Knowledge of helium diffusion kinetics is critical for materials in which helium measurements are made, particulary for thermochronology. In most cases the helium ages were younger than expected, an observation attributes to diffusive loss of helium and the ejection of high energy alpha particles. Therefore it is important to accurately calculate the distribution of the source term within a sample. In this paper, the prediction of the helium concentrations as function of a spatially variable source term are considered. Both the forward and inverse solutions are presented. Under the assumption of radially symmetric geometry, an analytical solution is deduced based on the eigenfunction expansion. Two regularization methods, the Tikhonov regularization and the spectral cutoff regularization, are considered to obtain the regularized solution. Error estimates with optimal convergence order are shown between the exact solution and the regularized solution. Numerical examples are presented to illustrate the validity and effectiveness of the proposed methods

Cooling methods are needed for turbine blade tips to ensure a long durability and safe operation. A common way to cool a tip is to use serpentine passages with 180-deg turn under the blade tip-cap taking advantage of the three-dimensional turning effect and impingement like flow. Improved internal convective cooling is therefore required to increase the blade tip lifetime. In the present study, augmented heat transfer of an internal blade tip with pin-fin arrays has been investigated numerically using a conjugate heat transfer method. The computational domain includes the fluid region and the solid pins as well as the tip regions. Turbulent convective heat transfer between the fluid and pins, and heat conduction within pins and tip are simultaneously computed. The main objective of the present study is to observe the effect of the pin material on heat transfer enhancement of the pin-finned tips. It is found that due to the combination of turning, impingement and pin-fin crossflow, the heat transfer coefficient of a pin-finned tip is a factor of 2.9 higher than that of a smooth tip at the cost of an increased pressure drop by less than 10%. The usage of metal pins can reduce the tip temperature effectively and thereby remove the heat load from the tip. Also, it is found that the tip heat transfer is enhanced even by using insulating pins having low thermal conductivity at low Reynolds numbers. The comparisons of overall performances are also included.

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller’s method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.

Thermochronometer data offer a powerful tool for quantifying a wide range of geologic processes, such as the deformation and erosion of mountain ranges, topographic evolution, and hydrocarbon maturation. With increasing interest to quantify a wider range of complicated geologic processes, more sophisticated techniques are needed. This paper is concerned with an inverse problem method for interpreting the thermochronometer data quantitatively. Two novel models are proposed to simulate the crustal thermal fields and paleo mountain topography as a function of tectonic and surface processes. One is a heat transport model that describes the change of temperature of rocks; while the other is surface process model which explains the change of mountain topography. New computational algorithms are presented for solving the inverse problem of the coupled system of these two models. The model successfully provides a new tool for reconstructing the kinematic and the topographic history of mountains.

We study a point process model with stochastic intensities for a particular branching population of individuals of two types. Type-I individuals immigrate into the population at the times of a Poisson process. During their lives they generate type-II individuals according to a random age dependent birth rate, which themselves may multiply and die. Living type-II descendants increase the death intensity of their type-I ancestor, and conversely, the multiplication and dying intensities of type-II individuals may depend on the life situation of their type-I ancestor. We show that the probability generating function of the marginal distribution of a type-I individual's life process, conditioned on its individual infection and death risk, satisfies an initial value problem of a partial differential equation, and derive its solution. This allows for the determination of additional distributions of observable random variables as well as for describing the complete population process.