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.