In this paper we propose an approximate analytic solution to the steady state, three-dimensional model of 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 describing the conservation of energy, and a radiative transport equation describing the propagation of radiation through the nanofluid. Writing the model in non-dimensional form leads to four controlling non-dimensional numbers, specifically one describing the relative importance of conduction and advection and three representing the heat loss to the surroundings. We use realistic parameter values to reduce the, model further and show that two of the non-dimensional groups have a much lesser impact on the performance of the solar collector. Our reduced model suggests that the nanofluid's temperature rise is linear as it flows through the receiver. The resulting solution is used to investigate the efficiency of the collector and permits optimisation of design parameters such as particle loading, particle type, solar absorption characteristics of the fluid, receiver dimensions, the inlet temperature, and solar concentration ratio. Further analysis of the collector efficiency reveals an inequality that determines whether or not it is reasonable to incorporate a heat-mirror into the solar collector's design.