An analytical approach is presented in the current study regarding the laminar two-dimensional natural convection in a shallow cavity, which is filled with an aqueous Carbon Nanotube (CNT) nanofluid in the presence of internal heating as well as an external constant magnetic field. The experimentally observed formation of CNT aggregations is included in the problem formulation concerning both the effective viscosity and thermal conductivity of the nanofluid. Thus, special attention is given in the non-Newtonian nature of the working nanofluid which is evident for relatively large values of CNT concentrations. It is concluded that the rheological properties of the nanofluid influence the flow and heat transfer problem to a great extent. In particular, as CNT content increases convection currents are depressed leading to the deceleration of the flow and, as a result, to deterioration of the heat transfer which is obvious via the lowering of the temperature in the core region. The derived asymptotic solutions accomplish to capture the experimental behavior of CNT-water nanofluids pertaining to natural convection within enclosures, thus, demonstrating the crucial effect of aggregates as well as indicating themselves as useful theoretical tool in future industrial and bioengineering applications.
