Two-phase analysis on transient conjugate heat transfer in pipes with nanofluids

The present study deals with the numerical analysis of transient conjugate heat transfer with nanofluid flow in a thick-walled pipe. Laminar, hydrodynamically developed and thermally developing flow is considered and both radial and axial conduction terms are taken into account both in the wall and nanofluid energy equations. The pipe is two-regional and extends infinitely in both directions. The upstream region is externally insulated while a uniform heat flux is suddenly applied on the outer surface of the wall in the downstream region. The two-phase modified Buongiorno model that fully accounts for the effects of nanoparticle volume fraction distribution is employed and the Navier's slip boundary condition is applied on the wall-nanofluid interface. To better map the effects of defining parameters of the problem, a parametric study is done i.e.; wall thickness ratio (d' = 0.02, 0.1 and 0.3), wall-to-nanofluid thermal conductivity ratio (kwnf = 1,10 and 20), wall-to-nanofluid thermal diffusivity ratio (αwnf =1, 5 and 20), the Peclet number (Pe =3, 5 and 10), bulk mean nanoparticle volume fraction (ϕb = 0, 0.02 and 0.04, velocity slip parameter(λ = 0, 0.1 and 0.3), and the ratio of Brownian to thermophoretic diffusivities(NBT = 0.1, 0.5, 5 and 10). The governing equations are solved numerically using the finite volume method. A new MATLAB code is written for the study and the results are obtained for two types of nanofluids, namely alumina-water and titania-water, and compared with the results for the base fluid. Transient distributions of outer and inner wall temperatures, bulk temperature, interfacial heat flux and Nusselt number are investigated. In addition, the effects of defining parameters on the migration of nanoparticles across a given section are also analyzed. The results revealed that heat transfer characteristics can not only be improved by adding nanoparticles to the base fluid, but the type of nanoparticles and that selecting appropriate values for the defining parameters are also crucial. Moreover, the uniformity of nanoparticles over the pipe's cross-section depends on the magnitude of the value of the defining parameter taken into account.