The thermofluid characteristics of the infrared suppression (IRS) device used in the marine gas turbine as an exhaust system are numerically investigated here. The prime objective is to observe the impact of convection united with surface radiation on the cooling of the IRS. Furthermore, the time taken to cool down the device is also estimated. A comparison exercise is also carried out to elucidate the impact of radiation considering the surface radiation and without it (taking only convection). The numerical solution of the Navier–Stokes equation, energy equation, and radiation equation, along with the turbulence equations, are performed using ANSYS FLUENT 15.0. Various relevant parameters are taken for the analysis, namely, Rayleigh number (Ra) (1 × 1010 ≤ Ra ≤ 1 × 1012), diameter ratio (DR) (1.01 ≤ DR ≤ 1.3), funnel overlapping (OL) (−20% ≤ OL ≤ 20%), and emissivity of the surface (ε) (0 ≤ ε ≤ 1). It is noticed that surface radiation has an enormous contribution to the total heat transfer and, thus, could not be neglected. The total heat transfer rate and mass flowrate increase with Ra and DR. Also, the contribution of convective heat transfer drops with the rise in emissivity. In addition, the convection united with surface radiation case reduces the cooling time (almost half) than the natural convection alone case.