Recent experimental evidence has clearly demonstrated that nanofluids do not provide the greatly enhanced heat transfer predicted in the past. Despite seemingly conclusive proof there is still a great deal of current mathematical research asserting the opposite result. In this paper we scrutinise the mathematical work and demonstrate that the disagreement can be traced to a number of issues. These include the incorrect formulation of the governing equations; the use of parameter values orders of magnitude different to the true values (some requiring nanoparticle volume fractions greater than unity and nanoparticles smaller than atoms); model choices that are based on permitting a reduction using similarity variables as opposed to representing an actual physical situation; presentation of results using different scalings for each fluid. (C) 2017 Elsevier Ltd. All rights reserved.