In this paper, a 2-D numerical investigation and a sensitivity analysis have been done utilizing two phase mixture model on the combined mixed convection and surface radiation heat transfer in a solar heat exchanger. To serve the purpose, the effects of four parameters, the Richardson number (10-2 ≤ Ri ≤ 102), the volume fraction of nanoparticles (0.00 ≤ ϕ ≤ 0.04), nanoparticles diameter (40 nm ≤ dp ≤ 60 nm) and wall surface emissivity (0 ≤  ≤ 1), are taken into account. Discretization of the governing equations is performed using a finite volume method and are solved with SIMPLE algorithm. The effective parameters analysis is processed utilizing the Response Surface Methodology (RSM). It is found that the mean total Nusselt number increases by decreasing and increasing of Ri number and ϕ, dp and ε respectively. Also, decreasing of Ri number and ϕ and increasing of dp and ε cause an increase in the pressure drop ratio. The sensitivity of the mean total Nusselt number to ϕ, dp and ε is observed positive whereas negative sensitivity of the pressure drop ratio to ϕ and ε. The sensitivity of the pressure drop ratio to dp is also found positive. The effects of physical parameters are illustrated graphically.

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