Computation of rheological nanofluid coating boundary layer transport with convective wall heating

Abstract

Non-Newtonian nanofluids offer significant advantages in thermal enhancement in a variety of applications including in numerous areas of engineering including solar collectors and nano-coating manufacturing processes. When combined with porous media, yet further benefits can be gained in for example flow and heat transfer manipulation in nano-rheological coating extrusion. Motivated by exploring this industrial application, to furnish a deeper understanding of the rheological and nanoscale effects of such fluids in porous media, we examine the steady two dimensional (2-D) laminar buoyancy-driven boundary layer flow of power-law nanofluids along vertically upward surface adjacent to an isotropic Darcian porous filtration medium. Buongiorno’s two-component nanofluid model is deployed. Scaling group transformations followed by dimensional analysis is used to developed group invariants and hence the primitive conservation equations for momentum, heat and NVF are transformed from partial differential equations into ordinary differential equations with associated wall and free stream boundary conditions. The reduced nonlinear boundary value problem has been solved computationally with the stable, rapidly convergent Runge-Kutta-Fehlberg fourth-fifth order numerical method available in the symbolic platform, Maple 18. Verification of the methodology with earlier Blottner finite difference computations in the literature for the special case of Nc = Nd = 0 is included. It is found that the reduced Nusselt number increases with convective-conduction parameter, Nc, while it is suppressed with increasing power-law index, n, and thermophoresis parameter, Nt. The reduced Sherwood number is enhanced with Lewis number, Le and convective-diffusion parameter, Nd whereas it is substantially depleted with increasing power-law index, n. Strong boundary layer flow acceleration is induced with higher Nc values. Temperature is also strongly boosted with an elevation in power-law index and both convection-conduction Nc and convection-diffusion Nd parameters. Dilatant i. e. shear-thickening nanofluids (n > 1) are observed to achieve the best thermal enhancement. The novelty of the current work is the rigorous analysis of different rheological and wall heating and nanoparticle volume fraction effects on nano-polymer coating flows which significantly extends existing studies.