer in microchannels. Int J Heat Mass Transfer 46 1359-1369... 

The dimensionless quantity on the left-hand side of Eq. (7.3) labeled as M by the above-cited authors, allows for the comparison of heat transfer by axial conduction in the wall to the convective heat transfer in the flow. 

Maranzana G, Perry I, Maillet D (2004) Mini and Micro-channels Influence of axial conduction in the wads. Int J Heat Mass Transfer 47 3993 004 Platzer B, Plot A, Maurer G (1990) Thermophysical properties of refrigerants. Springer, Berlin Heidelberg New York... 

The heat transfer model, energy and material balance equations plus boundary condition and initial conditions are shown in Figure 4. The energy balance partial differential equation (PDE) (Equation 10) assumes two dimensional axial conduction. Figure 5 illustrates the rectangular cross-section of the composite part. Convective boundary conditions are implemented at the interface between the walls and the polymer matrix. 

Yoder showed that radiation heat transfer and axial conduction heat transfer in the tube wall have a negligible effect on predicting wall temperatures. The following equations were used by Yoder and Rohsenow (1980) as well as previous investigators such as Bennett et al. (1967b), Hynek (1969), and Groeneveld (1972). 

As indicated earlier, the axial conduction term is almost always negligible compared to the convective enthalpy transport term. Therefore, equation 12.7.47 is usually simplified to give... 

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