Abstract
In this paper, the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied. The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow. Further, the novel features of heat generation/absorption, thermal radiation, and Joule heating are studied to control the rate of heat transfer. The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno. The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations (PDEs) and transformed into nonlinear ordinary differential equations (ODEs) with the help of the suitable flow ansatz. Numerically acquired results through the technique bvp4c are reported graphically with physical explanation. Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature (CWT) as compared with the prescribed surface temperature (PST). Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid. Moreover, the temperature distribution increases with increasing values of the radiation parameter and the Eckert number. It is also noted that an increase in Reynolds number reduces the penetration depth, and as a result the flow and transport of energy occur only near the surface of the cylinder.
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Abbreviations
- α :
-
stretching rate (T−1)
- B :
-
magnetic field
- B 0 :
-
strength of magnetic field (N·m·A−1)
- C :
-
concentration in fluid
- C w :
-
wall concentration
- Re :
-
Reynolds number
- Sh :
-
Sherwood number
- T :
-
temperature of fluid (K)
- T w :
-
wall temperature (K)
- T ∞ :
-
ambient fluid temperature (K)
- C ∞ :
-
ambient concentration
- c p :
-
specific heat capacity (J·K−1·kg−1)
- D B :
-
mass diffusivity (m2·s−1)
- D T :
-
thermophoresis coefficient (m2·s−1)
- E :
-
rotational velocity (m·s−1)
- Ec 1 :
-
Eckert number due to surface stretching
- Ec 2 :
-
Eckert number due to surface rotation
- f′:
-
dimensionless axial velocity
- \(\frac{f(\eta)}{\eta^{1/2}}\) :
-
dimensionless radial velocity
- g :
-
dimensionless azimuthal velocity
- h t :
-
heat transfer coefficient (W·m−2·K−1)
- Le :
-
Lewis number
- M :
-
magnetic number
- N t :
-
thermophoretic parameter
- N b :
-
Brownian diffusion parameter
- Nu :
-
Nusselt number
- Pr :
-
Prandtl number
- Q 0 :
-
heat source/sink coefficient
- r :
-
radial coordinate
- R d :
-
radiation parameter
- u :
-
axial velocity component
- u s :
-
surface stretching velocity (m·s−1)
- V :
-
velocity field
- v :
-
azimuthal velocity component
- v r :
-
surface rotation velocity (m·s−1)
- w :
-
radial velocity components (m·s−1)
- z :
-
axial coordinate
- φ :
-
azimuthal coordinate
- λ 1 :
-
fluid relaxation time (T−1)
- ν :
-
kinematic velocity (m2·s−1)
- σ :
-
electric conductivity of fluid (S·m−1)
- ρ :
-
density of fluid (kg·m−3)
- η :
-
dimensionless variable
- α 1 :
-
thermal diffusivity of fluid (m2·s−1)
- μ :
-
dynamic viscosity (kg·m−1·s−1
- θ :
-
dimensionless temperature
- β 1 :
-
Maxwell parameter
- γ 1 :
-
Biot number
- τ :
-
heat capacity ratio
- δ :
-
source/sink parameter
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Ahmed, A., Khan, M. & Ahmed, J. Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder. Appl. Math. Mech.-Engl. Ed. 41, 1417–1430 (2020). https://doi.org/10.1007/s10483-020-2643-7
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DOI: https://doi.org/10.1007/s10483-020-2643-7
Key words
- Maxwell nanofluid
- rotating cylinder
- heat source/sink
- Joule heating
- convective condition
- numerical solution