Abstract
The thermal radiation energy is the clean energy with a much lower environmental impact than the conventional energy. The objective of the present work is to investigate theoretically the effect of copper nanoparticles and carbon nanotubes (CNTs) in the presence of base fluid (water) with the variable stream condition due to the thermal radiation energy. Single-walled carbon nanotubes (SWCNTs) in the presence of base fluid flow over a porous wedge play a significant role compared to those of copper nanoparticles on absorbing the incident solar radiation and transiting it to the working fluid by convection.
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Abbreviations
- B 0 :
-
magnetic flux density, kg·s−2·A −1
- C T :
-
temperature ratio
- c p :
-
specific heat at constant pressure, J·kg−1·K−1
- Ec :
-
Eckert number, \(\frac{{{U^2}}}{{{{\left( {{c_p}} \right)}_f}\left( {{T_w} - {T_\infty }} \right)}}\)
- g :
-
acceleration due to gravity, m·s−2
- Gr :
-
Grashof number, \(\frac{{g{{\left( \beta \right)}_f}\Delta T{x^3}}}{{\nu _f^2}}\)
- k 1 :
-
rate of chemical reaction, mol·m−1·s−1
- k*:
-
mass absorption coefficient, m−1
- k f :
-
thermal conductivity of base fluid, kg·m·s−3·K−1
- K :
-
permeability of porous medium, m2
- k s :
-
thermal conductivity of nanoparticle, kg·m·s−3·K−1
- M :
-
magnetic parameter, \(\frac{{\sigma B_0^2x}}{{{U_{\rho f}}}}\)
- k nf :
-
effective thermal conductivity of nanofluid, kg·m·s−3·K−1
- Pr :
-
Prandtl number, \(\frac{{{\nu _f}}}{{{\alpha _f}}}\)
- N :
-
thermal radiation parameter, \(\frac{{4{\sigma _1}\theta _w^3}}{{{k_f}k*}}\)
- Re :
-
Reynolds number, \(\frac{{Ux}}{{{\nu _f}}}\)
- q″rad :
-
incident radiation flux of intensity, kg·m−1·s−3·K−1
- Q 0 :
-
rate of source/sink, kg·m−2
- t :
-
time, s
- T :
-
temperature of fluid, K
- T w :
-
temperature of wall, K
- x, y :
-
streamwise coordinate, m
- T ∞ :
-
temperature far away from wall, K
- U(x):
-
flow velocity of fluid, m·s−1
- u, v :
-
velocity components in x- and y-directions, m·s−1
- V 0 :
-
velocity of suction/injection, m·s−1
- α nf :
-
thermal diffusivity of nanofluid, m2·s−1
- β f :
-
thermal expansion coefficients of base fluid, K−1
- ρ f :
-
density of base fluid, kg·m−3
- ρ s :
-
density of nanoparticle, kg·m−3
- ρ nf :
-
effective density of nanofluid, kg·m−3
- σ :
-
electric conductivity, Ω−1·m−1
- (ρc p )nf :
-
heat capacitance of nanofluid, J·m−3·K−1
- δ :
-
time-dependent length scale, s
- (ρβ)nf :
-
volumetric expansion coefficient of nanofluid, K−1
- Ω:
-
resistance, kg·m2·s−3·A−2
- σ 1 :
-
Stefan-Boltzman constant, kg·s−3·K−4
- ξ :
-
distance along wedge, m
- μ f :
-
dynamic viscosity of base fluid, kg·m−1·s−1
- ζ :
-
nanoparticle volume fraction
- ν nf :
-
dynamic viscosity of nanofluid, m2·s−1
- ψ :
-
stream function
- η :
-
similarity variable
- f :
-
dimensionless stream function
- μ nf :
-
effective dynamic viscosity of nanofluid, kg·m−1·s−1
- λ:
-
porous parameter, \(\frac{{{\nu _f}x}}{{KU}}\)
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Kandasamy, R., Mohammad, R. & Muhaimin, I. Carbon nanotubes on unsteady MHD non-Darcy flow over porous wedge in presence of thermal radiation energy. Appl. Math. Mech.-Engl. Ed. 37, 1031–1040 (2016). https://doi.org/10.1007/s10483-016-2115-8
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DOI: https://doi.org/10.1007/s10483-016-2115-8