The flow structure and convective heat transfer behavior of a free liquid jet ejecting from a round nozzle impinging vertically on a hemispherical solid plate and a slot nozzle impinging vertically on a cylindrical curved plate have been studied using a numerical analysis approach. The simulation model incorporated the entire fluid region and the solid hemisphere or curved plate. Solution was done for both isothermal and constant heat flux boundary conditions at the inner surface of the hemispherical plate and the constant heat flux boundary condition at the inner surface of the cylindrical shaped plate. Computations for the round nozzle impinging jet on the hemispherical plate and cylindrical plate were done for jet Reynolds number (ReJ) ranging from 500 to 2000, dimensionless nozzle to target spacing ratio (β) from 0.75 to 3, and for various dimensionless plate thicknesses to diameter nozzle ratio (b/dn) from 0.083-1.5. Also, computations for the slot nozzle impinging jet on the cylindrical plate were done for inner plate radius of curvature to nozzle diameter ratio (Ri/dn) of 4.16-16.66, plate thickness to nozzle diameter ratio (b/dn) of 0.08-1.0, and different nozzle diameters (dn), Results are presented for dimensionless solid-fluid interface temperature, dimensionless maximum temperature in the solid, local and average Nusselt numbers using the following fluids: water (H2O), flouroinert (FC-77), and oil (MIL-7808) and the following solid materials: aluminum, copper, Constantan, silver, and silicon. Materials with higher thermal conductivity maintained a more uniform temperature distribution at the solid-fluid interface. A higher Reynolds number increased the Nusselt number over the entire solid-fluid interface. Local and average Nusselt number and heat transfer coefficient distributions showed a strong dependence on the impingement velocity or Reynolds number. As the velocity increases, the local Nusselt number increases over the entire solid-fluid interface. Decreasing the nozzle to target spacing favors the increasing of the Nusselt number. Increasing the nozzle diameter decreases the temperature at the curved plate outer surface and increases the local Nusselt number. Similarly, local and average Nusselt number was enhanced by decreasing plate thickness. Numerical simulation results are validated by comparing with experimental measurements and related correlations.