Natural convective flow of a chemically reacting fluid in an annulus

Abstract

We examine the heat transfer and flow properties induced by natural convection in an annulus between a square enclosure and a circular cylinder filled with a chemically reacting fluid. During the exothermic reaction process in the reacting fluid, there generates heat that induces natural convection in the annulus. The problem is developed defining the vorticity‐stream function. We solve it with the use of the finite difference method. The results show that two counter‐rotating vortices generate in each half about the vertical symmetry line through the center of the inner cylinder. The lower eddies of the inner vortices get closer and closer with the decrease of the aspect ratio and the increase of the Rayleigh number, Frank‐Kamenetskii number, buoyancy force parameter, and Lewis number. Besides this, the eyes of the outer vortices expose similar characteristics for increasing values of the Rayleigh number and buoyancy force parameter, and for decreasing values of the aspect ratio and the Lewis number. It is remarkable that the flow field and the Nusselt number demonstrate completely distinct characteristics for the Lewis number unity, the aspect ratio equal to 0.1, and in the absence of the buoyancy force parameter.

Natural convection of a reacting hybrid nanofluid in an open porous cavity bounded by vertical wavy walls

“…In the porous media, homogeneity and local thermal equilibrium are presumed. Under aforesaid assumptions, the governing equations are (Roy et al , 2019; Sheremet et al , 2016): where u¯ is the velocity in x¯ -direction and truev¯ is the velocity in y¯ -direction, t¯ is the time, p¯ is the pressure, ρ hnf is the density, μ hnf is the dynamic viscosity, α hnf is the thermal diffusivity, σ hnf is the electrical conductivity, ( ρβ ) hnf is the effective thermal expansion coefficient, ( ρc ) hnf is the effective specific heat at constant pressure, T denotes temperature, B 0 is the strength of the magnetic field, δ is the magnetic field’s inclination angle with respect to the horizontal axis, Q is the exothermicity of reaction, D is the diffusion coefficient, g is gravitational acceleration, K is the permeability of the porous medium, R is the universal gas constant, E is the activation energy, k 0 is the pre-exponential factor and C is the concentration of the reactant. The subscript hnf indicates the properties of hybrid nanofluid.…”

Magnetohydrodynamic natural convection of a reacting hybrid nanofluid in a porous wavy‐walled cavity

“…In the porous medium, homogeneity and local thermal equilibrium are presumed. Under these assumptions, the governing equations for mass, momentum, and energy are [29,32,45]:…”

“…They illustrated that the shape of the vortices depends on the parameters used in this study. Roy et al [45] investigated the chemical reaction-induced convection behaviors in a space between a cylinder and a square enclosure. For higher values of the Lewis number, Rayleigh number, and Frank-Kamenetskii number the magnitude of the stream function increased and the maximum temperature increased with the increment of Frank-Kamenetskii number and lower Lewis number, and aspect ratio.…”

Developing buoyant convection in vertical porous annuli with unheated entry and exit

“…The influence of discrete heating on buoyant convection of nanofluids in a vertical annulus with different nanoparticles has also been analyzed in the literature 43,44 . Some of the recent studies in an annular enclosure investigated the exothermic reaction process of a chemically reacting fluid 45 fully developed MHD free convection with Hall currents and heat source/sink 46 …”

“…43,44 Some of the recent studies in an annular enclosure investigated the exothermic reaction process of a chemically reacting fluid 45 fully developed MHD free convection with Hall currents and heat source/sink. 46 A careful review of the existing literature reveals that a substantial amount of research is devoted mainly to a fully heated porous channels as well as partially heated vertical channels formed by three vertical parallel plates. However, there is lack of fundamental information regarding the flow structure and the corresponding heat transfer in double-passage annular channels with unheated entry and exit.…”