**4. Results**

260 Heat Exchangers – Basics Design Applications

*c c co ci hi ci c c co ci hi ci*

, , , , *c c co ci h c c c co ci h c*

By using the estimated errors of parameters listed in Table 3, the maximum experimental uncertainties in determining q, k, Re, , and were 2.1%, 2.2%, 3.1%, 0.9%, and 3.3%,

Numerical study of the behavior of the microchannel heat exchanger with 3D single-phase fluid flow and heat transfer was done by using the COMSOL Multiphysics software, version 3.5. The algorithm of this software was based on the finite element method. For the COMSOL package, the generalized minimal residual (GMRES) method was used to solve for the model used in this study; the GMRES method was an iterative method for general linear systems. At every step, the method performed minimization of the residual vector in a Krylov subspace [32], and the Arnoldi iteration was used to find this residual vector. To improve the convergence of the iterative solver used by the GMRES method, the Incomplete LU (lower-upper) pre-conditioner was selected for nonsymmetric systems, where LU is a matrix which was the product of a lower triangular matrix and an upper triangular matrix. For the study, water was used as the working fluid. With the mass flow rate of water from 0.1667 to 0.8540 g/s, the Reynolds number was lower than 400 and the working fluid in the microchannels of the heat exchanger was under laminar flow condition [2]. No internal heat generation was specified, resulting in *Qi* = 0. The finite elements in the grid meshes were partitioned to be triangular, as shown in Fig. 5. The maximum element size scaling factor was 1.9, with element growth rate of 1.7, mesh curvature factor of 0.8, and mesh curvature cut-off of 0.05. In Fig. 4, the schematic meshing of the heat exchanger consists of 26,151 mesh

elements, the number of degrees of freedom is 76,411, and a relative tolerance is 10-6.

Fig. 5. Grid mesh diagram of the microchannel heat exchanger.

*Um c m c TT TT m c m c TT TT*

*U m c T T p p m c TT p p*

respectively, for all cases being studied.

**3. Numerical simulation** 

1/2 2 2 2 2 2 2

1/2 2 2 <sup>2</sup> 2 2

, , ,, , , ,,

(15)

(16)
