This study inspects the heat transport of a ternary hybrid nanofluid flow inside a receiver tube in a parabolic trough solar collector. The mathematical model of the flow is modeled inside the receiver tube using rotating parallel plates. The analysis discusses the influence of the Hall effect, the Cattaneo-Christov model, suction/injection, and thermal radiation (linear and quadratic). Traditional approaches to the parametric study which involve a large number of parameters sometimes fail to infer meaningful outcomes due to the high complexity of the model and numerical methods. To resolve this matter, this study evaluates the capability of soft computing techniques to foresee the behavior of a problem with various interrelated parameters. The data obtained by simulation is used to train the artificial neural network and particle swarm optimization algorithm. Thereafter artificial neural network and particle swarm optimization algorithm is utilized to precisely estimate the values of the Nusselt number at the lower and upper plates. The prediction performance of the developed algorithms is analyzed with the help of mean squared error, average forecasting error rate, and coefficient of correlation. The analysis shows the advantages of soft computing techniques to study the behavior of complex flow models with high accuracy.