Deterministic matrix-based radiative design using a new general formulation of exergy and exergy efficiency for hybrid solar collectors

•New balances of first and second law for gray surfaces with one or two sources.•A new GS (Gray Surface) model of radiative exergy efficiency is proposed.•A matrix-based analytic method of radiative design for hybrid solar collectors.•A methodology to compute the thermal radiation losses through lateral walls.•Collector thickness impact is quantified by the radiative lateral losses. This paper provides two main contributions: a new general formulation of radiation exergy and exergy efficiency of photovoltaic (PV) panels as grey surface absorbers; the development of an analytic method of radiative design of hybrid solar collectors by using matrix formalism. The new proposed GS (Gray Surface) model of exergy efficiency applicable for gray surfaces is proposed and compared with the classical models (in the first case study) and with its value of 0.939 reveals a difference of up to 1% compared with Petela-Landsberg-Press model (0.932) or Jeter-Carnot model (0.949). The new methodology is able to determine the thermal radiation losses through the lateral walls. The second case study includes an estimation of these losses at 2.63% for the analyzed design. A sensitivity analysis of thickness vs. exergy efficiency is performed, showing that each increase of the thickness of the collector by 10 mm determines a decrease of the extracted power (work) by 1.6% while the radiative exergy efficiency decreases by 0.75%. By including, in future research, the effect of the convection heat transfer, the proposed methodology could stand as a theoretical reference that can be compared with other two paths of research: numerical (CFD) and empirical.