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This paper describes a computational study of the cooling airflow around an engine block in a prototypical engine compartment. The three-dimensional Navier-Stokes equations expressed in strong conservation law form are solved on a general curvilinear coordinate system. A single block grid with multiple flow blockages of arbitrary shape is used. From the CFD results, an engine compartment resistance curve is computed and is matched with a representative fan performance curve. The fan operating condition is determined and the corresponding heat rejection rate for the engine compartment is obtained. This systematic approach for predicting the cooling airflow through an engine compartment provides a fast and cost-effective design methodology for use in the development of vehicle engine cooling system.