Abstract
The non-Newtonian effect in the boundary layer flow over a horizontal elliptical cylinder is investigated numerically. A modified power-law viscosity model is used to correlate the non-Newtonian characteristics of the fluid flow. For natural convection flows, the surface of the cylinder is maintained by the uniform surface temperature (UST) or the uniform heat flux (UHF) condition. The governing equations corresponding to the flow are first transformed into a dimensionless non-similar form using suitable transformations. The resulting equations are solved numerically by an efficient finite difference scheme. The numerical results are presented for the skin friction coefficient and the local Nusselt number with the eccentric angle for different values of the power-law index n. The local skin friction coefficient and the local Nusselt number are found to be higher and lower, respectively, for the shear thickening fluids (n > 1) than the other fluids (n ⩽ 1). The effects of different elliptical configurations on the average Nusselt number are also presented and discussed for both conditions of the surface temperature.
Abbreviations
- a, b :
-
lengths of the semi-major and semi-minor axes of an ellipse
- C :
-
constant
- C f :
-
dimensionless skin-friction coefficient
- c p :
-
specific heat at constant pressure
- D :
-
non-dimensional viscosity of the fluid
- e :
-
eccentricity
- g :
-
gravitational acceleration
- Gr :
-
Grashof number
- k :
-
thermal conductivity of the fluid
- m :
-
dimensional constant
- n :
-
non-Newtonian power-law index
- Nu :
-
local Nusselt number
- Pr :
-
Prandtl number
- T :
-
dimensional temperature of the fluid
- T w :
-
temperature at the surface
- T ∞ :
-
ambient temperature of the fluid
- x̄, ȳ :
-
coordinate along the surface of the cylinder and coordinate normal to the surface, respectively
- ū, v̄ :
-
fluid velocities in the x̄ and ȳ directions
- X, Y :
-
axial direction along the elliptical cylinder, and pseudo-similarity variable, respectively
- U, V :
-
dimensionless fluid velocities in the X- and Y-directions, respectively
- α :
-
eccentric angle
- β :
-
coefficient of thermal expansion
- γ :
-
shear rate
- θ, Θ :
-
dimensionless temperatures of the fluid
- ν :
-
kinematic viscosity of the fluid
- ν 1 :
-
reference viscosity of the fluid
- ρ :
-
density of the fluid
- ϕ :
-
angle between the line normal to the cylinder and the one parallel to the gravitational direction.
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Project supported by the North South University, Bangladesh (Nos. NSU-RP-18-067 and CTRG-19/SEPS/15)
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Nag, P., Molla, M.M. & Hossain, M.A. Non-Newtonian effect on natural convection flow over cylinder of elliptic cross section. Appl. Math. Mech.-Engl. Ed. 41, 361–382 (2020). https://doi.org/10.1007/s10483-020-2562-8
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DOI: https://doi.org/10.1007/s10483-020-2562-8