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Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

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Summary

A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, ζ in the range of 0 to 10 and the vortex viscosity parameters, Δ=0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.

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Abbreviations

f, F,\(\hat f\) :

dimensionless stream function for forced convection free convection and mixed convection, respectively

g :

acceleration due to gravity

Grx :

local Grashof number

j :

micro-inertia density

m 23 :

distribution of couple stress

N :

microrotation component normal to (x, y)-plane

p :

pressure of the fluid

q :

dimensionless rate of heat transfer

Rex :

local Reynolds number

T :

temperature of the fluid in the boundary layer

T ∞ :

temperature of the ambient fluid

T ω :

temperature at the surface

u, v :

thex andy-components of the velocity field

U ∞ :

free stream velocity

x, y :

axis in direction along and normal to the plate

α:

thermal diffusivity

β:

coefficient of volume expansion

Δ:

vortex viscosity parameter

ψ:

stream function

η,\(\bar \eta \),\(\hat \eta \) :

nondimensional similarity variables

ζ:

buoyancy parameter (=Gr x Re /5/2 x )

κ:

vortex viscosity

ϱ:

density of the fluid

v :

kinematic coefficient of viscosity

ψ:

spin-gradient viscosity

γ:

stream function

τ:

dimensionless skin-friction

μ:

fluid viscosity

References

  1. Eringen, A. C.: Theory of micropolar fluid. J. Math. Mech.16, 1–18 (1966).

    Google Scholar 

  2. Eringen, A. C.: Theory of thermomicrofluids. J. Math. Anal. Appl.38, 480–496 (1966).

    Google Scholar 

  3. Khonsari, M. M.: On the self-excited whirl orbits of a journal in a sleeve, bearing lubricated with micropolar fluids. Acta Mech.81, 235–244 (1990).

    Google Scholar 

  4. Khonsari, M. M., Brewe, D.: On the performance of finite journal bearing lubricated with micropolar fluids. STLE Tribology Trans.32, 155–160 (1989).

    Google Scholar 

  5. Hadimoto, B., Tokioka, T.: Two-dimensional shear flows of linear micropolar fluids. Int. J. Eng. Sci.7, 515–522 (1969).

    Google Scholar 

  6. Lockwood, F., Benchaita, M., Friberg, S.: Study of polyotropic liquid crystals in viscometric flow and elastohydrodynamic contact. ASLE Tribology Trans.30, 539–548 (1987).

    Google Scholar 

  7. Lee, J. D., Eringen, A. C.: Boundary effects of orientation of nematic liquid crystals J. Chem. Phys.55, 4509–4512 (1971).

    Google Scholar 

  8. Ariman, T., Turk, M. A., Sylvester, N. D.: Microcontinuum fluid mechanics — a review. Int. J. Eng. Sci.11, 905–930 (1973).

    Google Scholar 

  9. Kolpashchikov, V., Migun, N. P., Prokhorenko, P. P.: Experimental determinations of material micropolar coefficients. Int. J. Eng. Sci.21, 405–411 (1983).

    Google Scholar 

  10. Ariman, T., Turk, M. A., Sylvester, N. D.: Application of microcontinuum fluid mechanics. Int. J. Eng. Sci.12, 273–293 (1974).

    Google Scholar 

  11. Ahmedi, G.: Self-similar solution of incompressible micropolar boundary layer flow over a semi infinite plate. Int. J. Eng. Sci.14, 639–646 (1976).

    Google Scholar 

  12. Jena, S. K., Mathur, M. N.: Similarity solution for laminar free convection flow of thermomicropolar fluid past a non-isothermal vertical flat plate. Int. J. Eng. Sci.19, 1431–1439 (1981).

    Google Scholar 

  13. Jena, S. K., Mathur, M. N.: Free convection in the laminar boundary layer flow of thermomicropolar fluid past a non-isothermal vertical flat plate with suction/injection. Acta Mech.42, 227–238 (1982).

    Google Scholar 

  14. Gorla, R. S. R.: Combined forced and free convection in micropolar boundary layer flow on a vertical flat plate. Int. J. Eng. Sci.26, 385–391 (1983).

    Google Scholar 

  15. Yucel, A.: Mixed convection micropolar fluid flow over horizontal plate with surface mass transfer. Int. J. Eng. Sci.27, 1593–1608 (1989).

    Google Scholar 

  16. Hossain, M. A., Chowdhury, M. K., Takhar, H. S.: Mixed convection flow of micropolar fluids with variable spin gradient viscosity along a vertical plate. J. Theor. Appl. Fluid Mech.1, 64–77 (1995).

    Google Scholar 

  17. Chiu, C.-P.; Chou, H.-M.: Free convection in boundary layer flow of a micropolar fluid along a vertical wavy surface. Acta Mech.101, 161–174 (1993).

    Google Scholar 

  18. Mori, Y.: Buoyancy effects in forced laminar convection flow over a horizontal flat plate. J. Heat Transfer83, 479–482 (1961).

    Google Scholar 

  19. Sparrow, P. M., Minkowycz, W. J.: Buoyancy effects on horizontal boundary layer flow and heat transfer. Int. J. Heat Mass Transfer5, 505–511 (1962).

    Google Scholar 

  20. Chen, T. S., Sparrow, E. M., Mucoglu, A.: Mixed convection in boundary layer flow on a horizontal plate. J. Heat Transfer99, 66–71 (1977).

    Google Scholar 

  21. Ramachandran, N., Armaly, B. F., Chen, T. S.: Mixed convection over a horizontal plate. J. Heat Transfer105, 420–423 (1983).

    Google Scholar 

  22. Raju, M. S., Liu, X. Q., Law, C. K.: A formulation of combined forced and free convection past horizontal and vertical surfaces. Int. J. Heat Mass Transfer27, 2216–2224 (1984).

    Google Scholar 

  23. Risbeck, W. R., Chen, T. S., Armalt, B. F.: Laminar mixed convection over horizontal surface with power law variation in surface temperature. Int. J. Heat Mass Transfer36, 1859–1866 (1993).

    Google Scholar 

  24. Cebeci, T., Bradshaw, P.: Momentum transfer in boundary layers. Washington: Hemisphere 1977.

    Google Scholar 

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Author notes

  1. M. A. Hossain

    Present address: Department of Mathematics, University of Dhaka, 1000, Dhaka, Bangladesh

  2. M. K. Chowdhury

    Present address: Department of Mathematics, Bangladesh University of Engineering and Technology, 1000, Dhaka, Bangladesh

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    1. M. A. Hossain
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    2. M. K. Chowdhury
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    Hossain, M.A., Chowdhury, M.K. Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity. Acta Mechanica 131, 139–151 (1998). https://doi.org/10.1007/BF01177221

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