The Problem With National Institute of Standards and Technology Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology (NIST) report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ, and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Near-field radiative transfer between two unequal sized spheres with large size disparities.

We compute near-field radiative transfer between two spheres of unequal radii R1 and R2 such that R2 ≲ 40R1. For R2 = 40R1, the smallest gap to which we have been able to compute radiative transfer is d = 0.016R1. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit d ≪ R1, and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation.

Convergence of vector spherical wave expansion method applied to near-field radiative transfer.

Near-field radiative transfer between two objects can be computed using Rytov's theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green's function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green's function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.

Surface phonon polaritons mediated energy transfer between nanoscale gaps.

Surface phonon polaritons are electromagnetic waves that propagate along the interfaces of polar dielectrics and exhibit a large local-field enhancement near the interfaces at infrared frequencies. Theoretical calculations show that such surface waves can lead to breakdown of the Planck's blackbody radiation law in the near field. Here, we experimentally demonstrate that surface phonon polaritons dramatically enhance energy transfer between two surfaces at small gaps by measuring radiation heat transfer between a microsphere and a flat surface down to 30 nm separation. The corresponding heat transfer coefficients at nanoscale gaps are 3 orders of magnitude larger than that of the blackbody radiation limit. The high energy flux can be exploited to develop new radiative cooling and thermophotovoltaic technologies.

Measuring thermal conductivity of polystyrene nanowires using the dual-cantilever technique.

Thermal conductance measurements are performed on individual polystyrene nanowires using a novel measurement technique in which the wires are suspended between two bi-material microcantilever sensors. The nanowires are fabricated via electrospinning process. Thermal conductivity of the nanowire samples is found to be between 6.6 and 14.4 W m(-1) K(-1) depending on sample, a significant increase above typical bulk conductivity values for polystyrene. The high strain rates characteristic of electrospinning are believed to lead to alignment of molecular polymer chains, and hence the increase in thermal conductivity, along the axis of the nanowire.

Measurement of optical coupling between adjacent bi-material microcantilevers.

Low thermal conductance bi-material microcantilevers are fabricated with a pad area near the free end to accommodate a focused laser spot. A pair of such cantilevers are proposed as a configuration for measuring thermal conductance of a nanostructure suspended between the two. We determine the resolution of such a device by measuring the stray conductance it would detect in the absence of any nanostructure. Stray conductance, primarily due to optical coupling, is measured for cantilevers with varying pad size and found to be as low as 0.05 nW K(-1), with cantilevers with larger pad size yielding the smallest stray conductance.

Thermal radiation from photonic crystals: a direct calculation.

A classical simulation of equilibrium thermal emissivity from dispersive, lossy photonic crystals is presented. Normal emission results consistent with those assuming Kirchoff's law are obtained; i.e., a photonic crystal does not emit more than what a blackbody does. Significant enhancement, however, can be achieved over the radiation intensity from a uniform slab, indicating the potential usefulness of photonic crystals in incandescent lighting and thermal photovoltaic applications.