The key incentive of current research is to perform numerically a parametric investigation of the thermal-hydraulic performance in a fin-and-tube compact heat exchanger (FTCHE) presenting innovative design of fin profiles and oval form of tubes. Three different corrugated profiles of fin design consist of ONCF (corrugated fin with one fluted domain), TWCF (corrugated fin with two fluted domains), and THCF (corrugated fin with three fluted domains) shapes are investigated by a parametric design exploration technique combined with response surface methodology (RSM). The impacts of the nine geometrical factors counting fin pitch (Fp), longitudinal tube spacing (SL), transverse tube spacing (ST), fin thickness (δf), fin width (Fw), fluted height (hf), wing length of corrugated fin (Wout), wing angle (α), and fluted angle (β) on improving the heat transfer performance of a corrugated-fin-and-tube compact heat exchangers with a four-row inline oval tube bank are studied for the range of Reynolds number between 500 and 5000. Fluid flow and heat transfer are simulated using Realizable k–ε turbulence model with steady and incompressible fluid flow. The numerical outcomes show that the fins with corrugated profiles can significantly increase heat transfer enhancement through modification of the situation with respect to the shape of oval tube, fluted number and different parameters of fluted areas. The outcomes of study indicated that the η-factor (Thermal-hydraulic performance criteria) of the FTCHE with one-corrugated fin is superior than that of conventional and other case studies. The η-factor in FTCHEs with THCF, TWCF, and ONCF designs displayed 20.9%, 13.3%, 36.0% augmentation compared with its conventional smooth fin and oval tubes counterpart, respectively. Furthermore, FTCHE with ONCF design has the best performance between other fin designs. The investigation indicated that the corrugated fins can significantly advance the heat transfer and performance of the FTCHEs.