Thermoelastic waves in an infinite solid caused by a line heat source

The generalized thermoelasticity theory recently developed by Green and Naghdi is employed to investigate thermoelastic interactions caused by a continuous line heat source in a homogeneous isotropic unbounded solid. Hankel-Laplace transform technique is used to solve the problem. Explicit expressions, for stress and temperature fields, are obtained for small time approximation. Numerical values are displayed graphically. Our results show that this theory predicts an infinite speed for heat propagation in general, and includes the second sound phenomena as a special case.

An Approximate Analysis of Laminar Dispersion in Circular Tubes

The combined effects of convection and diffusion for dispersion on mass transport in fully developed laminar flow through circular tubes are investigated. The present method, which in general may be used to yield solutions at any arbitrary dimensionless time, in its zeroth-order approximation is identical to Taylor’s analysis for the average concentration. Solutions to the basic differential equation for an initial input of solute either concentrated at a section of the tube or uniformly distributed in the form of a slug of finite axial extension are developed. Numerical results for the former input are presented over a large range of dimensionless time and Peclet numbers. The time limitations of Taylor’s solution and Lighthill’s small time approximation [15] are placed on more reliable quantitative bases by comparison with the present calculations.