Hayat, T.; Fetecau, Constantin; Sajid, M. On MHD transient flow of a Maxwell fluid in a porous medium and rotating frame. (English) Zbl 1217.76086 Phys. Lett., A 372, No. 10, 1639-1644 (2008). Summary: Analytic solution for unsteady magnetohydrodynamic (MHD) flow is constructed in a rotating non-Newtonian fluid through a porous medium. Constitutive equations for a Maxwell fluid have been taken into consideration. The hydromagnetic flow in the uniformly rotating fluid is generated by a suddenly moved infinite plate in its own plane. Analytic solution of the governing flow problem is obtained by means of the Fourier sine transform. It is shown that the obtained solution satisfies both the associate partial differential equation and the initial and boundary conditions. The solution for a Navier-Stokes fluid is recovered if \(\lambda \rightarrow 0\). The steady state solution is also obtained for \(t\rightarrow \infty \). Cited in 18 Documents MSC: 76W05 Magnetohydrodynamics and electrohydrodynamics 76S05 Flows in porous media; filtration; seepage 76A05 Non-Newtonian fluids 76U05 General theory of rotating fluids 82D10 Statistical mechanics of plasmas 76D05 Navier-Stokes equations for incompressible viscous fluids Keywords:analytic solution; Maxwell fluid; rotating frame; porous medium; MHD flow PDFBibTeX XMLCite \textit{T. Hayat} et al., Phys. Lett., A 372, No. 10, 1639--1644 (2008; Zbl 1217.76086) Full Text: DOI References: [1] Zhaosheng, Y.; Jianzhong, L., Appl. Math. Mech., 19, 671 (1998) [2] Shifang, H., Constitutive Equation and Computational Analytical Theory of Non-Newtonian Fluids (2000), Science Press: Science Press Beijing [3] Dunn, J. E.; Rajagopal, K. R., Int. J. Eng. Sci., 33, 689 (1995) [4] Aksel, N., Acta Mech., 157, 235 (2002) [5] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 985 (2003) [6] Fetecau, C.; Zierep, J., Z. Angew. Math. Phys., 54, 1086 (2003) [7] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 423 (2003) [8] Fetecau, C.; Fetecau, C., Int. J. Non-Linear Mech., 38, 603 (2003) [9] Tan, W. C.; Pan, W. X.; Xu, M. Y., Int. J. Non-Linear Mech., 38, 645 (2003) [10] Hayat, T.; Nadeem, S.; Asghar, S., Appl. Math. Comput., 151, 153 (2004) [11] Singh, M. P.; Sathi, H. L., J. Math. Mech., 17, 3, 193 (1968) [12] Tan, W. C.; Masuoka, T., Phys. Fluids, 17, 023101 (2005) [13] Rajagopal, K. R.; Gupta, A. S., Meccanica, 19, 158 (1984) [14] Rajagopal, K. R., On boundary conditions for fluids of the differential type, (Sequiera, A., Navier-Stokes Equations and Related Non-linear Problems (1995), Plenum Press: Plenum Press New York), 273-275 · Zbl 0846.35107 [15] Srivastava, P. M., Arch. Mech. Stos., 2, 18, 145 (1966) [16] Hayat, T.; Siddiqui, A. M.; Asghar, S., Int. J. Eng. Sci., 39, 135 (2001) [17] C. Fetecau, S.C. Prasad, K.R. Rajagopal, Appl. Math. Mod. (2006), in press; C. Fetecau, S.C. Prasad, K.R. Rajagopal, Appl. Math. Mod. (2006), in press [18] Sneddon, I. N., Functional Analysis, Encyclopedia of Physics, vol. II (1955), Springer: Springer Berlin, Gottingen, Heidelberg 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.