×

Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study). (English) Zbl 1105.76006

This work is a further study of the title problem investigated earlier by I. A. Hassanien and A. A. Salam [Energy Convers. Management 38(3), 301–310 (1997)]. In that paper, the effect of variation of such properties as density, viscosity and thermal conductivity was neglected. In the current work such variation is taken into consideration and studied using numerical techniques. The asumptions made are that the fluid, density and the thermal conductivity vary linearly with temperature while the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The mathematical technique utilized here is to use the similarity solution to transform the problem into a boundary value problem for nonlinear coupled ordinary differential equations which is then solved by using the Chebyshev finite difference method. A detailed analysis of the results is carried out demonstrating the effects on the micropolar coefficient, Reynolds and Prandtl numbers.

MSC:

76A05 Non-Newtonian fluids
76M55 Dimensional analysis and similarity applied to problems in fluid mechanics
76M20 Finite difference methods applied to problems in fluid mechanics
80A20 Heat and mass transfer, heat flow (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Eringen, A. C.: Theory of micropolar fluids. Math. Mech. 16, 1–18 (1966). · Zbl 0145.21302
[2] 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). · Zbl 1299.76170
[3] 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).
[4] 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). · Zbl 1083.92010
[5] 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).
[6] 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).
[7] 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).
[8] Slattery, J. C.: Momentum, energy and mass transfer in continua. New York: McGraw-Hill 1972.
[9] EI-Gendi, S. E.: Chebyshev solution of differential, integral, and integro-differential equations. Comput. J. 12, 282–287 (1969). · Zbl 0198.50201
[10] Fox, L., Parker, I. B.: Chebyshev polynomials in numerical analysis. Oxford: Clarendon Press 1968. · Zbl 0153.17502
[11] 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. · Zbl 0412.65058
[12] Canuto, C., Hussaini, M. Y., Quarterini, A., Zang, T. A.: Spectral methods in fluid dynamics. Berlin: Springer 1988. · Zbl 0658.76001
[13] Nasr, H., EI-Hawary, H. M.: Chebyshev method for the solution of boundary value problems. Int. J. Comput. Math. 40, 251–258 (1991). · Zbl 0782.65105
[14] Voigt, R. G., Gottlieb, D., Hussaini, M. Y.: Spectral methods for partial differential equations. Philadelphia, PA: SIAM 1984. · Zbl 0534.00017
[15] Elbarbary, E. M. E.: Chebyshev finite difference method for the solution of boundary-layer equations. Appl. Math. Comput. 160, 487–498 (2003). · Zbl 1059.76043
[16] Elbarbary, E. M. E., EI-Kady, M.: Chebyshev finite difference approximation for the boundary value problems. Appl. Math. Comput. 139, 513–523 (2003). · Zbl 1027.65098
[17] Elbarbary, E. M. E., El-Sayed M. S.: Higher-order pseudospectral differentation matrices. Appl. Numer. Math. (accepted). · Zbl 1086.65016
[18] Baltensperger, R., Trummer, M. R.: Spectral differencing with a twist. SIAM J. Sci. Comput. 24, 1465–1487 (2003). · Zbl 1034.65016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.