Analytical Treatment of Temperature Distribution, Stress and Strain Using Uniform Pumped Laser Rod

The analytical solution of axis-symmetry heat equation produced a uniform heat generation has been solved using integral transform method. The temperature distribution, stress and stress have also been obtained. Realistic conviction boundary conditions have been applied to the rod edge and facets. It has been found that increasing edge cooling reduces the temperature distribution but produces more temperature gradient that induces more hoop stress but reduces the longitudinal strain. Optical path also increased as cooling reduces with the difference between optical paths at center to the edge held constant with cooling temperature difference increased but longitudinal strain is decreased. This resulted in constant optical path difference. The limiting factor in decreasing edge cooling is the increase in the produced hoop stress as well.