Graduation date: 1975

Heat transfer in moist porous media has been given extensive theoretical consideration. In attempting to define the problem mathematically, either one of two approaches has been followed. There is the mechanistic approach which is based upon the diffusion of vapor and the capillary movement of liquids, and there is the approach which applies the theory of the thermodynamics of irreversible processes. The latter is the more general but both approaches give rise to simultaneous equations for the steady-state flow of matter and energy. These equations contain coefficients which are measures of physical properties of the particular medium under study. In this dissertation two heat transfer coefficients are evaluated: "real" thermal conductivity and "real" thermal diffusivity. Real thermal conductivity is one of the coefficients referred to above and real thermal diffusivity is a coefficient that appears in the equations for the transient flow of heat in moist porous media. Both thermal constants are those that would be obtained if measurements could be made without the interference of moisture transfer. A large-diameter, cylindrical thermal probe was designed and used for evaluation of these real thermal constants. The probe is heated uniformly at a constant rate and as the heat is dissipated in the surrounding medium, the probe temperature is recorded as a function of time. Thermal constants are obtained by comparing a theoretical expression with the experimental data. The theoretical expression includes the probe diameter, the heat capacity per unit length of the probe, and the thermal contact "resistance" between the probe and the surrounding medium. The analysis requires evaluation of the thermal contact resistance from the experimental data and independent determination of the volumetric heat capacity of the surrounding medium. Thermal constants close to real values but which include effects of distillation are obtained from the initial portion of the experimental record. These are then corrected for distillation by subtracting out a small quantity which can be evaluated theoretically. Values of real thermal conductivity and diffusivity were obtained at different moisture contents for 20/30 mesh Ottawa sand and for a sandy loam soil. Real thermal conductivity of the Ottawa sand (with a dry bulk density of approximately 1,7 gms/cm³) increases rapidly from a value of 0.000870 cal/°C/cm/sec when dry to 0.00Lt4 cal/°C/cm/sec at about 15% of saturation. Thereafter it apparently increases at a rate equal to the rate of increase of the volumetric heat capacity of the sand-water system to a value of 0.00755 cal/°C/cm/sec at saturation. Real thermal diffusivity of this material increases from 0.00275 cm²/sec when dry to 0,012 cm²/sec at about 15% of saturation. It remains nearly constant with further increase in water content. In a similar manner, real thermal conductivity of the sandy loam soil (with a dry bulk density of approximately 1.5 gms/cm³) increases rapidly from a value of 0,000605 cal/°C/cm/sec when dry to 0.0036 cal/°C/cm/sec at about 30% of saturation. It then increases at a rate approximately equal to the rate of increase of the volumetric heat capacity of the soil-water system to 0.00595 cal/°C/cm/ sec at saturation. Real thermal diffusivity for this material increases from 0.00223 cm²/sec when dry to 0.0090 cm²/sec at about 30% of saturation. Thereafter it remains essentially constant with further increase in water content. Thus, a single measurement of thermal diffusivity in the saturated sand and soil is sufficient to define real thermal diffusivity over a wide range of moisture contents.

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A simulation program to study the three dimensional temperature distributions produced by hyperthermia in anatomically realistic inhomogeneous tissue models has been developed. The anatomical data for the inhomogeneous tissues of the human body are entered on a digitizing tablet from serial CT scans. The program not only predicts temperature distributions in regions dominated by blood perfusion (with large number of small capillaries), but it can also predict the temperatures inside of and at the vicinity of large blood vessels. The program can be used for different power deposition patterns from various heating modalities, but they must be calculated independently. In this study, the author's attention has been focused on ferromagnetic implants. The program has been used to comparatively evaluate two and three dimensional simulations in a series of parametric calculations based on simple tissue models for both uniform power deposition and ferromagnetic implants. The conclusions drawn from these studies are that two dimensional simulations can lead to significant errors in many situations, and therefore three dimensional simulations will be necessary for accurate patient treatment planning. The conclusion from the geometrically simple model is substantiated by the results obtained using the full 3D model for actual patient anatomical simulations. The program has also been used for several parametric studies. The effect of the thermal conductivity used in the models on the temperature field has been studied, and the results show that its value in the range of 0.4 to 0.6 W/m/°C (valid for most soft tissues) has only a slight effect on the resultant temperature fields. The heating ability of the ferromagnetic implants has also been investigated for different blood perfusions. The effects of the Curie point of the ferromagnetic seeds, and seed spacing are also studied. Finally, the impact of large blood vessels on the resultant temperatures are studied, and the results show that the effect is dramatic and therefore it must be included in the simulations in order to predict accurate temperature fields. Finally, the program has been used to analyze a previously performed dog experiment, and a previously performed clinical treatment. A comparison between the predicted temperatures and the measured ones show that good agreement has been achieved for the clinical treatment, but not for the dog experiment. These results are studied in detail, and the conditions under which this program can be used as a hyperthermia patient treatment planning tool is discussed.

Vita. / Digitized by Kansas Correctional Industries

Thesis. 1976. Sc.D.--Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. / Microfiche copy available in Archives and Science. / Vita. / Includes bibliographical references. / Sc.D.

A first generation, one-dimensional predictive model is proposed for designing heat sinks with fractal flow networks. A three-dimensional computational fluid dynamics (CFD) model is analyzed as a means for validating the model and identifying areas for improvement. Two separate CFD models were developed. One was analyzed with conjugate heat transfer whereas the other was not. For the conjugate heat transfer model, heat flux was provided at a single surface, simulating a heat source. Energy addition to the latter model, referred to as the non-conjugate model, was uniform to all surfaces and was developed to assess the assumptions employed in the one-dimensional model. Both CFD models were run with and without variable properties and are compared to results with a series of parallel channels with identical convective surface areas. In all cases, with and without conjugate heat transfer and with and without variable fluid properties, the fractal flow network showed lower maximum surface temperatures than the straight channel network for identical pumping powers. The pumping power, however, was determined assuming constant fluid properties. The variation in fluid viscosity with temperature was determined to have a significant impact on the pressure distribution, which indicates that variable fluid viscosity needs to be included in the one-dimensional model. Also varied in the analyses were heat sink material, heat flux and flow rate. Qualitative results show that temperature variations within the copper substrate are less significant than in the stainless steel substrate. All analyses, including the one-dimensional model, were restricted to laminar flow conditions. / Graduation date: 2002

The problem of simple mathematical models of laminar natural convective flow within a long vertical parallel-plate channels and circular tubes kept at uniformly heated walls is revisited to seek a clear physical understanding of heat transfer mechanisms. A series solution method to analyze the fully developed flow and an integral solution method to analyze the developing flow are used. Chapters 3, 4, and 5 of this dissertation constitute a series of three-paper manuscripts for submission to archival journals. The channels and circular tubes considered here are assumed to be sufficiently long to yield a fully developed flow thermally as well as hydrodynamically before the exit is encountered. In such fully developed flow situation, the fluid mass flow rate naturally induced into the channel due to buoyancy is found to be a function of the wall heating condition. The predicted average Nusselt number as a function of GrPrD/L not only agrees with the existing literature but also is found to be in a functional form comparable to that proposed by Elenbaas (1942 a and b). Our results show that, in spite of being driven by buoyancy (rather than by a pump or a blower), the flow and heat transfer characteristics in the fully developed regime are essentially the same as those of fully developed laminar forced convection in which the flow is externally driven. This observation is confirmed to be valid also in the study (Chapter 5) of laminar natural convection in the developing (entrance) region within a long vertical parallel-plate channel and circular tube. The mass flow rate, which has to remain invariant with axial location even in the entry region, is determined by the flow in the fully developed region. This is the same mechanism involved in forced convection in which the fluid outside the developing boundary layers (i.e. the core flow) is forced to accelerate in the entrance region. The entrance length of channel natural convection is also discovered to be about the same as that in forced convection. / Graduation date: 2001

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. / published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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