A numerical study on natural convection along with surface radiation heat transfer in an inclined porous solar cavity receiver by means of response surface methodology (RSM) is investigated. Discretization of the governing equations is first performed using a finite volume method and then solved with SIMPLE algorithm. Effects of physical parameters such as Rayleigh number (10(4) <= Ra <= 10(6)), Darcy number (10(-5) <= Da <= 10(3)), inclination angles (0 degrees <= theta <= 90 degrees), dimensionless porous substrate thickness (1/3 <= delta <= 1), wall surface emissivity (0 <= epsilon <= 1) and surface radiation heat transfer rate are examined. The sensitivity analysis is also presented. It is found that the sensitivity of mean Nusselt number increases by increasing Rayleigh number, Darcy number and inclination angle theta whereas the sensitivity of mean Nusselt number of natural convection heat transfer to porous substrate thickness delta declines. Consequently increase in the thickness of porous substrate reduces mean Nusselt number of natural convection heat transfer. Also, the sensitivity of mean Nusselt number of natural convection heat transfer to Rayleigh number Ra, porous substrate thickness delta, Darcy number Da and the inclination angle theta is found to be higher than the mean Nusselt number of radiation heat transfer. However, the sensitivity of mean Nusselt number of radiation heat transfer to the surface emissivity a is higher than the mean Nusselt number of natural convection. (C) 2016 Elsevier Ltd. All rights reserved.