In this work, a laminar forced convection air flow in a rectangular vertical venturi has been numerically simulated. Mathematical transformation has been used to transform the irregular profile of the venturi wall into straight line. Transfers equations are solved using finite volume method, Gauss and Thomas algorithms. A computing algorithm has been generated for the problem simulation. Hydrodynamics and thermals effects are investigated in detail. Results are presented as velocity and streamlines patterns, and temperature profiles.