In this paper we propose a time-dependent, three-dimensional model for the efficiency of a nanofluid-based direct-absorption parabolic trough solar collector under a turbulent flow regime. The model consists of a system of equations: a partial differential equation for conservation of energy, and a time-dependent radiative transport equation describing the propagation of solar radiation through the nanofluid. Writing the model in dimensionless form reveals four controlling dimensionless numbers: one describing the relative importance of conduction and advection and three describing the heat loss to the surroundings. Realistic parameter values are applied to reduce the model further and these indicate that two of the dimensionless groups have a much smaller impact on the performance of the solar collector. We use the resulting solution for the temperature to calculate an analytic expression for the collector's efficiency. This expression permits optimisation of design parameters such as particle loading, incoming radiative intensity, receiver dimensions, the inlet temperature, and solar concentration ratio.