a numerical investigation of conjugated-natural convection heat transfer enhancement of a nanofluid in an annular tube driven by inner heat generating solid cylinder

laminar conjugate heat transfer by natural convection and conduction in a vertical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal cylindrical boundary has been studied by a numerical method. it is assumed that the two sealed ends of the tube to be adiabatic. governing equations are derived based on the conceptual model in the cylindrical coordinate system. the governing equations have been solved using the finite volume approach, using simple algorithm on the collocated arrangement. results are presented for the flow and temperature distributions and nusselt numbers on different cross sectional planes and longitudinal sections for rayleigh number ranging from 10⁵ to 10⁸, solid volume fraction of 0‹φ‹0.05 with copper-water nanofluid as the working medium.