THE ADOMIAN DECOMPOSITION METHOD FOR THE SOLUTION OF THE TRANSIENT ENERGY EQUATION IN ROCKS SUBJECTEDTO LASER IRRADIATION

Abstract

A 2-D heat conduction model has been solved by using the Adomian Decomposition Method topredict the transient temperature and heat flux distribution in a thick solid that is irradiated by a laser source.The laser source may operate in a continuous wave (CW) mode or repeated pulse (RP) mode and may havearbitrary, spatial and temporal profiles.A generalized solution containing five-terms approximation of a rapidly convergent series is obtained.The solution is then applied to some special cases of practical interest, such as laser irradiation of sandstonesand limestones. Laser drilling of geologic formations is being considered by the petroleum industry in theforeseeable future. The 2-D transient temperature distribution is presented in a graphical form and discussed.A comparison between the results obtained from the Adomian method and those obtained numerically byusing the Crank-Nicholson method is also presented.