Micro axial heat conduction

The subject of this chapter is single-phase heat transfer in micro-channels. Several aspects of the problem are considered in the frame of a continuum model, corresponding to small Knudsen number. A number of special problems of the theory of heat transfer in micro-channels, such as the effect of viscous energy dissipation, axial heat conduction, heat transfer characteristics of gaseous flows in microchannels, and electro-osmotic heat transfer in micro-channels, are also discussed in this chapter. 

The numerical and experimental study of Tiselj et al. (2004) (see Fig. 4.17) was focused on the effect of axial heat conduction through silicon wafers on heat transfer in the range of Re = 3.2—84. Figure4.17 shows their calculation model of a triangular micro-channels heat sink. The results of calculations are presented in Fig. 4.18. 

In this work, heat and fluid flow in some common micro geometries is analyzed analytically. At first, forced convection is examined for three different geometries microtube, microchannel between two parallel plates and microannulus between two concentric cylinders. Constant wall heat flux boundary condition is assumed. Then mixed convection in a vertical parallel-plate microchannel with symmetric wall heat fluxes is investigated. Steady and laminar internal flow of a Newtonian is analyzed. Steady, laminar flow having constant properties (i.e. the thermal conductivity and the thermal diffusivity of the fluid are considered to be independent of temperature) is considered. The axial heat conduction in the fluid and in the wall is assumed to be negligible. In this study, the usual continuum approach is coupled with the two main characteristics of the microscale phenomena, the velocity slip and the temperature jump. 

The heat exchanger efficiency was investigated as function of the heat conductivity of the wall for a countercurrent micro heat exchanger. At very low heat conductivity (2 aii <0.1 W m K ), the heat conductivity through the wall becomes the limiting factor for heat transfer. No influence of the axial heat conduction within the wall Is observed, on account of the low heat conductivity. The picture... 

Recent modeling studies of micro- and minichannel networks have argued the importance of solid-phase axial heat conduction [5]. The axial heat conduction in the channel wall in large pipes can indeed be neglected because the wall thickness is usually... 

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 ... 

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. 

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... 

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... 

Table 1.6 Characteristic quantities to be considered for micro-reactor dimensioning and layout. Steps 1, 2, and 3 correspond to the dimensioning of the channel diameter, channel length and channel walls, respectively. Symbols appearing in these expressions not previously defined are the effective axial diffusion coefficient D, the density thermal conductivity specific heat Cp and total cross-sectional area S, of the wall material, the total process gas mass flow m, and the reactant concentration Cg [114].

Microscale heat transfer has attracted researchers in the last decade, particularly due to developments and current needs in the small-scale electronics, aerospace, and bioengineering industries. Although some of the fundamental differences between micro and macro heat transfer phenomenon have been identified, there still is a need for further experimental, analjdical and numerical studies to clarify the points that are not yet understood, such as the effect of axial conduction, friction factors, compressibility effects, critical Reynolds number, and accommodation coefScients less then unity. 

G. Maranzana, I. Perry, D. Maillet, Mini-and microaxial conduction in the walls. International Journal of Heat and Mass Transfer, 2004,47, 3993-4004. 

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