Modelling the efficiency of a nanofluid direct absorption solar collector

In this paper we present an approximate analytical solution to the steady state, two-dimensional model for the efficiency of an inclined nanofluid-based direct absorption solar collector. The model consists of a system of two differential equations; a radiative transport equation describing the propagation of solar radiation through the nanofluid and an energy equation. The heat source term is obtained via the radiative flux integral, which is highly non-linear with respect to wavelength due to the spectral-dependent fluid and nanoparticle indices of refraction and absorption. To make analytical progress we introduce an approximate power-law function for the radiative flux. Applying the method of separation of variables, the resulting solution is used to investigate the efficiency of the collector subject to variation in model parameters. In addition our approach allows for the inclusion of wavelength-dependent absorption and scattering due to both the base fluid and nanoparticles and also an approximation for reflectance and absorptance due to the collector and its associated surfaces.