Abstract
The unsteady double diffusion of the boundary layer with the nanofluid flow near a three-dimensional (3D) stagnation point body is studied under a microgravity environment. The effects of g-jitter and thermal radiation exist under the microgravity environment, where there is a gravitational field with fluctuations. The flow problem is mathematically formulated into a system of equations derived from the physical laws and principles under the no-slip boundary condition. With the semi-similar transformation technique, the dimensional system of equations is reduced into a dimensionless system of equations, where the dependent variables of the problem are lessened. A numerical solution for the flow problem derived from the system of dimensionless partial differential equations is obtained with the Keller box method, which is an implicit finite difference approach. The effects studied are analyzed in terms of the physical quantities of principle interest with the fluid behavior characteristics, the heat transfer properties, and the concentration distributions. The results show that the value of the curvature ratio parameter represents the geometrical shape of the boundary body, where the stagnation point is located. The increased modulation amplitude parameter produces a fluctuating behavior on all physical quantities studied, where the fluctuating range becomes smaller when the oscillation frequency increases. Moreover, the addition of Cu nanoparticles enhances the thermal conductivity of the heat flux, and the thermal radiation could increase the heat transfer properties.
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Abbreviations
- a :
-
principal curvature in the x-direction
- b :
-
principal curvature in the y-direction
- C :
-
concentration of the fluid
- C fx :
-
skin friction in the x-direction
- C fy :
-
skin friction in the y-direction
- C w :
-
wall concentration
- c p :
-
specific heat capacity at constant pressure
- C ∞ :
-
nanofluid concentration
- c :
-
curvature ratio
- D :
-
mass diffusion
- f :
-
dimensionless function
- Gr :
-
thermal Grashof number
- Gm :
-
mass Grashof number
- g :
-
gravitational field acceleration
- g 0 :
-
mean gravitational acceleration
- h :
-
dimensionless function
- k :
-
thermal conductivity
- k*:
-
mean absorption coefficient
- Nu :
-
Nusselt number
- Nr :
-
thermal radiation parameter
- Pr :
-
Prandtl number
- q r :
-
nonlinear radiative heat flux
- Sc :
-
Schmidt number
- Sh :
-
Sherwood number
- T :
-
temperature
- T ∞ :
-
nanofluid temperature
- T w :
-
wall temperature
- t :
-
dimensional time
- t*:
-
dimensionless parameter of time
- u :
-
velocity of the fluid in the x-direction
- v :
-
velocity of the fluid in the y-direction
- w :
-
velocity of the fluid in the z-direction.
- α :
-
thermal diffusion
- β :
-
thermal expansion
- β c :
-
concentration expansion
- ε :
-
the amplitude of modulation
- η :
-
boundary layer thickness
- θ :
-
dimensionless temperature parameter
- μ :
-
dynamic viscosity
- ν :
-
kinematic viscosity of fluid
- ρ :
-
density
- σ* :
-
Stefan-Boltzman constant
- τ :
-
dimensionless parameter of time
- ϕ :
-
nanoparticles volume fraction
- Φ :
-
dimensionless concentration parameter
- ω :
-
frequency of oscillation
- Ω :
-
dimensionless frequency of oscillation.
- *:
-
dimensionless parameter
- ′:
-
differentiation with respect to η
- nf:
-
nanofluid
- f:
-
base fluid
- s:
-
solid nanoparticle
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Citation: KAMAL, M. H. A., RAWI, N. A., ALI, A., and SHAFIE, S. Effects of g-jitter and radiation on three-dimensional double diffusion stagnation point nanofluid flow. Applied Mathematics and Mechanics (English Edition), 41(11), 1707–1722 (2020) https://doi.org/10.1007/s10483-020-2666-6
Project supported by the Ministry of Education (MOE) and Research Management Centre, Universiti Teknologi Malaysia (Nos. 5F166, 5F004, 07G70, 07G72, 07G76, and 07G77)
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Kamal, M.H.A., Rawi, N.A., Ali, A. et al. Effects of g-jitter and radiation on three-dimensional double diffusion stagnation point nanofluid flow. Appl. Math. Mech.-Engl. Ed. 41, 1707–1722 (2020). https://doi.org/10.1007/s10483-020-2666-6
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DOI: https://doi.org/10.1007/s10483-020-2666-6