Conjugate heat transfer

The contribution of the axial heat conduction in the chaimd walls to the total heat transfer depends on the ratio of the conductivities of the wall and the fluid, on the ratio of the wall thickness and channel diameter and on the Pedet number. As the wall thickness in macroscale applications is of small size compared with the chaimel diameter, axial conduction in the channel walls is neglected [41]. 

At low Re and when conjugate effects have to be considered, the temperature distribution along the microchannel is not linear. Under constant heat flux boundary conditions, Nu decreases with decreasing ratio of outer to inner channel diameter, approaching the constant temperature solution. A decrease in Nu is also seen with increasing wall conductivity. For constant temperature boundary conditions, Nu will increase approaching the constant heat flux solution with axial heat conduction in the wall. The values for local Nusselt number for the conjugated problem lie between the values for the two boundary conditions constant heat flux and constant temperature. 

A criterion for the indication of axial heat transfer in the channel walls of heat exchangers has been proposed by Chiou [42], introducing a conduction parameter that represents the influence of axial heat conduction in the channel wall on the performance of the heat exchanger  

In microchannels, conjugate heat transfer leads to a complex three-dimensional heat flow pattern and Poiseuille flow may no longer be accurate [43]. Numerical simulations show that axial conduction in the channel wall does lower the Nusselt number but it is still in the range of conventional values [38]. The work of Gamrat et al. [44], in contrast, could not explain the lower Nusselt number by the axial conduction in the channel walls by numerical simulations. 

Maranzana et al. [45] assumed a uniform heat transfer coefficient between a parallel plate microchannel. A dimensionless number M is introduced, which compares the conductive and convective heat flux in the walls and in the fluid, respectively  

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Within such objects, conductive heat flow can be solved as well. This is sometimes called conjugate heat transfer in the literature. 

For the lower heat transfer surfaces in Fig. 2.60 to contribute to the energy transport, the solid should be an effective conductor of heat through its thickness. In other words, conjugate heat transfer effects should not create a more significant resistance to heat flow than that of the fluid in the channel. Since the heat transfer coefficient is generally a maximum at CHF, this leads to... 

Qu et al. (2000) carried out experiments on heat transfer for water flow at 100 < Re < 1,450 in trapezoidal silicon micro-channels, with the hydraulic diameter ranging from 62.3 to 168.9pm. The dimensions are presented in Table 4.5. A numerical analysis was also carried out by solving a conjugate heat transfer problem involving simultaneous determination of the temperature field in both the solid and fluid regions. It was found that the experimentally determined Nusselt number in micro-channels is lower than that predicted by numerical analysis. A roughness-viscosity model was applied to interpret the experimental results. 

For high values of the Reynolds number, the mean value of the Nusselt number does not differ significantly from the theoretical value for fully developed flow. On the contrary, at low Re the effects of conjugate heat transfer on the mean value of... 

The focus of the remainder of this chapter is on interstitial flow simulation by finite volume or finite element methods. These allow simulations at higher flow rates through turbulence models, and the inclusion of chemical reactions and heat transfer. In particular, the conjugate heat transfer problem of conduction inside the catalyst particles can be addressed with this method. 

When conjugate heat transfer through solid particles in the tube is to be included, the energy balance must be solved in the solid particles, in addition to the fluid flow regions. The energy balance for a solid region is defined by ... 

Solution of condensed-phase heat transfer equation is needed to analyze structural response to fires and simulate flame spread on solid surfaces. The solution of this conjugate heat transfer problem simulate is typical for fires, but rarely found in commercial CFD packages. Over the years, different techniques have been developed to tackle this problem. Since solid-phase heat transfer... 

Conjugate heat transfer and natural convection within an enclosed system... 

Schematic representation of these three possible boundary conditions at the wall is shown in Fig. 2.5 for the enthalpy/temperature equation. For systems with conjugate heat transfer, continuity of the temperature and the normal component of fluxes are specified at the walls. For systems with reactions occurring on solid surfaces, generally, accumulation of species at the solid surface is neglected and the diffusive flux at the wall is equated to the surface reaction rate.

Figure 1. Geometry and eoordinates system for asymmetric conjugated heat transfer in micro-channels.

I S. Nunes, P. Couto, and R.M. Cotta, Conjugated Heat Transfer Problem in Rectangular Micro-channels under Asyimnetric Condihons, Proc. of 5th Nahonal Congress of Mechanical Engineering, CONEM 2008, ABCM, Paper no. CON08-0739, Salvador, BA, August 2008. 

R.O.C. Guedes, R.M. Cotta, and N.C.L. Bram, Conjugated Heat Transfer in Laminar Flow Between Parallel - Plates Channel, 10th Brazilian Congress of Mechanical Engineering, Rio de Janeiro, Brazil, 1989. 

F.G. Elmor, R.O.C. Guedes, and F.N. Scofano, Improved Lumped Solution for Conjugate Heat Transfer In Channel Flow with Convective Boundary Condition, Int. J. Heat Technology, pp. 78-88 (2005). 

G. S. Barozzi, and G. Pagliarini, A Method to Solve Conjugate Heat Transfer Problems The Case of Fully Developed Laminar Flow in a Pipe, J. Heat Transfer, (107) 77-83,1985. 

J. C. Kuo, and T. F. Lin, Steady Conjugate Heat Transfer in Fully Developed Laminar Pipe Flows, J. of Thermophysics and Heat Transfer, (2/3) 281-283,1988. 

G. Pagliarini, Conjugate Heat Transfer for Simultaneously Developing Laminar Flow in a Circular Tube, J. of Heat Transfer, (113) 763-766,1991. 

Conjugate Heat Transfer to Moving Materials. In the previous two subsections, the thickness of the material was assumed to be small, so that the controlling resistance was on the fluid side therefore, the thermal coupling between heat transfer within the moving material and the convective flow and heat transfer in the fluid could be neglected. However, in many... 

FIGURE 18.15 Schematic of velocity and temperature profiles in the conjugate heat transfer problem on a continuous moving flat plate. 

Heat Transfer to Opaque and Moving Continuous-Sheet Multimode and Conjugate Heat Transfer Effects. In the previous discussion, convective heat transfer coefficients were obtained from empirical correlations. Therefore, coupling between convection and radiation... 

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