<p>We present analytical models for variable cross-section absorber plate solar collectors, where the thermal conductivity, overall heat loss coefficient, and incident solar heat flux are power-law functions of temperature. The rectangular cross-section absorber plate (RE) serves as the base cross-section, while four reduced cross-section absorber plates namely the bigger edge convex (BE), conventional convex (Conv), smaller edge convex (SE), and triangular cross-section (TR) can be progressively derived by altering the thickness from the base cross-section. The governing equation for the rectangular cross-section is non-singular, while all the reduced cross-sections represent distinct singular value problems. The non-singular and singular value problems are solved using the classical Adomian decomposition method (ADM) and the modified Adomian decomposition method (MADM), respectively. For the present analysis, the average solar heat flux, along with the maximum and minimum declination angles, for a particular site in Santiniketan has been selected. Graphical plots of various absorber plate cross-sections, considering significant power index parameters, thermal conductivity, overall heat transfer coefficient, and solar heat flux based on the maximum and minimum declination angles, aspect ratio, and Biot number, are presented and physically interpreted. From the comparative studies, it has been observed that the mid point temperature of each cross-section of the absorber plate shows a progressively decreasing trend with increasing thickness. Furthermore, the study reveals that the efficiency of the reduced profiles lies between their decreasing tip thickness values.</p>