Stochastic scattering model of anomalous diffusion in arrays of steady vortices.

We investigate the occurrence of anomalous transport phenomena associated with tracer particles propagating through arrays of steady vortices. The mechanism responsible for the occurrence of anomalous transport is identified in the particle dynamic, which is characterized by long collision-less trajectories (Lévy flights) interrupted by chaotic interactions with vortices. The process is studied via stochastic molecular models that are able to capture the underlying non-local nature of the transport mechanism. These models, however, are not well suited for problems where computational efficiency is an enabling factor. We show that fractional-order continuum models provide an excellent alternative that is able to capture the non-local nature of anomalous transport processes in turbulent environments. The equivalence between stochastic molecular and fractional continuum models is demonstrated both theoretically and numerically. In particular, the onset and the temporal evolution of heavy-tailed diffused fields are shown to be accurately captured, from a macroscopic perspective, by a fractional diffusion equation. The resulting anomalous transport mechanism, for the selected ranges of density of the vortices, shows a superdiffusive nature.

Anomalous diffusion of acoustic waves in 2D periodic media: Radiative transport and renormalization analysis.

This work investigates the occurrence of anomalous transport of acoustic waves propagating in two-dimensional (2D) perfectly periodic media and presents dedicated analysis tools to explore and understand the properties of the medium controlling the transitions between different transport regimes. By leveraging a two-fold approach that combines both radiative transport and renormalization theory, the propagation properties of the inhomogeneous medium can be characterized both near and at the transition from normal to anomalous diffusion. The proposed approach builds upon the classical radiative transfer theory of bulk materials, and it is specifically designed to study 2D systems. The ability to simulate and interpret the field quantities that describe such transport mechanisms can play a significant role in the development of wave-based imaging technology for highly inhomogeneous and scattering media.

Evaluation of heat current formulations for equilibrium molecular dynamics calculations of thermal conductivity.

Equilibrium molecular dynamics combined with the Green-Kubo formula can be used to calculate the thermal conductivity of materials such as germanium and carbon. The foundation of this calculation is extracting the heat current from the results and implementing it into the Green-Kubo formula. This work considers all formulations from the literature that calculate the heat current for the Tersoff potential, the interatomic potential most applicable to semiconductor materials. The formulations for the heat current are described, and results for germanium and carbon are presented. The formulations are compared with respect to how well they capture the physics of the Tersoff potential and how well the calculated value of the thermal conductivity reflects the experimentally measured value.

Analytical solution of the Pennes equation for burn-depth determination from infrared thermographs.

A serious problem in emergency medicine is the correct evaluation of skin burn depth to make the appropriate choice of treatment. In clinical practice, there is no difficulty in classifying first- and third-degree burns correctly. However, differentiation between the IIa (superficial dermal) and IIb (deep dermal) wounds is problematic even for experienced practitioners. In this work, the use of surface skin temperature for the determination of the depth of second-degree burns is explored. An analytical solution of the 3D Pennes steady-state equation is obtained assuming that the ratio between burn depth and the burn size is small. The inverse problem is posed in a search space consisting of geometrical parameters associated with the burned region. This space is searched to minimize the error between the analytical and experimental skin surface temperatures. The technique is greatly improved by using local one-dimensionality to provide the shape of the burned region. The feasibility of using this technique and thermography to determine skin burn depth is discussed.

Particle motion in unsteady two-dimensional peristaltic flow with application to the ureter.

Particle motion in an unsteady peristaltic fluid flow is analyzed. The fluid is incompressible and Newtonian in a two-dimensional planar geometry. A perturbation method based on a small ratio of wave height to wavelength is used to obtain a closed-form solution for the fluid velocity field. This analytical solution is used in conjunction with an equation of motion for a small rigid sphere in nonuniform flow taking Stokes drag, virtual mass, Faxén, Basset, and gravity forces into account. Fluid streamlines and velocity profiles are calculated. Theoretical values for pumping rates are compared with available experimental data. An application to ureteral peristaltic flow is considered since fluid flow in the ureter is sometimes accompanied by particles such as stones or bacteriuria. Particle trajectories for parameters that correspond to calcium oxalates for calculosis and Escherichia coli type for bacteria are analyzed. The findings show that retrograde or reflux motion of the particles is possible and bacterial transport can occur in the upper urinary tract when there is a partial occlusion of the wave. Dilute particle mixing is also investigated, and it is found that some of the particles participate in the formation of a recirculating bolus, and some of them are delayed in transit and eventually reach the walls. This can explain the failure of clearing residuals from the upper urinary tract calculi after successful extracorporeal shock wave lithotripsy. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.

Efecto en la hidrodinámica y transferencia de calor del desfasamiento entre placas de un intercambiador de calor placas onduladas / Effects on the hydrodynamics and heat transfer of dephasing between plates in wavy plate passages

Se utilizó un programa numérico para obtener información respecto a los campos de velocidad, presión y temperatura de un canal que asemeja la parte central de un intercambiador de calor de placas corrugadas. Los resultados buscan analizar el efecto de la diferencia de ángulo de fase entre placas en el desempeño global del intercambiador de calor. El problema requirió la solución de la hidrodinámica y transferencia de calor bajo condiciones bidimensionales de estado permanente con flujo laminar en el canal formado por un par de placas sinusoidales de igual amplitud y longitud de onda entre las cuales existe una diferencia de temperatura. Se consideró un dominio computacional suficientemente largo que incluye varias corrugaciones para poder asumir condiciones periódicas para una longitud de onda de una corrugación. Se presentan resultados de transferencia de calor local y global analizados para un rango de ángulos de defasamiento entre placas. Se obtuvo una configuración para la cual la relación de transferencia de calor adimensional global a caída de presión adimensional es máxima. Los resultados obtenidos son explicados por la relación de los campos de velocidad y temperatura obtenidos en la simulación numérica

Estudio de los parámetros que afectan la transferencia de calor conjugada en intercambiador de calor de tubos y placas-aleta / Study of the parameters affecting conjugated heat transfer in plate-fin and tube heat exchanger

Se utilizó un método numérico para analizar el efecto conjugado de la conducción de calor a través de las aletas y la convección de calor desde la superficie de las mismas en un intercambiador de calor de tubos y placas-aleta. Las simulaciones se desarrollaron con valores de parámetros similares a los encontrados en intercambiadores de calor comerciales. Se analizó el efecto de varios parámetros en la transferencia de calor conjugada. La superficie de la aleta es dividida en dos regiones: aguas arriba del tubo donde la transferencia de calor es elevada, y aguas debajo del tubo donde la transferencia es limitada. La región aguas arriba del tubo se ve más afectada por la conducción a través de las aletas, con disminución de la transferencia de calor cuando la conducción es considerable. Es posible identificar una región de transferencia de calor inversa aguas abajo del tubo. Los parámetros que afectan mayormente la transferencia de calor conjugada son la conductividad y espesor de la aleta, el número de Reynolds y la excentricidad del tubo respecto a la aleta. Existe la posibilidad de mejorar la transferencia de calor del intercambiador haciendo el tubo excéntrico respecto a la longitud de la aleta. Al mover el tubo más cerca del borde de salida de las aletas el área de baja transferencia de calor detrás de los tubos se reduce en tamaño y, al mismo tiempo, la mayor longitud de la parte frontal de la aleta causa un incremento del área frontal, con una reducción del valor local del coeficiente convectivo. Esto sugiere la existencia de una posición óptima del tubo respecto a la longitud de la aleta