Summary
In this work we formulate the state space approach for one-dimensional problems of viscoelastic magnetohydrodynamic unsteady free convection flow through a porous medium past an infinite vertical plate. Laplace transform techniques are used. The resulting formulation is applied to a thermal shock problem and to a problem for the flow between two parallel fixed plates both without heat sources. Also a problem with a distribution of heat sources is considered. A numerical method is employed for the inversion of the Laplace transforms. Numerical results are given and illustrated graphically for the problem considered.
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Abbreviations
- C ϱ :
-
specific heat at constant pressure
- g :
-
acceleration due to gravity
- ϱ:
-
density
- ′ :
-
time
- u′ :
-
velocity component parallel to the plate
- H x′ :
-
induced magnetic field
- x′, y′ :
-
coordinates system
- T′ :
-
temperature distribution
- T o′:
-
temperature of the plate
- T′∞ :
-
temperature of the fluid away from the plate
- μ0 :
-
limiting viscosity at small rates to shear
- v o * :
-
μ/ϱ
- v m :
-
magnetic diffusivity
- α:
-
Alfven velocity
- β* :
-
coefficient of volume expansion
- λ:
-
thermal conductivity
- λ* :
-
thermal diffusivity
- G:
-
Grashof number
- Pr:
-
Prandtl number
- L :
-
some characteristic length
- k o :
-
the elastic constant
- K′ :
-
permeability of the porous medium
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Ezzat, M., Zakaria, M., Shaker, O. et al. State space formulation to viscoelastic fluid flow of magnetohydrodynamic free convection through a porous medium. Acta Mechanica 119, 147–164 (1996). https://doi.org/10.1007/BF01274245
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DOI: https://doi.org/10.1007/BF01274245