Summary.
In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Eringen, A. C.: Theory of micropolar fluids. Math. Mech. 16, 1–18 (1966).
Eldabe, N. T., E1shehawey, E. F., Elbarbary, E. M. E., Elgazery, N. S.: Chebyshev finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer. Appl. Math. Comput. 160, 437–450 (2005).
Lai, F. C., Kulacki, F. A.: The effect of variable viscosity on convective heat transfer along a vertical surface in a saturated porous medium. Int. J. Heat Mass Transfer 33, 1028–1031 (1990).
Ghaly, A. Y., Seddeek, M. A.: Chebyshev finite difference method for the effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate with temperature dependent viscosity. Chaos Solitons Fractals 19, 61–70 (2004).
Elbarbary, E. M. E., Elgazery, N. S.: Chebyshev finite difference method for the effects of radiation and variable viscosity on magneto-micropolar fluid flow through a porous medium. Int. Comm. Heat Transfer 31(3), 409–419 (2004).
Elbarbary, E. M. E., Elgazery, N. S.: Chebyshev finite difference method for the effects of variable viscosity and variable thermal conductivity on heat transfer from moving surfaces with radiation. lnt. J. Thermal Sciences (accepted).
Hassanien, I. A., Salama, A. A.: Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder. Energy Convers. Mgmt. 38(3), 301–310 (1997).
Slattery, J. C.: Momentum, energy and mass transfer in continua. New York: McGraw-Hill 1972.
EI-Gendi, S. E.: Chebyshev solution of differential, integral, and integro-differential equations. Comput. J. 12, 282–287 (1969).
Fox, L., Parker, I. B.: Chebyshev polynomials in numerical analysis. Oxford: Clarendon Press 1968.
Gottlieb, D., Orszag, S. A.: Numerical analysis of spectral methods: Theory and applications. CBMS-NSF Regional Conference Series in Applied Mathematics 26. Philadelphia, PA: SIAM 1977.
Canuto, C., Hussaini, M. Y., Quarterini, A., Zang, T. A.: Spectral methods in fluid dynamics. Berlin: Springer 1988.
Nasr, H., EI-Hawary, H. M.: Chebyshev method for the solution of boundary value problems. Int. J. Comput. Math. 40, 251–258 (1991).
Voigt, R. G., Gottlieb, D., Hussaini, M. Y.: Spectral methods for partial differential equations. Philadelphia, PA: SIAM 1984.
Elbarbary, E. M. E.: Chebyshev finite difference method for the solution of boundary-layer equations. Appl. Math. Comput. 160, 487–498 (2003).
Elbarbary, E. M. E., EI-Kady, M.: Chebyshev finite difference approximation for the boundary value problems. Appl. Math. Comput. 139, 513–523 (2003).
Elbarbary, E. M. E., El-Sayed M. S.: Higher-order pseudospectral differentation matrices. Appl. Numer. Math. (accepted).
Baltensperger, R., Trummer, M. R.: Spectral differencing with a twist. SIAM J. Sci. Comput. 24, 1465–1487 (2003).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Elbarbary, E., Elgazery, N. Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study). Acta Mechanica 176, 213–229 (2005). https://doi.org/10.1007/s00707-004-0205-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00707-004-0205-z