A hyperbolic-shaped cavity-type receiver with a second stage reflection for a 40 m2 solar parabolic dish concentrator (PDC) is presented in this paper, along with optical and thermal modeling. The receiver geometry and the secondary reflector complete the hyperbolic geometrical shape of the present receiver. This study aims to estimate heat losses owing to natural convection and radiation under influential parameters associated with solar parabolic dish system. Optical modeling has been performed with verified model using ASAP® 2013 V1R1. The optical simulations have been carried out for varying receiver height (h_1), height of the secondary (h_2) and diameter-to-total height ratio (d/h) of 0.5, 1, and 1.5 while keeping the diameter of the plane aperture of the receiver (d) constant. The optimum receiver geometry has been selected based on the performance in terms of optical efficiency. The maximum efficiency found is 91.72% for h_1 = 0.75 m and d/h = 0.5 for the mounting distance of 4.21 m. The optimized shape is further studied to determine how the receiver absorptivity and the secondary reflector’s reflectivity affect the optical performance. The absorptivity and reflectivity range from 0.86 to 0.94. Obtained optimum receiver geometry from the optical investigation is further analyzed to estimate the heat transfer rate. The thermal modeling is performed for 0°, 30°, 60°, and 90° orientations of the receiver in ANSYS® Fluent 2020 R1. This work has developed a free convective Nusselt number correlation. Finally, energy, economic and sensitivity analyses are carried out of a solar parabolic dish plant for Indian conditions. The net present value, benefit-to-cost ratio, discounted payback period and levelized electricity cost are determined.