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Mathematical Problems in Engineering
Volume 2009, Article ID 582732, 16 pages
Research Article

Modeling of the Radial Heat Flow and Cooling Processes in a Deep Ultraviolet Ne-CuBr Laser

1Department of Physics, Technical University of Plovdiv, 25 Tzanko Djusstabanov Street, 4000 Plovdiv, Bulgaria
2Department of Applied Mathematics and Modeling, Faculty of Mathematics and Informatics, Paisii Hilendarski University of Plovdiv, 24 Tsar Assen Street, 4000 Plovdiv, Bulgaria
3Metal Vapour Lasers Department, Georgi Nadjakov Institute of Solid State Physics, Bulgarian Academy of Sciences, 72 Tsarigradsko Shaussee Boulevard, 1784 Sofia, Bulgaria

Received 17 April 2009; Accepted 3 August 2009

Academic Editor: Saad A Ragab

Copyright © 2009 Iliycho Petkov Iliev et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An improved theoretical model of the gas temperature profile in the cross-section of an ultraviolet copper ion excited copper bromide laser is developed. The model is based on the solution of the one-dimensional heat conduction equation subject to special nonlinear boundary conditions, describing the heat interaction between the laser tube and its surroundings. It takes into account the nonuniform distribution of the volume power density along with the radius of the laser tube. The problem is reduced to the boundary value problem of the first kind. An explicit solution of this model is obtained. The model is applied for the evaluation of the gas temperature profiles of the laser in the conditions of free and forced air-cooling. Comparison with other simple models assumed constant volume power density is made. In particular, a simple expression for calculating the average gas temperature is found.