We present a mathematical model of flat-plate solar collector whose thermal conductivity is a power law function of temperature, and non-dimensional length is governed by a profile index. The rectangular, convex and triangular shape absorber plates are obtained by changing the value of an index of non-dimensional length 0, ½ and 1, respectively. The energy equation governing the temperature of rectangular absorber plate is a non-singular-type equation, and convex and triangular cross-section absorber plate are two different singular type equations. One non-singular and two different singular value equations are solved separately by different operators, as explained separately in classical and modified Adomian decomposition method (ADM) theory respectively. The results obtained for the case of the rectangular, convex and triangular cross-section plate are validated by comparison with the exact analytical solution for special case as available in literature. The effects of various thermo-physical parameters such as power law thermal conductivity parameter, Biot number, aspect ratio, absorbed solar heat flux, overall heat transfer coefficient on the temperature distribution are analyzed.