Impingement/effusion cooling has no cross-flow in the impingement gap if all the coolant flow through the impingement wall passes through the effusion wall. In this investigation, the impingement part of the impingement/effusion cooling was investigated by minimising the cross-flow using a four sided exit impingement cooling geometry. The impingement geometry investigated was a square array of 10 by 10 impingement holes with a pitch to diameter, X/D, of 11, hole density, n, of 4306m−2, and gap to diameter ratio, Z/D, of 7.25 for coolant mass flux G of 0.2–1.1 kg/sm2bar. The impingement target and jet walls were modelled as Nimonic-75 as used in the experimental work used for validation of the computational methods. Conjugate heat transfer (CHT) computational fluid dynamics (CFD) was used with ANSYS Fluent code. The measured impingement target wall pressure loss ΔP/P% and target wall surface averaged heat transfer coefficient together with the heat transfer to the impingement jet wall were all predicted in agreement with the measurements, within the measured error bars. The predicted surface distributions of Nu and turbulent kinetic energy (TKE) were compared with predictions for impingement single sided exit flow and the impingement/effusion approach (target) walls. This showed that the reduced crossflow with the four sided exit gave higher surface averaged heat transfer. However, comparison with the impingement/effusion wall heat transfer, for the same impingement wall geometry, showed that the removal of coolant through the effusion wall reduced the recirculating flow in the impingement gap and this reduced the heat transfer to the impingement jet wall, but increased it to the target effusion wall.