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This study presents a computational investigation on heat and flow behaviors between non parallel plates with the influence of a transverse magnetic field when the medium is filled with solid nanoparticles. The nonlinear governing equations are treated analytically via Differential Transform Method (DTM). Thereafter, obtained DTM results are validate with the help of numerical fourth order Runge-Kutta (RK4) solution. The main aim of this research work is to analyze the influence of varying physical parameters, in particular Reynolds number, nanofluid volume fraction, and Hartmann number. It was found that the presence of solid nanoparticles in a water base liquid has a notable effect on the heat transfer improvement within convergent-divergent channels. The comparison of DTM results with numerical RK4 solution also shows the validity of the analytical DTM technique. In fact, results demonstrate that the DTM data match perfectly with numerical ones and those available in literature.