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In this study, a magnetohydrodynamic Jeffrey-Hamel flow of a viscous, fluid that conducts electricity and is incompressible through a divergent conduit in presence of inclined variable magnetic field with heat and mass transfer has been investigated. The solutions of the governing equations of the MHD flow are obtained numerically since they are nonlinear. The numerical scheme used is implemented in a computer software program and the results presented in graphical form. The velocity profile, the temperature profiles, the effect of variable magnetic field and of varying various dimensionless numbers on the flow are analyzed. Jeffrey-Hamel flows are also applied in the diffuser development. Some of the systems include; the channel between the compressor and gas turbine engine burner, the canal at departure from a gas turbine linked to the jet pipe, the canal subsequent to the impellor of a centrifugal compressor, wind tunnels with closed circuits, and water turbine draft tubes among several others. The results provide significant information for the improvement of proficiency and performance of technologies in aerospace, chemical, civil, environmental, industrial and mechanical applications.