A Simplified ‘Effective Circuit’ Fluid Flow Model for Forced Convection in Oblique Fin Configuration

Abstract

In this paper, a simplified ‘effective circuit’ fluid flow model is proposed to complement full-domain (geometry based) simulations of fluid flow in novel discrete oblique fin heat sinks. In the proposed model, the discrete flow paths are modeled as effective resistances, and the intersections between discrete flow paths are modeled as ‘nodes’. In an electrical circuit, the current of each branch can be derived from the current division rule, and hence the actual flow rates in the effective circuit are determined by the effective resistances. Simulink R2011b, a graphical extension to MATLAB for modeling and simulation of systems, is chosen to construct the equivalent circuit. The effective resistances are calculated using the well-known friction factor expressions for laminar flow in micro-channels. A full-domain geometry-based simulation is performed on CFX 14.0 serving as a benchmark for the developed ‘effective circuit’ fluid flow model. The results show that for a given total current value and mass flow rate, the difference of pressure drop over the whole heat sink between the simplified flow model and CFX simulation is within 13%. The mass flow distributions obtained from the simplified flow model and the CFX simulation exhibit a common distribution pattern. Interestingly, the simplified flow model is even able to capture flow migration — a distinctive phenomenon of flow in oblique fin geometries. We thus confirm the feasibility of the method of construction of our simplified ‘effective circuit’ fluid flow model.