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The superstructure of a modern naval ship is fitted with multitude of sensors for electronic surveillance, weapon discharge, navigation, communication and varieties of deck handling equipment. Locating these electronic equipment/sensors and its integration on board is of paramount importance to achieve optimal operational performance of the naval vessel. Among the many problems in locating these sensors (like stability, EMC EMI etc.,), the presence of entrapped hot gases from the ship exhaust affects the functioning of these electronics. Hence the prediction of temperature profile and trajectories of the ship exhaust plume from the funnel around the superstructure during the design stage is a mandatory requirement for positioning the sensors on superstructure. This trajectory prediction is not amenable to theoretical analysis or empirical calculation procedures in the modern warship superstructure. Experimental and CFD studies conducted on ship superstructure are the only reliable tools that are available to estimate temperature field as well as to study the exhaust smoke superstructure interaction on ships. This paper presents the CFD simulation of the published results for two cases, namely hot jet in a cross flow and hot exhaust with a cross flow on a generic frigate. Simulations have been made using k-ɛ turbulence model with different values of turbulent Schmidt number. It has been observed that temperature field is predicted with reasonable accuracy with turbulent Schmidt number of 0.2.