Three‐dimensional boundary layer flow over a rotating disk with power‐law stretching in a nanofluid containing gyrotactic microorganisms

Abstract

The nanofluid model containing microorganisms over a rotating disk with power‐law stretching is constructed in this paper. The combined effects of nanoparticles and microorganisms in nanofluid are investigated by solving the governing equations numerically. The numerical solutions of the skin friction coefficient and local Nusselt number are in agreement with the corresponding previously published results. The quantities of physical interest are graphically presented and discussed in detail. It is found that the power‐law stretching index has produced profound influence on the flow as well as the heat and mass transfer.

Heat transfer in the flow of blood‐gold Carreau nanofluid induced by partial slip and buoyancy

“…In the report of Raju et al ., thermo‐diffusion effect on mixed convection unsteady magnetohydrodynamic flow through boundary layer formed on a semi‐infinite vertical permeable moving plate was investigated. Chen et al . deliberated on the heat transfer in the flow of nanofluid containing microorganisms within the boundary layer formed on a rotating disk with power‐law stretching.…”

Importance of activation energy and heat source on nanoliquid flow with gyrotactic microorganisms

“…Our intention now is to predict the characteristics of sundry variables on velocity components (radial . Here radial velocity enhances for higher  whereas reverse trend is observed for power law index n (see Tables 1 and 2. From Table 1 Table 3 shows the comparison of presented investigation with Chen et al [47] in a limiting sense for ,…”

“…(iii) The nanoparticles have uniform size and shape (iv) There is relative movement between nanoparticles and regular liquid. (1) Considered [16,47]:…”

Magnetohydrodynamic bio-nano-convective slip flow with Stefan blowing effects over a rotating disc

“…59 The validation of the numerical method used was carried out for particular cases of the model and the results obtained were compared with the existing solutions in the technical literature. In the absence of slips and magnetic field along with m = (1 À n)=2, du = dr = dt = dc = dn = a = 0, our model reduces to the problem examined by Chen et al 58 for solid disc (s = 0). More generally, in the absence of concentration and microorganism profile and Nt = Nb !…”

“…where T, C, n are the temperature, nanoparticle concentration and number of motile microorganisms, respectively; s is the electric conductivity; r f is the density of the base fluid; m is the dynamic viscosity; y( = m=r f ) is the kinematic viscosity; B 2 ( = B 0 2 r À2m ) is the magnetic field applied along the z axis; B 0 is constant magnetic field; m is power law exponent; 58 R is the reference scale length; a( = k=(rc) f ) is the thermal diffusivity of the fluid; k is the thermal conductivity of the fluid; (rc) f is the fluid heat capacity, (rc) p is the effective nanoparticles heat capacity; t is the ratio of effective nanoparticle material heat capacity and fluid heat capacity; D B is the Brownian diffusion coefficient; D T is the thermophoretic diffusion coefficient; D n is the microorganism diffusion coefficient; T w is the surface temperature and T ' is the ambient temperature; C w is the surface mass concentration and C ' is the ambient mass concentration; N 1 ( = (N 1 ) 0 r m ) is the velocity slip factor for u; N 2 ( = (N 2 ) 0 r m ) is the velocity slip factor for v, D 1 ( = (D 1 ) 0 r m ) is the thermal slip factor; E 1 ( = (E 1 ) 0 r m ) is the mass slip factor; n w is the wall motile microorganisms; F 1 ( = (F 1 ) 0 r m ) is the microorganism slip factor; e v( = ( e bW c =DC)(∂ C=∂ z)) is the average directional swimming velocity of microorganisms along z axis; e b is the chemotaxis constant; W c is the maximum cell swimming speed using the following dimensionless variables (10)…”