Journal of Physics A Mathematical and General · 2003 · 54 citations · 17 references
Natural SciencesPhysicsDifferential EquationsFluid DynamicsFluid MechanicsFluid PropertiesMagnetohydrodynamicsViscous FlowBessel FunctionsMagnetic Reynolds Number EffectsMagnetic ViscosityMagnetohydrodynamic EffectsPerturbation ModelingPoiseuille FlowReynolds NumberViscosity
We formulate this problem under an infinitely long wavelength approximation, a negligible Reynolds number and a small magnetic Reynolds number. We decide on a perturbation method of solution. The viscosity parameter α ≪ 1 is chosen as a perturbation parameter. The governing equations are developed up to first-order in the viscosity parameter (α). The zero-order system yields the classical Poiseuille flow when the Hartmann number M tends to zero. For the first-order system, we simplify a complicated group of products of Bessel functions by approximating the polynomial. The results show that the increasing magnetic field increases the pressure rise. In addition, the pressure rise increases as the viscosity parameter decreases at zero flow rate. Moreover, it is independent of the Hartmann number and viscosity parameter at certain values of flow rate. We make comparisons with other studies.
17
M Y Jaffrin, A H Shapiro · Annual Review of Fluid Mechanics · 1971 · 495 citations
J. C. Burns, T. Parkes · Journal of Fluid Mechanics · 1967 · 326 citations
Peristaltic Waves in Circular Cylindrical Tubes
F. Yin, Y. C. Fung · Journal of Applied Mechanics · 1969 · 178 citations