Porous materials have a positive effect upon the heat transfer enhancement and a negative impact on pressure drop. Combined convection-radiation heat transfer inside a porous solar heat exchanger with a sensitivity analysis is performed to calculate the effects of porous material on the heat transfer rate and the pressure drop. Reynolds and Darcy numbers and porous substrate thicknesses are selected as the influence parameters. The analysis is carried out by using Response Surface Methodology (RSM). Also, the input parameters for optimization process are obtained by numerical methods. The computational simulations are done for different Reynolds numbers (1 <= Re <= 100), Darcy number (10(-6) <= Da <= 10(-2)) and dimensionless porous substrate thickness (1/3 <= delta <= 1). It is found that the reductions in pressure drop ratio with increasing Darcy number are in the vicinity of 58% and 23% for delta = 1/3 and 1, respectively and Da = 10(-6)-10(-2). Note that above values are obtained at Re = 100. However, the augmentation in Nusselt number with increasing the porous substrate thicknesses is in the vicinity of 96% for delta = 1/3-1 and Da = 10(-2). Also, the maximum errors between the RSM and CFD results are in the vicinity of 3% and 1.37% for the Nusselt number and pressure drop ratio, respectively. (C) 2015 Elsevier Ltd. All rights reserved.