  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.
