End pumped lasers are highly efficient lasers particularly in diode lasers using micro lenses. The common cooling method for end-pumped systems is using water jacket or copper tube surrounding the laser rod. In this paper, the temperature distribution within a water jacket and a fiber laser end pumped by a top hat beam is studied analytically. The temperature distribution is obtained by considering the radial heat convection with fully developed laminar flow neglecting the axial heat conduction. The effect of laser dimensions and the Brinkman number on the temperature distribution are presented. The results indicate that the temperature distribution is strongly dependent on the Brinkman number. The results are presented in dimensionless form so that they can be applied to any end-pumped laser rod and fluid types. The main output of this work is that it is better for cooling purposes to have low Br values.

Analysis of entropy generation in a rectangular slab with a nonuniform internal heat generation is presented. Dimensionless local and total entropy generation during steady state heat conduction through the slab are obtained. Two different boundary conditions have been considered in the analysis, the first with asymmetric convection and the second with constant slab surface temperature. Temperature distribution within the slab is obtained analytically. The study investigates the effect of some relevant dimensionless heat transfer parameters on entropy generation. The results show that there exists a minimum local entropy generation but there does not exist a minimum total entropy generation for certain combinations of the heat transfer parameters. The results of calculations are presented graphically