We invstigate the effect of Frank-Kamenetskii parameter d on the thermal explosion in a flammable gas with fuel droplets. It is shown that the induction period decreases as d increases. The droplets increases the volumes of the gas as they evaporate. The combustion medium is quasi-steady after explosion and the medium could no longer be regarded as homogeneous.

A premixed reactive mixture of oxidizer and fuel reacting exothermally subjected to one-step Arrhenius kinetics is modelled mathematically. Theorem on the existence of unique solution of the problem is formulated and proved. Analytical expressions for the thermal ignition time , with and without reactant consumption, under the assumptions of constant thermophysical properties and Frank-Kamenetskii approximation of large activation energy are derived. In general, the problem formulated is solved numerically when the new parameter is strictly greater than modified characteristic time .

This paper discusses the effect of viscosity and viscous dissipation (due to a high velocity gradient) on the steady flow of a viscous liquid in a symmetrically heated channel. The coupled non-linear differential equations arising in the planar Poiseuille flow are not amendable to analytical solutions. Therefore, numerical solutions based on finite-difference scheme are presented. The effects of various flow controlling parameters such as temperature difference α, dimensionless pressure gradient, and the dimensionless viscous heating parameter δ on the dimensionless velocity and temperature are analyzed. The analysis reveals that when viscous heating parameter δ=0, we obtained zero solution for the dimensionless temperature.

The behaviour of a single initial reactant producing different products simultaneously subjected to two-step Arrhenius kinetics is modelled. The model is transient, one-dimensional and includes the effects of activation energy on the explosion time and maximum temperature of the reactant. The problem formulated is solved numerically, theorem on the existence of unique solution is stated and proved, and conditions for the uniqueness of solution are provided in a case of interest.

The development of optimization theory originated with economic requirements and problems, where optimal strategy was to be determined mathematically.At about the same time, approximation theory, which was already well developed, experienced a reinvigoration brought about by the advent of electronic computers. In this paper, what follows, we recall the functional analysis that constitutes the framework of our development of an extended conjugate gradient algorithm that does not involve any approximation in any of its steps. This is a computational enhancement over the conventional conjugate gradient method which is dependent on some approximation theory.We use this improved algorithm for the construction of some functional inequalities.

This paper treats certain analytical properties of the conjugate gradient methods for solving a class of optimal control problems equipped with linear-system integral quadratic cost.

The paper revisits the ignition times of Varatharajan and Wiliams [5] and extends theory to account for heat loss. The paper shows how severe the heat loss could be to prevent ignition from occurring.

In this paper, we examine a non-homogeneous steady branched-chain explosion with slow radical recombination. We show that the problem has a unique solution.

We show that a two-step Arrhenius combustion with finite activation energy has a unique solution. The condition for the uniqueness of solution were provided in case of interest. The theorem on the nature of the solution was stated and proved.

This paper examines finite-amplitude perturbation in macroscopically uniform chemically non-equillibrium system with fluctations close self-ignition. The paper discusses the criteria for attenuation and amplification of waves.