Mixed convective flow of Maxwell nanofluid induced by vertically rotating cylinder


A study of mixed convection phenomenon in 3D flow of Maxwell nanofluid induced by vertically rotating and stretching cylinder is presented in current article. The Boussinesq approximation is used to predict the force of buoyancy due to which the free convection occurs in the fluid. Moreover, a popular Buongiorno model is utilized to reveal the influence of thermophoretic and Brownian forces for the transportation of energy in nanoliquid. The current physical problem of Maxwell nanofluid flow with energy transport is modeled under above consideration in form of partial differential equations (PDEs). Using the suitable flow similarities, the PDEs transformed into the set non-linear ordinary differential equations (ODEs) and then solved numerically by MATLAB built in scheme bvp4c. The outcomes of the problem are explored graphically and discussed with physical justification in rigorous way. In the flow and thermal analysis, it is noted that the higher values of both buoyancy and mixed convection parameters enhance the axial velocity and decline the swirl velocity, while these parameters decline the temperature and solutal fields, respectively. The higher value of thermophoretic force increases the thermal and solutal energy transport in the nanoliquid. Overall, it is revealed from the analysis that for large values of Reynolds number, the flow and energy transport decay exponentially faster to free stream conditions.

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\(r,\phi ,z\) :

Cylindrical coordinates

uvw :

Velocity components

T :

Temperature of fluid

\(T_{w}\) :

Wall temperature

a :

Stretching rate

\(\nu\) :

Kinematic viscosity

\(\sigma\) :

Conductivity of fluid

\(T_{\infty }\) :

Ambient fluid temperature

\(B_{T}\) :

Thermal expansion coefficient

\(g_{1}\) :

Gravity strength

\(\alpha _{1}\) :

Thermal diffusivity

\(D_{B}\) :

Mass diffusivity

\(Q_{0}\) :

Heat source/sink

\(u_{\hbox {ss}}\) :

Surface stretching velocity

\(\eta\) :

Dimensionless variable

g :

Dimensionless azimuthal velocity

\(\theta\) :

Dimensionless temperature

\(\hbox {Re}\) :

Reynolds number

\(N_{t}\) :

Thermophoretic parameter

\(N_{1}\) :

Mixed convection parameter

\(\hbox {Gr}\) :

Grashof numbers for temperature

\(\hbox {Nu}\) :

Nusselt number

\(\Pr\) :

Prandtl number

\(\lambda _{1}\) :

Fluid relaxation time

\(\mathbf {B}\) :

Magnetic field

C :

Concentration in fluid

\(C_{w}\) :

Wall concentration

E :

Rotational velocity

\(\mu\) :

Dynamic viscosity

\(\rho\) :

Density of fluid

\(C_{\infty }\) :

Ambient concentration

\(B_{C}\) :

Solutal expansion coefficient

\(B_{0}\) :

Strength of magnetic field

\(\tau\) :

Heat capacity ratio

\(D_{T}\) :

Thermophoresis coefficient

\(c_{p}\) :

Specific heat capacity

\(v_{\hbox {sr}}\) :

Surface rotation velocity

\(f^{\prime }\) :

Dimensionless axial velocity

\(\frac{f}{\sqrt{\eta }}\) :

Dimensionless radial velocity

\(\beta _{1}\) :

Maxwell parameter

M :

Magnetic number

\(N_{b}\) :

Brownian diffusion parameter

\(\lambda\) :

Buoyancy parameter

\(\hbox {Gr}^{*}\) :

Grashof numbers for concentration

\(\hbox {Sh}\) :

Sherwood number

\(\hbox {Le}\) :

Lewis number


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Correspondence to Awias Ahmed.

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Ahmed, A., Khan, M. & Ahmed, J. Mixed convective flow of Maxwell nanofluid induced by vertically rotating cylinder. Appl Nanosci 10, 5179–5190 (2020). https://doi.org/10.1007/s13204-020-01320-2

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  • Maxwell fluid
  • Nanoparticles
  • Mixed convection
  • Vertical rotating cylinder
  • Bvp4c scheme