Heat transport in nanofluids and biological tissues

Abstract

The present work contains two parts: nanofluids and bioheat transport, both involving multiscales and sharing some common features. The former centers on addressing the three key issues of nanofluids research: (i) what is the macroscale manifestation of microscale physics, (ii) how to optimize microscale physics for the optimal system performance, and (iii) how to effectively manipulate at microscale. The latter develops an analytical theory of bioheat transport that includes: (i) identification and contrast of the two approaches for developing macroscale bioheat models: the mixture-theory (scaling-down) and porous-media (scaling-up) approaches, (ii) rigorous development of first-principle bioheat model with the porous-media approach, (iii) solution-structure theorems of dual-phase-lagging (DPL) bioheat equations, (iv) practical case studies of bioheat transport in skin tissues and during magnetic hyperthermia, and (v) rich effects of interfacial convective heat transfer, blood velocity, blood perfusion and metabolic reaction on blood and tissue macroscale temperature fields. Nanofluids, fluid suspensions of nanostructures, find applications in various fields due to their unique thermal, electronic, magnetic, wetting and optical properties that can be obtained via engineering nanostructures. The present numerical simulation of structure-property correlation for fourteen types of two/three-dimensional nanofluids signifies the importance of nanostructure’s morphology in determining nanofluids’ thermal conductivity. The success of developing high-conductive nanofluids thus depends very much on our understanding and manipulation of the morphology. Nanofluids with conductivity of upper Hashin-Shtrikman bounds can be obtained by manipulating structures into an interconnected configuration that disperses the base fluid and thus significantly enhancing the particle-fluid interfacial energy transport. The numerical simulation also identifies the particle’s radius of gyration and non-dimensional particle-fluid interfacial area as two characteristic parameters for the effect of particles’ geometrical structures on the effective thermal conductivity. Predictive models are developed as well for the thermal conductivity of typical nanofluids. A constructal approach is developed to find the constructal microscopic physics of nanofluids for the optimal system performance. The approach is applied to design nanofluids with any branching level of tree-shaped microstructures for cooling a circular disc with uniform heat generation and central heat sink. The constructal configuration and system thermal resistance have some elegant universal features for both cases of specified aspect ratio of the periphery sectors and given the total number of slabs in the periphery sectors. The numerical simulation on the bubble formation in T-junction microchannels shows: (i) the mixing enhancement inside liquid slugs between microfluidic bubbles, (ii) the preference of T-junctions with small channel width ratio for either producing smaller microfluidic bubbles at a faster speed or enhancing mixing within the liquid phase, and (iii) the existence of a critical value of nondimensional gas pressure for bubble generation. Such a precise understanding of two-phase flow in microchannels is necessary and useful for delivering the promise of microfluidic technology in producing high-quality and microstructure-controllable nanofluids. Both blood and tissue macroscale temperatures satisfy the DPL bioheat equation with an elegant solution structure. Effectiveness and features of the developed solution structure theorems are demonstrated via examining bioheat transport in skin tissues and during magnetic hyperthermia.