The objective of the current study is to investigate the forced convection laminar boundary layer flow over a flat plate in a diverging channel with variable viscosity. The physical governing equations are converted to nondimensional partial differential equations (PDEs) using similarity transformation. The coupled PDEs with boundary constrains are solved numerically using quasilinearization technique. Computational results are given in terms of flow parameter (Formula presented.), suction or injection A, and viscous dissipation parameter Ec. Stability analysis was conducted and the solutions were found to be stable for real values of (Formula presented.). We found that variable Prandtl number with quasilinearization technique method gives smoothness of solution compared to fixed Prandtl number. This is shown graphically for different fluids in Section 5. Also, the significant effect of the suction/injection parameter (Formula presented.) on velocity, temperature profiles, skin friction, and heat transfer is observed. © 2020 Wiley Periodicals LLC