A theory of heating of Voigt solids and fluids by external energy sources and flame theory

The purpose of this paper is to develop

1. a theory of laser stimulated vaporization of droplets,

2. a theory of internal heating resulting from vibration waves in linearly responding elastic material, and

3. flame theory.

There are applications to sending information through clouds on laser beams and to the control of temperature in ultrasonic welding, and improvement of the design of aircraft engines and the processes used for the destruction of toxic chemicals.

We develop a theory of thermal excursions resulting from ultrasonic welding in 3 and 7 dimensions, and interpret it as an elastic interaction with damping in a Voigt solid. It is hypothesized that with good control of temperature, one could achieve strong and uniform welds by this process and greatly reduce the cost of manufacturing aircraft, and other aluminum structures. We consider equations describing the conservation of mass, momentum, and energy coupled by an equation of state, and consider general mass, momentum, and energy transfer relationships in a compressible body subjected to external stimuli. For the Voigt solid theory, a linear elastic theory with damping forces, we show how some simple local time averaging gives us a dovetailed system consisting of the elastic wave equations whose solution provides the source term for an otherwise uncoupled heat equation. For the more general theory of droplet vaporization, we illustrate a general nonlinear energy equation which includes a radiation energy conductivity term. We get a class of exact solutions for a nonlinear flame front boundary value problem.