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Homotopy Algorithms for Engineering Analysis
Published in Hojjat Adeli, Supercomputing in Engineering Analysis, 2020
Layne T. Watson, Manohar P. Kamat
Further, Eqs. (128)–(130) assume that the induced electric field is negligible compared with the imposed magnetic field. This assumption is valid for flow at low magnetic Prandtl number. The energy equation is (u∂∂r+w∂∂z)T=α∇2T
M
Published in Carl W. Hall, Laws and Models, 2018
Keywords: dynamics, ferro, fluids Source: Land, N. S. 1972. MAGNETIC (OHM)--SEE ROWLAND MAGNETIC PRANDTL NUMBER, PrM A dimensionless group in magnetohydrodynamics: PrM = where = magnetic permeability = electrical conductivity = kinematic viscosity Keywords: electrical, magnetic, magnetohydrodynamics PRANDTL, Ludwig, 1875-1953, German engineer and physicist Sources: Bolz, R. E. and Tuve, G. L. 1970; Land, N. S. 1972; Parker, S. P. 1992. MAGNETIC PRESSURE NUMBER, S A dimensionless group in magnetohydrodynamics relating the magnetic pressure and the dynamic pressure: S = H2/V2 where H V = = = = magnetic permeability magnetizing force mass density velocity
Integrated intelligent neuro computing technique for mixed convective flow and heat transfer in heterogeneous permeability media
Published in Waves in Random and Complex Media, 2023
Figure 3(a) depicts Hartmann number impact on the velocity profile for the three permeability cases. The velocity profile drops in all three cases with increase in M. When an electrically conducting fluid is exposed to a magnetic field, it causes the Lorentz force to act in the reverse direction of the flow, causing flow retardation hence the fluid velocity falls. However, this reduction in the flow is coupled with rise in the thermal state of the fluid. This phenomenon is readily demonstrated by the drop in fluid velocity and raise in fluid temperature. Figure 3(b) shows the impact of the magnetic Prandtl number, Pm, on fluid velocity in three permeability cases. The velocity profile reduces in all cases when the Pm is augmented. The velocity profile is lowest near the non-conducting wall, gradually increases in the center of the channel and acquires a parabolic shape, and is maximum near the channel conducting wall. As a result, fluid velocity drops with a strong external magnetic field.
Magnetoconvection in a rotating spherical shell in the presence of a uniform axial magnetic field
Published in Geophysical & Astrophysical Fluid Dynamics, 2022
Stephen J. Mason, Céline Guervilly, Graeme R. Sarson
The magnetic Prandtl number is set to 1 in all our simulations, so the magnetic Reynolds number is equal to the Reynolds number. In self-sustained spherical convective dynamos, the magnetic Reynolds numbers (based on the total velocity) needs to be greater than approximately 40 for dynamo action (Christensen and Aubert 2006). This is verified in our simulations with , where the dynamo onsets at with a Reynolds number based on the total velocity of 73 and . Since the Reynolds number is essentially similar for all at a given , we might consider that cases with for have magnetic Reynolds numbers that are large enough for dynamo action, so these solutions might behave essentially as dynamo solutions. This point will be explored in more detail in section 5.
Dual solutions of magnetite/cobalt/manganese-zinc-aqueous nano-ferrofluids from a stretching sheet with magnetic induction effects: MHD stagnation flow computation and analysis
Published in International Journal for Computational Methods in Engineering Science and Mechanics, 2023
M. Ferdows, Tahia Tazin, O. Anwar Bég, T. A. Bég, Kadir Ali
However, there is no solution in the range, It is observed that an increase in induces the skin friction and the heat transfer to decrease. Magnetic Prandtl number is the ratio of magnetic Reynolds number to ordinary Reynolds number. It expresses also the ratio of viscous diffusion rate (viscosity) to magnetic diffusivity. The reciprocal of this number therefore quantifies the ratio of magnetic diffusion rate viscous diffusion rate. As this parameter increases, the higher order term, in the magnetic induction boundary layer, Eq. (22) is boosted. The viscous diffusion rate is reduced and, therefore, skin friction is suppressed (flow is inhibited), in consistency with Figure 5. Via the coupling term in the energy Eq. (23), there will also be a concomitant suppression in heat transfer rate to the wall i. e. reduced Nusselt number will be decreased (Figure 6). Since Prandtl number is fixed at 6.2, the thermal diffusivity is greater than momentum diffusivity with increasing values, and this energizes the boundary layer leading to higher temperature. Less heat is therefore transported to the sheet surface and this manifests in a plummet in reduced Nusselt number at the wall. A modification in reciprocal of magnetic Prandtl number clearly has a substantial impact on momentum and heat transfer characteristics both in the boundary layer regime and at the wall (sheet).