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This study consists of proposing a new mathematical method to develop a new model for evaluating thermal distributions throughout convergent-divergent channels between non-parallel plane walls in Jeffery Hamel flow. Subsequently, dimensionless equations that govern temperature fields and velocity are numerically tackled via the Runge–Kutta-Fehlberg approach based on the shooting method. Additionally, an analytical study is performed by applying an effective computation technique named Adomian Decomposition Method. Determining the effect of Reynolds and Prandtl numbers on the heat transfer and fluid velocity inside converging/diverging channels can be mentioned as the fundamental purpose of this research. Based on the results obtained for dimensionless velocity and thermal distributions, a supreme match can be observed between numerical and analytical results indicating the adopted ADM method is valid, applicable, and has great precision.