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Investigation of thermal transport in nanofluid flow squeezed inside a channel formed by two sheets with zero slope is common in industrial and engineering applications. The heat transmission could be affected by various physical constraints which reduce the machine efficiency for desired products. Therefore, this attempt clearly focus on the development of new nanofluid thermal transport model using the significance effects of Koo-Kleinstreuer-Li correlation which used for the estimation of nanofluid thermal conductivity, impacts of magnetic field, internal heating species, and thermal radiations. Then, the LSM (Least Square Method) is magnificently implemented and obtained the physical results for multiple ranges of parameters. It is noticed that when the squeezed parameter varied in the ranges of − 0 . 1 to − 2 . 6 and 0 . 1 to 2 . 6 , the fluid loss their velocity and more reduction is occurred about η = 0 . 0 . However, outward movement of the plate lead to quick declines in the velocity. Further, when the Hartmann number increased for 1 . 0 – 6 . 0 then the fluid moves slowly and stronger magnetic field resists its motion. Moreover, the Eckert and Radiation numbers boosted the fluid temperature by keeping the feasible nanoparticles concentration in the range of ϕ = 0 . 02 – ϕ = 0 . 12 .