In this paper, a 2-D numerical investigation and a sensitivity analysis of combined turbulent mixed convection and radiation heat transfer have been done using two phase mixture model in a solar heat exchanger. Numerical simulations are carried out to study the effects of the four parameters, the Richardson number (10(-2) <= Ri <= 10(2)), volume fraction of nanoparticles (0.00 <= phi <= 0.04), nanoparticles diameter (40 nm <= d(p) <= 60 nm) and the wall surface emissivity (0 <= epsilon <= 1). The effective parameters analysis is processed utilizing the RSM (Response Surface Methodology). It is found that decreasing the Ri number and phi and also increasing in epsilon and d(p), increases the mean total Nusselt number. Due to a decrease in Ri number and increase in phi , epsilon and d(p) the pressure drop ratio enhances. The sensitivity of the mean total Nusselt number and pressure drop ratio to Ri number is negative. The sensitivity of the mean total Nusselt number to d(p) and epsilon is positive but to phi is negative. Moreover, the sensitivity of the mean Nusselt number to Ri number, phi, d(p) and epsilon is more than the sensitivity of the pressure drop ratio to these parameters. (C) 2016 Elsevier Ltd. All rights reserved.