Analytical study of impact of the wick’s fractal parameters on the heat transfer capacity of a novel micro-channel loop heat pipe

This paper presents an analytical study of the impact of a wick’s fractal geometrical parameters on the heat transfer capacity of a novel micro-channel loop heat pipe (MCLHP) which is applicable to solar heating system. By treating the wick of the micro-channel evaporator of the MCLHP as a thin porous layer, i.e. a combination of random/tortuous pores and water-containing skeletons, the impact of the fractal geometrical parameters of the wick on the heat transport capacity of the MCLHP was investigated. Based on the classical heat transfer limits and fractal equations, a dedicated computerised analytical model was developed by using the Newton-Raphson method; this model was then applied to analyze a few macro parameters of the wick (i.e., effective thermal conductivity and permeability) and heat transfer limits of the MCLHP, including capillary, viscous, entrainment, sonic and boiling ones. Comparison among these five limits was made using the minimum value searching approach, leading to the determination of the final heat transfer constraint of the MCLHP, which is identified as the capillary limit. A higher effective porosity and a larger pore diameter lead to an increased wick fractal dimension and thus a higher capillary limit. An increased height difference between the evaporator and the condenser also increases the heat transfer (i.e. capillary) limit of the MCLHP. Decreased effective porosity (ε), pores portion, and increased tortuosity of capillaries help enhance the heat transfer (boiling) limit of the MCLHP. Overall, fractal theory is thought to be an ideal method to address the impact of an irregular porous wick on the heat transfer performance of a MCLHP.