Mixed Convection Boundary-Layer Flow Along a Vertical Cylinder Embedded in a Porous Medium Filled by a Nanofluid

• Published in: Transport in porous media Vol. 96; no. 2; pp. 237 - 253
• Main Authors: Rohni, Azizah Mohd, Ahmad, Syakila, Merkin, John H., Pop, Ioan
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 2013; Springer; Springer Nature B.V
• Subjects: Asymptotic methods; Circular cylinders; Civil Engineering; Classical and Continuum Physics; Curvature; Cylinders; Differential equations; Differential thermal analysis; Earth and Environmental Science; Earth Sciences; Earth, ocean, space; Engineering and environment geology. Geothermics; Exact sciences and technology; Free convection; Geotechnical Engineering & Applied Earth Sciences; Hydrocarbons; Hydrogeology; Hydrology. Hydrogeology; Hydrology/Water Resources; Industrial Chemistry/Chemical Engineering; Mathematical analysis; Mathematical models; Nanocomposites; Nanofluids; Nanomaterials; Nanoparticles; Nanostructure; Ordinary differential equations; Parameters; Partial differential equations; Pollution, environment geology; Porous media; Sedimentary rocks; Vertical cylinders; Vertical cylinder; Mixed convection; Nanofluid; Dual solutions; Porous medium; boundary layer; transport; velocity; buoyancy; convection; solution; temperature; copper; porous media; heat transfer
• ISSN: 0169-3913; 1573-1634
• DOI: 10.1007/s11242-012-0085-y

The steady mixed convection boundary-layer flow on a vertical circular cylinder embedded in a porous medium filled by a nanofluid is studied for both cases of a heated and a cooled cylinder. The governing system of partial differential equations is reduced to ordinary differential equations by assuming that the surface temperature of the cylinder and the velocity of the external (inviscid) flow vary linearly with the axial distance x measured from the leading edge. Solutions of the resulting ordinary differential equations for the flow and heat transfer characteristics are evaluated numerically for various values of the governing parameters, namely the nanoparticle volume fraction , the mixed convection or buoyancy parameter λ and the curvature parameter γ . Results are presented for the specific case of copper nanoparticles. A critical value λ c of λ with λ c < 0 is found, with the values of | λ c | increasing as the curvature parameter γ or nanoparticle volume fraction is increased. Dual solutions are seen for all values of λ >  λ c for both aiding, λ > 0 and opposing, λ < 0, flows. Asymptotic solutions are also determined for both the free convection limit and for large curvature parameter .