This study examines how boundary conditions affect the modeling of mixed convection flow in an inclined tube for ciliary motion of a non-Newtonian fluid. Understanding mixed convection flow from this study can be useful for environmental engineering tasks like contaminant dispersion in soil or water bodies. The governing equations for non-newtonian fluid and heat are simplified by assuming low Reynolds numbers and long wavelengths. To solve the momentum problem for velocity and temperature equations, Particle Swarm Optimization (PSO) is employed using an unsupervised artificial neural network method. The proposed approach achieves promising results with up to one hundred (100) independent algorithm evaluation runs to predict the non-Newtonian flow behavior of liquids under different temperature conditions. An efficient way for finding approximations of solutions was the ANN-PSO method with optimized weights and fitness function. The fitness function value decreases when the right weights are chosen, showing that the approximation is becoming more accurate. The temperature is an increasing function of the cilia length factor and inversely proportional to the heat absorption factor near the middle of the channel.