A Decomposition Solution of Variable Thickness Absorber Plate Solar Collectors With Power Law Dependent Thermal Conductivity

We present a mathematical model of flat-plate solar collector whose thermal conductivity is a power law function of temperature, and nondimensional 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 nondimensional length 0, 1/2, and 1, respectively. The energy equation governing the temperature of rectangular absorber plate is a nonsingular-type equation, and convex and triangular cross-sectional absorber plates are two different singular-type equations. One nonsingular and two different singular value equations are solved separately by different operators, as explained separately in classical and modified Adomian decomposition method (ADM), respectively. The results obtained for the case of the rectangular, convex, and triangular cross-sectional plates are validated by comparison with the exact analytical solution for special case as available in literature. The effects of various thermophysical parameters such as power law thermal conductivity parameter, Biot number, aspect ratio, absorbed solar heat flux, and overall heat transfer coefficient on the temperature distribution are analyzed.