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This work presents a finite element methodology for solving convection-diffusion problems; the method is a modification of its original version and includes a streamline upwind technique so that false diffusion numerical errors can be decreased. The problem of simultaneous heat, mass and momentum transfer around a horizontal infinite cylinder was solved for natural, mixed and forced convection conditions, as specified by the following conditions: Reynolds numbers less than 10, ambient temperature and cylinder wall temperature in the range from 25 to 60 0C and from 30 to 80 0C, respectively; cylinder wall humidity ratio ranged from 0.0198 to 0.1330 kg-vapor/kg-dry air while the ambient humidity ratio was kept at 0.0099 kg-vapor/kg-dry air . The simulated data agreed with the available experimental data and regression equation within the associated experimental errors. A large number of simulations involving benchmark problems allow inferring that the present method can be applied to anomalously shaped bodies and other conditions.