Abstract
This article presents a numerical solution for the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with the power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing partial differential equations (PDEs) are transformed into a system of coupled non-linear ordinary differential equations (ODEs) with appropriate boundary conditions for various physical parameters. The remaining system of ODEs is solved numerically using a differential transformation method (DTM). The effects of the porous parameter, the wall thickness parameter, the radiation parameter, the thermal conductivity parameter, and the Prandtl number on the flow and temperature profiles are presented. Moreover, the local skin-friction and the Nusselt numbers are presented. Comparison of the obtained numerical results is made with previously published results in some special cases, with good agreement. The results obtained in this paper confirm the idea that DTM is a powerful mathematical tool and can be applied to a large class of linear and non-linear problems in different fields of science and engineering.
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Abbreviations
- A, b :
-
constants
- C f :
-
skin friction coefficient
- c p :
-
specific heat at constant pressure
- D :
-
porous parameter
- f(η):
-
similarity variable
- k :
-
permeability of porous medium
- k*:
-
mean absorption coefficient
- k 0 :
-
permeability parameter
- m :
-
velocity power index
- Nu :
-
Nusselt number
- Pr :
-
Prandtl number
- q r :
-
radiative heat flux
- q eff :
-
effective conduction-radiation flux
- R :
-
radiation parameter
- Re x :
-
local Reynolds number
- T :
-
temperature of fluid
- T w :
-
temperature of sheet
- T ∞ :
-
free-stream temperature
- u :
-
velocity component in x-direction
- v :
-
velocity component in y-direction
- U :
-
stretching velocity
- U 0 :
-
reference velocity
- v w :
-
suction or injection velocity
- x :
-
coordinate measured along surface
- y :
-
coordinate normal to surface
- α :
-
thickness of wall parameter
- η :
-
similarity variable
- ε :
-
thermal conductivity parameter
- κ :
-
fluid thermal conductivity
- κ eff :
-
effective thermal conductivity
- ψ :
-
stream velocity function
- ρ :
-
fluid density
- σ*:
-
Stefan-Boltzmann constant
- θ :
-
dimensionless temperature
- μ :
-
fluid viscosity
- ν :
-
kinematic viscosity of the fluid
- ∞:
-
free stream condition
- w:
-
condition at surface
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Khader, M.M., Megahed, A.M. Differential transformation method for studying flow and heat transfer due to stretching sheet embedded in porous medium with variable thickness, variable thermal conductivity, and thermal radiation. Appl. Math. Mech.-Engl. Ed. 35, 1387–1400 (2014). https://doi.org/10.1007/s10483-014-1870-7
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DOI: https://doi.org/10.1007/s10483-014-1870-7
Key words
- Newtonian fluid
- stretching sheet
- differential transformation method (DTM)
- thermal radiation
- variable thermal conductivity
- variable thickness