**2. Analysis**

190 Heat Exchangers – Basics Design Applications

There has been much effort to analytically model the microchannel heat sink. Knight et al. [9] used empirical correlations to evaluate the performance of a microchannel heat sink. Koh and Colony [17] first modeled microstructures as a porous medium using Darcy's law. Later on Tien and Kuo [18] developed a model for heat transfer in microchannels using the modified Darcy equation and the two-equation model. Another method to model the microchannel heat sink analytically is to use the fin and plate theory. In this way, the solid walls are assumed to be as fins that are connected to the base plate. Applying this assumption, the thermal resistance and other thermal characteristics of the system could be derived using the fin and plate heat transfer relations. Because of limiting and less accuracy of the analytical approach in some phenomenons, e.g. conjugate heat transfer the numerical method is being used vastly to simulate the performance of microchannels like other fields

Webb and Zhang [19] claim that the accepted single-phase flow correlations adequately predict their experimental data for round and rectangular tubes with hydraulic diameter of the order of 1 mm. Wesberg et al. [8] solved a two-dimensional conjugate heat transfer problem for microchannel heat sinks to obtain detailed spatial distributions of the temperature of the heat sink cross-section along the length of the channels. Fedorov and Viskanta [6] developed a three dimensional model to investigate the conjugate heat transfer in a microchannel heat sink with the same channel geometry used in the experimental work done by Kawano et al. [14]. This simulation showed that the average channel wall temperature along the flow direction was nearly uniform except in the region close to the channel inlet, where very large temperature gradients were observed. Qu and Mudawar [5] conducted a three-dimensional fluid flow and heat transfer analysis for a rectangular microchannel heat sink with a geometry similar to that of Kawano et al. [14] using a numerical method similar to that proposed by both Kawano et al. [14] and Fedorov and Viskanta [6]. This model considered the hydrodynamic and thermal developing flow along the channel and found that the Reynolds number will influence the length of the developing flow region. It was also found that the highest temperature is typically encountered at the heated base surface of the heat sink immediately adjacent to the channel outlet and that the temperature rise along the flow direction in the

In this study the SIMPLE pressure correction approach has been chosen. For simplicity the equations are solved in a segregated manner. An effective multigrid solver is developed for pressure correction equation. Methods for calculating cell-face velocities are studied. Convection and diffusion terms are modeled using upwind and the central difference stencil, respectively. The variables are located in the cell-centred colocated grid. The general coordinates are described using the pure control volume approach with vector notations. In the method developed herein, the velocity field is first solved and then the mean velocity derived. The thermophysical properties are chosen at a reference temperature (an estimated averaged liquid bulk temperature) determined from the energy balance and then a new final velocity field and temperature distribution for the microchannel is defined. A numerical model with fully developed flow is presented and used to analyze the heat transfer in a microchannel heat sink for low Re numbers. The numerical model is based upon a three dimensional conjugate heat transfer approach (3D fluid flow and 3D heat transfer). Computations were performed for different total pressure drops in the channel. The system of three-dimensional Navier-Stokes equations for conservation of mass, momentum, and energy based on the

continuum flow assumption is used as a mathematical model of the process.

solid and fluid regions can both be approximated as linear.

of heat transfer.
