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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

mathematical problems in engineering

Modeling of the Radial Heat Flow and Cooling Processes in a Deep Ultraviolet<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>Cu</mml:mtext><mml:mo mathvariant="bold">+</mml:mo></mml:msup></mml:math>Ne-CuBr Laser

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