Kunal Mitra

Experimental Evidence of Hyperbolic Heat Conduction in Processed Meat

The objective of this paper is to present experimental evidence of the wave nature of heat propagation in processed meat and to demonstrate that the hyperbolic heat conduction model is an accurate representation, on a macroscopic level, of the heat conduction process in such biological material. The value of the characteristic thermal time of a specific material, processed bologna meat, is determined experimentally. As a part of the work different thermophysical properties are also measured. The measured temperature distributions in the samples are compared with the Fourier results and significant deviation between the two is observed, especially during the initial stages of the transient conduction process. The measured values are found to match the theoretical non-Fourier hyperbolic predictions very well. The superposition of waves occurring inside the meat sample due to the hyperbolic nature of heat conduction is also proved experimentally. 14 refs., 7 figs., 2 tabs.

Development and comparison of models for light-pulse transport through scattering–absorbing media

We examine the transport of short light pulses through scattering-absorbing media through different approximate mathematical models. It is demonstrated that the predicted optical signal characteristics are significantly influenced by the various models considered, such as P(N) expansion, two-flux, and discrete ordinates. The effective propagation speed of the scattered radiation, the predicted magnitudes of the transmitted and backscattered fluxes, and the temporal shape and spread of the optical signals are functions of the models used to represent the intensity distributions. A computationally intensive direct numerical integration scheme that does not utilize approximations is also implemented for comparison. Results of some of the models asymptotically approach those of direct numerical simulation if the order of approximation is increased. In this study therefore we identify the importance of model selection in analyzing short-pulse laser applications such as optical tomography and remote sensing and highlight the parameters, such as wave speed, that must be examined before a model is adopted for analysis.

Microscale Aspects of Thermal Radiation Transport and Laser Applications

Abstract This chapter briefly discusses current and future applications in which the range of parameters makes the classical models and associated phenomenological descriptions of transport processes no longer adequate. Some fundamental concepts of relevance to the development of models using a fundamental microscale approach are reviewed, as are microscale models for selected cases. Regime maps are developed to guide the model selection processes and to identify the phenomena that may or may not be important for a given set of conditions. It is seen that the microscale models match experimental data with less error than the classical macroscopic models for many applications in which extremes of size, time, and radiation intensity are present. Application areas discussed in detail are modeling of interference effects in evaluating the scattering and absorption characteristics, radiation transport in microstructures, short-pulse radiation transport through scattering and absorbing media, interaction of high-intensity lasers with metallic films and liquids, and ablation of polymers and tissues.

Transient Radiation Transport in Participating Media Within a Rectangular Enclosure

This paper outlines the formulation of the two-dimensional transient radiation transport through a scattering‐ absorbing medium. The P1 approximation in a Cartesian coordinate system is invoked to simplify the transient radiative transfer equation because it is very complicated to solve in its general form. A boundary-driven radiative problem is considered in which the radiation intensities at some areas on a surface are modeled as boundary conditions and maintained at constant values in all angular directions.

Temperature distribution in different materials due to short pulse laser irradiation

The purpose of this study is to analyze the heat-affected zone in materials such as meat samples, araldite resin-simulating tissue phantoms, and fiber composites irradiated using a mode-locked short pulse laser with a pulse width of 200 ps. The radial surface temperature profiles are compared with that of a continuous wave (CW) laser of the same average power. The short pulse laser results in a more localized heating than a continuous laser with a corresponding high peak temperature. A parametric study addressing the effect of pulse train frequency, material thickness, and amount of scatterers and absorbing agent in the medium and different initial sample temperatures is performed, and the measured temperature profiles are compared with the theoretical non-Fourier hyperbolic formulations and Fourier parabolic heat conduction formulations for both CW and pulsed laser cases.

Discrete Transfer Method Applied To Transient Radiative Transfer Problems in Participating Medium

Application of the discrete transfer method is extended to solve transient radiative transport problems with participating medium. A one-dimensional gray planar absorbing and aniso-tropically scattering medium is considered. Both boundaries of the medium are black. The incident boundary of the medium is subjected to pulse-laser irradiation, while the other boundary is cold. For radiative parameters such as optical thickness, scattering albedo, anisotropy factor, transmittance, and reflectance at the boundaries are found. Results obtained from the present work are compared with those available in the literature. The discrete transfer method has been found to give an excellent agreement.

Hyperbolic damped-wave models for transient light-pulse propagation in scattering media

Transient optical transport in highly scattering media such as tissues is usually modeled as a diffusion process in which the energy flux is assumed proportional to the fluence (intensity averaged over all solid angles) gradients. Such models exhibit an infinite speed of propagation of the optical signal, and finite transmission values are predicted even at times smaller than those associated with the propagation of light. If the hyperbolic, or wave, nature of the complete transient radiative transfer equation is retained, the resulting models do not exhibit such drawbacks. Additionally, the hyperbolic equations converge to the solution at a faster rate, which makes them very attractive for numerical applications in time-resolved optical tomography.

Analysis of short-pulse laser photon transport through tissues for optical tomography

We describe a method for analyzing short-pulse laser propagation through tissues for the detection of tumors and inhomogeneities in tissues with the goal of developing a time-resolved optical tomography system. Traditional methods for analyzing photon transport in tissues usually involve the parabolic or diffusion approximation, which implies infinite speed of propagation of the optical signal. To overcome such limitations we calculate the transmitted and reflected intensity distributions, using the damped-wave hyperbolic P(1) and the discrete-ordinates methods, for a wide range of laser, tissue, and tumor parameters. The results are compared with the parabolic diffusion P(1) approximation.

Hyperbolic temperature profiles for laser surface interactions

This study theoretically analyzes the transient temperature distributions in laser irradiated materials by considering a hyperbolic heat conduction model. Exact and limiting mathematical solutions for the temperature distributions are developed and important parameters are identified. Traditional Fourier transient heat conduction models are parabolic in nature, which imply an infinite speed of propagation of the thermal signal in the material. Hyperbolic non‐Fourier models have been introduced to account for the finite speed of the thermal wave. The effects of finite speed are significant in short‐pulse applications where the time period of the laser input is comparable to the thermal characteristic time of the material, and the resultant temperature variations are significantly different from that of traditional infinite‐speed Fourier predictions. Two different types of materials, biological materials and inorganic solids, are considered for laser‐surface interactions in the study. The parameter of greatest significance is found to be the ratio of thermal characteristic length to the laser beam width. Values of this parameter in the range between 0.1 and 3, corresponding to different applications, are examined and local temperature maximas, or hot spots, are found to occur at initial time periods for values greater than ∼0.2.

Transient radiative transfer equation applied to oceanographic lidar

We estimate the optical signal for an oceanographic lidar from the one-dimensional transient (time-dependent) radiative transfer equation using the discrete ordinates method. An oceanographic lidar directs a pulsed blue or green laser into the ocean and measures the time-dependent backscattered light. A large number of parameters affect the performance of such a system. Here the optical signal that is available to the receiver is calculated, rather than the receiver output, to reduce the number of parameters. The effects of albedo of a uniform water column are investigated. The effects of a school of fish in the water are also investigated for various school depths, thicknesses, and densities. The attenuation of a lidar signal is found to be greater than the diffuse attenuation coefficient at low albedo and close to it at higher albedo. The presence of fish in the water is found to have a significant effect on the signal at low to moderate albedo, but not at high albedo.