Magnetic Interaction Parameter Research Articles

Thermal attributes of sodium alginate (Na.C6H7O6) based binary and ternary hybrid nanofluids under activation energy and induced magnetic field environment

Ternary hybrid nanofluids possess several potential applications in the modern science beyond just the heat transfer efficiency. A continuous research and advancements on binary and ternary hybrid nanofluids might lead towards new developments in many technological and scientific zones. Ongoing research interprets and distinguishes the novel attributes of the sodium alginate (Na.C6H7O6) based unary, binary and ternary nanofluids through a porous medium under induced magnetic field environment. The nano-composition of single-wall carbon nanotubes (SWCNT) with silver (Ag) and molybdenum dioxide (MoS2) gives rise to the binary (SWCNT-Ag/Na.C6H7O6) and ternary hybrid (SWCNT-Ag-MoS2/Na.C6H7O6) nanofluids respectively. A complex and highly nonlinear system of differential equations, obtained via the boundary layer approximations, is tackled numerically. An algorithmic approach, using MATLAB software, is incorporated to determine the iterative solutions. The efficiency as well as validity of the developed algorithm is confirmed by equating the results with the previous ones. The results evidently portray the fact that the magnetic Prandtl number and magnetic interaction parameter not only dissuade the induced magnetic field but also resist the fluids’ speed. With the larger values of activation energy parameter, higher will be the concentration of fluid.

Thermohydrodynamics of Bödewadt hybrid-nanofluid flow in a horizontal magnetic field

Since disks, rotating or stationary, are integral in many thermal systems, such as rotating heat exchangers, thermoelectric coolers, solar energy systems, and geothermal plants, this study scrutinizes the thermohydrodynamics of rotating hybrid nanofluid flow over a stretchable disk at rest. Further, the shape of the nanoparticles and the choice of base fluid substantially impact the enhancement of the heat transfer rate in various such thermal systems. Therefore, the present investigation considers engineered colloids made of four distinct (sphere, cylinder, column, lamina) titania and copper nanoparticle shapes in two different base fluids: water and engine-oil. The problem is formulated mathematically in an externally applied horizontal magnetic field and incorporating a non-Fourier heat flux model in the presence of solar radiation. Analogous to the case of the conventional vertical magnetic field, a similarity solution is also possible when magnetic forces act horizontally, both towards and opposite to the direction of rotation. Thus, the governing partial differential equations (PDEs) are first reduced to a set of highly non-linear and coupled ordinary differential equations (ODEs) via similarity transformations. These resulting set of ODEs are then solved numerically using a rapid and efficient spectral quasilinearization method (SQLM). Obtained results show that lamina-shaped TiO2−Cu/ engine-oil hybrid-nanofluid is a better choice than the other shapes of nanoparticle suspension in water. The horizontally applied magnetic field exhibits a stronger influence on the flow and heat transfer characteristics when compared to a vertical magnetic field. Additionally increasing the thermal relaxation parameter αt from 0.1 to 0.35, the Nusselt number boost by 24.44%, 23.41%, 22.54%, and 17.93% for sphere, cylinder, column, and lamina nanoparticles of TiO2−Cu/water hybrid nanofluid. In the case of TiO2−Cu/engine-oil hybrid-nanofluid augmenting αt from 0.1 to 0.35, the Nusselt number rise by 23.95%, 22.83%, 21.82%, and 15.89% for sphere, cylinder, column, and lamina nanoparticles. Based on their increasing NS and Be values, the various shapes follow the sequence: lamina ¡ column ¡ cylinder ¡ sphere. Furthermore, entropy generation can be optimized through the augmentation of solar radiation factors QSR, δ, along with the reduction of the magnetic interaction parameter M, and by a proper selection of nanoparticle’s shape. Interestingly, dual solutions are observed for the case of a shrinking disk, i.e., for S<0, and a linear temporal stability analysis reveals that only one of these two branches, namely the first solution branch, is stable and the second branch unstable.

Computation of hydromagnetic tangent hyperbolic non-Newtonian flow from a rotating non-isothermal cone to a non-Darcy porous medium with thermal radiative flux

A theoretical and numerical study is conducted on nonlinear, steady-state thermal convection boundary layer flow of a magnetized incompressible Tangent Hyperbolic non-Newtonian fluid from a rotating cone to a non-Darcy porous medium. Power-law variation in temperature on the cone surface is considered and thermal radiation heat transfer is also present. The Brinkman-Darcy-Forchheimer model is deployed for the porous medium. The study is motivated by rotational (spin) coating with new emerging magnetic rheological polymers, a process which often utilizes filtration media and high temperatures. The transformed non-dimensional conservation equations are solved numerically subject to physically appropriate boundary conditions using a second-order accurate implicit finite-difference Keller Box technique. The numerical code is validated with previous studies. Extensive visualization of axial, tangential velocity components and temperature distributions with variation in key parameters including Rosseland radiative number, Darcy number, Forchheimer number (non-Darcy inertial parameter), magnetic interaction parameter, tangent-hyperbolic non-Newtonian power-law index and Weissenberg (non-Newtonian) number is included. Additionally, axial and tangential (circumferential) skin friction and Nusselt number values are tabulated for variation in key control parameters. With increasing Weissenberg number, axial velocity is depleted near the cone surface, tangential velocity is suppressed throughout the boundary layer regime and temperature is strongly enhanced. Axial flow is strongly decelerated further from the cone surface with increasing tangent-hyperbolic power-law index and there is also a significant depletion in tangential (swirl) velocity. Temperature is however boosted throughout the boundary layer transverse to the cone surface with a rise in tangent-hyperbolic power-law index. Both tangential and axial velocity are suppressed with increment in magnetic interaction parameter whereas temperature and thermal boundary layer thickness are enhanced. With larger Darcy number (i.e. greater permeability), axial velocity is strongly increased near the cone surface with no tangible modification further from the cone; However tangential velocity is consistently elevated throughout the boundary layer with greater Darcy number whereas temperature is depleted. An increase in Forchheimer number substantially damps both axial and tangential velocity whereas it elevates temperature. Increasing radiative flux strongly energizes the magnetic polymer and elevates temperature but suppresses the axial and tangential velocities. With elevation in non-isothermal wall exponent, axial skin friction is suppressed whereas Nusselt number are elevated at the cone vertex. Further along the cone surface a similar response is observed but there is also a reduction in magnitudes of tangential skin friction.

Effect of Magnetic Interaction Parameter and the Electrical Conductivity of the Fluid on the Stability of Hydromagnetic Channel Flow

The influence of magnetic interaction parameter and conductivity of the fluid on the stability against small perturbations on the streamlined base flow between two infinitely long parallel fixed plates is studied numerically. By normal mode analysis, the disturbance equations are reduced to Orr-Sommerfeld-type. Using the energy method, sufficient conditions for stability are derived by using the nature of the growth rate and sufficiently small values of the Reynold numbers. The disturbance equations are then solved using the Galerkin method corresponding to the base functions as Legendre-polynomials. Critical values for the Reynolds number, wave number, and speed of the wave are computed for various ranges of the magnetic interaction parameter and the magnetic Reynolds number. The curves of neutral stability are presented for different values of the nondimensional parameters that appeared in this study. The stability analysis is also discussed with the help of the plots of the rate of growth of disturbances for several values of the electrical conductivity and the magnetic interaction parameter. It is observed that both the fluid conductivity and the magnetic interaction parameter have direct control over fluctuations in the system. The results of this study are accurate and are comparable with the existing literature in the absence of a parallel magnetic field.

Bioconvection analysis for convectively heated radiative flow of Sutterby fluid involving efficacy of ferromagnetic nanoparticles

In this article explained about the study 2-D Sutterby fluid model with suspension of microorganisms in ferrofluid, while radiation aspect is also considered here. Basic purpose of using microorganism is to obtain more stability in suspension. Here the important characteristics of thermophoresis parameter, viscous dissipation, magnetic interaction parameter and Brownian motion parameter are examined. Now, the system of non-linear P.D.Es is changed into set of O.D.Es then we solved these equations by using famous mathematical scheme bvp4c. Graphical results showed that temperature of Sutterby ferrofluid intensifies with increase in the estimations of thermal Biot number as well as radiation effects whereas results in reduction of Prandtl number. The density of microorganism reduces for greater values of Peclet number.

Effects of a horizontal magnetic field on the cross-sectional distribution of gas bubbles chain rising in a gallium alloy

Understanding the behavior of rising bubbles in a liquid metal under the influence of a magnetic field (MF) is crucial for optimizing continuous casting processes. The study experimentally investigated the effects of a horizontal MF on the behavior of bubble chains in a gallium alloy. High-speed ultrasonic computed tomography was used to measure the instantaneous bubble crossing positions in a cylindrical column with an inner diameter of 50 mm. With an increase in the MF strength, the oscillations of the bubbles were suppressed, resulting in the crossing position being concentrated in a certain area of the cross-section. The fluctuations in the time intervals of the chain bubbles decreased. These effects were more pronounced when the magnetic interaction parameter (or Stuart number) was greater than 1. The distribution of bubbles in the direction perpendicular to the MF was widespread slightly compared to that in the direction parallel to the MF; this was noticeable at higher flow rates. The suppression of the wake turbulence induced by the Lorentz force was larger in the direction parallel to the MF than that in the direction perpendicular to the MF. Our results have the potential to be used for the direct verification of numerical models.

Unsteady flow of micropolar fluid on a magnetized sheet: Effects of magnetic and microrotation parameters on wall couple stress and skin friction

AbstractIn this study, we investigate the unsteady flow of a micropolar fluid past a magnetized stretchable/shrinkable sheet. Our research aims to analyze the effects of magnetic field, moving slit, and various parameters on the velocity, magnetic, and microrotation profiles of the fluid. By applying the Blasius–Rayleigh–Stokes variable, we derive ordinary differential equations from the partial differential equations that define the problem. We solve the transformed set of equations using the shooting method and obtain dual solutions. Our findings indicate that skin friction decreases with increasing values of the microrotation parameter and magnetic interaction parameter. We also observe that the magnetic interaction parameter enhances the microrotation of molecules. Overall, our study provides valuable insights into the behavior of unsteady flows in micropolar fluids and sheds light on the impact of various parameters on dual solutions.

Numerical analysis of ferromagnetic Carreau fluid flow comprising viscos dissipation aspects

Process of transportation of heat in ferrofluids has innumerable applications in the fields of electronics and automobile industry. By tracing the materials, the ferrofluid got popularity among researchers and engineers, also most ferrofluids are non-Newtonian in nature so here the non-Newtonian fluid is under consideration. In this study, the influences of viscous dissipation and magnetic parameter in the flow of ferromagnetic Carraeu fluid for a stretching surface are examined. Suitable similarity transformations in the system that consists of nonlinear form of Partial Differential Equations (PDEs) are transformed into a system of nonlinear form of ODEs, then the resulting Ordinary Differential Equations (ODEs) are resolved by use of a mathematical technique known as bvp4c. Effects of ferromagnetic interaction factor, Curie temperature, viscous dissipation and material parameter are examined for temperature profile as well as velocity fields. Moreover, the variations in velocity and thermal gradients are analyzed and described with the help of graphs. An upsurge in the values of magnetic interaction parameter and Weissenberg number causes a decline in the velocity field while the thermal gradient shows opposite behavior. It is detected that the temperature of Carreau fluid intensifies for larger [Formula: see text] and [Formula: see text].

Intelligent Bayesian regularization‐based solution predictive procedure for hybrid nanoparticles of AA7072‐AA7075 oxide movement across a porous medium

AbstractThe research community has shown great interest for investigation in the nanofluids models involving Aluminum Alloys AA7072 and AA7072 +AA7075 due to their advantageous impact on heat transfer, physical and mechanical characteristic exploiting in broad engineering applications such as manufacturing of spacecraft, aircraft parts and building testing. The hybrid nanomaterial AA7072‐AA7075 based fluidic system is investigated in this paper using an artificial neural network with Bayesian regularization scheme (ANNs‐BRS). The derived partial differential equations (PDEs) are transformed into ordinary differential equations system ODEs and obtained the reference datasets for the estimated solution dynamics of hybrid nanofluidic system. For prominent parameters, the influence of flow on the temperature distribution and velocity plot are investigated. The performance on 80% training samples, 5% testing and 15% validation dataset for ANNs‐BRS is well‐established in terms of error histogram plots, regression analysis, and MSE based statistics. The results for entropy generation, Eckert number Ec, magnetic interaction parameter M, suction parameter S, and heat generation parameter Q are also discussed. The results show that the Eckert number Ec has the effect of slowing down the rate of heat transfer while increasing the temperature and increases in suction parameter causes decrease in temperature while increase in temperature profile due to enhancement of suction parameter.

Computation of swirling hydromagnetic nanofluid flow containing gyrotactic microorganisms from a spinning disk to a porous medium with hall current and anisotropic slip effects

AbstractPrompted by the advancements in hybrid bio‐nano‐swirling magnetic bioreactors, a mathematical model for the swirling flow from a rotating disk bioreactor to a magnetic fluid saturating a porous matrix and containing nanoparticles and gyrotactic micro‐organisms has been developed. An axial magnetic field is administered which is perpendicular to the disk and Hall currents are included. The disk is assumed to be impervious and stretches in the radial direction with a power‐law velocity. The Buongiorno nanoscale, Kuznetsov bioconvection and Darcy porous media models are deployed. Anisotropic momentum, thermal, nanoparticle concentration and motile micro‐organism slip effects are incorporated. Stefan blowing is also simulated. The governing conservation equations are transformed with appropriate variables to ordinary nonlinear differential equations. MATLAB bvp4c shooting quadrature is used to solve the emerging nonlinear, coupled ordinary differential boundary value problem under transformed boundary conditions. Verification with earlier solutions for the non‐magnetic Von Karman bioconvection nanofluid case is conducted. Further validation of the general magnetic model is conducted with the Adomian decomposition method (ADM). Extensive visualization of velocity, temperature, nanoparticle concentration and motile microorganism density number profiles is presented for the impact of various parameters including magnetic interaction parameter, Hall current parameter, Darcy number, momentum slip, thermal slip, nanoparticle slip and microorganism slip. Computations are also performed for skin friction, Nusselt number, Sherwood number and motile micro‐organism density number gradient. The simulations provide a useful benchmark for further studies.

Magnetized Particles with Electric Charge around Schwarzschild Black Holes in External Magnetic Fields

We investigate the dynamics of test particles endowed with both electric charge and a magnetic dipole moment around a Schwarzschild black hole (BH) immersed in an externally asymptotically uniform magnetic field. We further analyse the effective potential and specific angular momentum and energy of the particles. Furthermore, we show that the upper limit for magnetic interaction parameter β increases with increasing cyclotron frequency ωB, while the radius of the innermost stable circular orbit (ISCO) for charged test particles decreases for the upper value of β=βupper. Furthermore, we show that the energy efficiency released from the BH increases up to about 90% due to the presence of the magnetic dipole moment of the test particle. We explore a degeneracy between the spin parameter of rotating Kerr BH and the magnetic parameter for the values of the ISCO radius and energy efficiency. We study in detail the centre of mass energy for collisions of charged and magnetized particles in the environment surrounding the Schwarzchild BH. Finally, as an astrophysical application, we explore the magnetized parameter and cyclotron frequency numerically for a rotating magnetized neutron star. Interestingly, we show that the corresponding values of the above-mentioned parameters for the magnetar PSR J1745-2900 that orbits around the supermassive black hole (SMBH) that exists at the centre of the Milky Way galaxy are ωB≃5 and β≃0.67, respectively, for the magnetic field is about 10 G.

MHD flow of submerged jets behind the inlet disturbance

AbstractIn a broad variety of configurations in technology and industrial applications, the properties of liquid metal flows subjected to strong magnetic fields, are largely governed by the dynamics of coherent structures, known to settle several basic types, such as thin shear layers, forming near the walls or within the fluid domain, vortices extended along the field, or planar and round jets. In some cases, these structures are created by the design, like a submerged jet formed by a sudden expansion from the nozzle into a blanket channel, or jets formed behind some flow obstruction. In the other cases this may be due to instability and evolution of secondary structures, for example, descending and ascending jets appearing as a result of convective instability in blanket channels. In this study, we undertake an attempt to affect liquid metal flow via inlet disturbance formed by a simple rod placed along the magnetic induction lines. The disturbance can generate flat jets behind the rod and, furthermore, a sustainable flow of anisotropic vortical perturbations further downstream the flow. We seek to analyze the most important mechanisms of the flow dynamics and effects of magnetic field on the integral system properties of enhancing mixing, mass and heat transport for such flow. The most optimal regimes of vortex generation are found to be governed by the magnetic interaction parameter (Stuart number). The exact ratio of the optimal Stuart number is found to be in a range between 20 and 40, based on the channel double width as a characteristic size. The observed vortices attain quasi‐2D shape and exist at a length of dozens of duct calibers, being the strongest at higher flow rates. The obtained flow regimes and their turbulent properties are also found to resemble significant similarity to the results on quasi‐2D turbulence found in prior studies of channel and duct flows under spanwise magnetic field.

Radiation Effects on Inclined Magnetohydrodynamics Mixed Convection Boundary Layer Flow of Hybrid Nanofluids over a Moving and Static Wedge

Nowadays, hybrid nanofluids play an important role in heat transfer systems. They are a good alternative to increase the efficiency of heat transfer and save the energy. Thermal radiation and mixed convection flow of hybrid nanofluids past a permeable moving and stationary wedge were studied in this research. This research uses water as a base fluid to investigate the effects of silver (Ag) and magnesium oxide (MgO) nanoparticles. Similarity transformation techniques are used to convert the partial differential equations of hybrid nanofluids to ordinary differential equations, which is then solved numerically by applying the implicit finite difference Keller box method. The results of the research are illustrated graphically to show the behavior of velocity and temperature profiles, as well as skin friction and Nusselt number. Increasing the parameters of the aligned magnetic field, magnetic field interaction, mixed convection, and wedge angle parameter results in higher velocity profiles but lower temperature profiles. As the radiation parameter and the nanoparticle volume fraction increase, the temperature rises and the velocity decreases. With the exception of the radiation parameter, the skin friction and Nusselt number increase as the alignment angle of the magnetic field, the interaction of the magnetic field, the mixed convection, the wedge angle parameter, and the volume fraction of nanoparticle Ag and MgO rise. As a result of these findings, the velocity profiles and Nusselt numbers of moving wedges are higher, but the temperature profiles and skin friction are lower than those of stationary and moving against flow wedges. In addition, a comparison with previously published research is presented, with excellent agreement discovered. The results of this research will contribute to the field of knowledge in mathematics by bringing additional information for mathematician interested in future research on hybrid nanofluids.

A Self-Similar Approach to Study Nanofluid Flow Driven by a Stretching Curved Sheet

Nano-fluids have considerable importance in the field of thermal development that relates to several industrial systems. There are some key applications in recent construction systems flow, as well as microscale cooling gadgets and microstructure electric gadgets for thermal migration. The current investigation concludes the study of electrically conducting nano-fluid flow and heat transfer analysis in two-dimensional boundary layer flow over a curved extending surface in the coexisting of magnetic field, heat generation and thermal radiation. The small sized particles of copper (Cu) are taken as nanoparticles and water is assumed to be the base fluid. We used quasi-linearization and central difference approximation to numerically solve the system of coupled equations obtained from the partial differential equations (PDEs) by incorporating the concept of similarity. The impacts of non-dimensional parameters on velocity, concentration and thermal profiles have been discussed with the help of suitable graphs and tables. It has been noticed that the velocity decelerated with the effect of the magnetic field interaction parameter. Thermal radiation caused an increase in temperature.

Explicit Solutions of MHD Flow and Heat Transfer of Casson Fluid over an Exponentially Shrinking Sheet with Suction.

In this study, the magnetohydrodynamic (MHD) flow and heat transfer of a Casson fluid over an exponentially shrinking sheet with suction is investigated using the homotopy analysis method (HAM). Different from previous numerical methods and analytical techniques, we have obtained an explicit formula solution to the presented nonlinear problem. The explicit solutions of and are obtained and are valid in the whole domain. The changes in velocity and temperature profiles are studied in cases of different Casson fluid parameter , magnetic interaction parameter M, suction parameter s, and Prandtl number . The convergent solutions are verified by comparison with the numerical results. In addition, the skin friction coefficient and local Nusselt number are analyzed using the analytic formulas of and , respectively. The analytical formulas help us intuitively analyze the influence of various parameters at the theoretical level. The effects of different physical quantities on and are thoroughly investigated.

An exploration of polymer presence in magneto‐hydrodynamic flow and heat transfer past a magnetized stretching surface with effects of Joule heating

AbstractThe consequences of polymer presences on magneto‐hydrodynamic flow and heat transfer of a viscous fluid induced by a magnetized permeable heated stretching surface are studied in this article. The Lorentz force and Joule heating are also taken into consideration. The Oldroyd‐B model of polymers is used to study polymer presence which adds an extra stress in the mathematical model due to the polymer stretching. An iterative numerical scheme is opted to solve the set of ruling equations of the problem. Polymers stretch in the boundary layer region due to high velocity gradients. Polymer stretching reduces the zero‐shear viscosity near the surface but the polymeric viscosity (the total contribution of viscosity due to polymer addition) still remains positive, which cause velocity to reduce in the boundary layer region. Polymers are found to have no impact on the bulk. Skin friction along with heat and magnetic fluxes at the surface are evaluated with increasing polymer concentration. Zero polymer concentration represents the absence of polymers. Reduction in heat and magnetic fluxes and drag at the surface is observed in consequence of polymer addition. Polymer effects on skin friction, heat flux, and magnetic flux with respect to different values of magnetic force parameter, magnetic Prandtl number, magnetic interaction parameter, and the Eckert number are also thoroughly analyzed and graphically presented.

Scrutiny of convective MHD second‐grade fluid flow within two alternatively conducting vertical surfaces with Hall current and induced magnetic field

AbstractThe focus of this paper is to examine the heat and mass transport behavior of transient magnetohydrodynamics second‐grade fluid (elastico‐viscous fluid) flow within a vertical channel bounding the porous regime with the Hall phenomenon and induced magnetic field (IMF). The flow system consists of a strong transverse magnetic field that gives rise to the Hall phenomenon and IMF. The right vertical surface of the channel is conducting and oscillations in its plane in the vertical direction while the left vertical surface of the channel is nonconducting and stationary. The suitable dimensionless setup transforms the flow model into a simplified comparable model which is solved analytically with the assistance of the method of separation of variables. Numerical computation is performed with the aid of MATHEMATICA software to explore the results from the analytical solutions. The results of the investigation are helpful in analyzing the nature of the elastic‐viscous fluids. A noteworthy result noted from the investigation is that there appears a reverse flow in the direction of normal flow when the magnetic interaction parameter is large. For the small magnetic interaction parameter, such a flow is not seen. Hall current reduces the strength of the principal IMF and induces the strength of the secondary generated magnetic field. Furthermore, it is explored that the elastico‐viscous nature of the second‐grade fluid has a tendency of enhancing the principal flow and principal‐produced magnetic field.

Aligned Magnetohydrodynamics Free Convection Flow of Magnetic Nanofluid over a Moving Vertical Plate with Convective Boundary Condition

Due to its substantial applications in physics, chemistry, and engineering, some emphasis has been given in recent years to explore the boundary layer flow of magnetohydrodynamic (MHD) nanofluids. The numerical study is conducted to investigate the behaviour of MHD free convection flow of magnetic nanofluids over a moving vertical plate with convective boundary conditions by taking a few types of parameters into consideration. The similarity transformation was used to reduce the partial differential governing equations into ordinary differential equations. Then, the reduced equations were solved using fourth-fifth order Runge–Kutta–Fehlberg and coded into Maple Software. The results of velocity and temperature profiles were illustrated graphically while the results of skin friction coefficient and Nusselt number were presented in tabulated data. As a result, inclination angle of magnetic field parameter, magnetic interaction parameter, Grashof number and Biot number improve the velocity field and lowers the momentum boundary layer thickness. However, the nanoparticle volume fraction parameter, and the Biot number parameter boost the temperature field and raise the thermal boundary layer thickness. The Nusselt number of the moving plate with the flow is the highest, whereas the skin friction coefficient of the moving plate against the flow is the highest. Fe3O4-kerosene has a better influence to the velocity and temperature profiles as well as skin friction coefficient and Nusselt number.

Formation of Bow Shock Waves Around a Blunt Body in Magnetohydrodynamics Flows

The diffraction of a shock wave over a stationary body is a problem of interest associated with the starting of shock tubes and expansion tubes, which are well suited to studies of hypersonic magnetohydrodynamic flows. However, these facilities are characterized by very short test times. The transient parameters during the establishment of the detached bow shock in such impulsive facilities are important for both data processing and experimental design. In the present study, based on the low magnetic Reynolds number assumption and dipole magnetic field distribution, the influence of magnetic field on the diffraction of an incident shock wave over a sphere was studied numerically. The incident shock Mach number ranges from 11 to 15 under different magnetic field intensities. Time histories of the shock-detached distance and stagnation pressure were first obtained. Moreover, the time needed to establish the steady flows over the sphere was also displaced against the magnetic interaction parameter. The larger the magnetic interaction parameter, the longer the time needed to establish a steady bow shock for experiments, which further challenges the facilities to have sufficient test times for conducting hypersonic magnetohydrodynamic flow experiments.

THEORETICAL ANALYSIS ON HYPERSONIC MHD SHOCK STAND-OFF DISTANCE OF BLUNT BODY

High speed and shock compression behind the bow shock of an aircraft head result in very high temperature, which would subsequently lead to a conductivity plasma flowfield around the vehicle. The plasma gas provides a direct working environment for the application of magnetic field. The magnetohydrodynamic (MHD) flow control, which uses the magnetic field to alter the trajectory of ions or electrons, can improve the aerodynamic characteristics of hypersonic vehicles effectively. As an intuitive aerodynamic phenomenon in the field of hypersonic MHD flow control, shock stand-off distance has attracted close attention from researchers. Under the influence of the applied magnetic field, the shock stand-off distance will change with it, of which the value can directly reflect the effect of the MHD flow control. However, the relevant theoretical models are still limited, and further development in this field is consequently needed. Focusing on dealing with this problem, MHD hypersonic shock stand-off distance of the spherical model is theoretically studied in this paper. By means of radially integrating the continuity equation and applying mathematical method of variable separation to the momentum equation, the analytical expression of MHD shock stand-off distance is obtained. The theoretical analysis was performed under the assumption of low magnetic Reynolds number, and the common-used dipole distribution of magnetic field as applied. The results show that the MHD stand-off distance of shock increases with the increase of magnetic interaction parameter. Moreover, the regularity can be found that as the speed of inflow becomes higher, magnetic interaction parameter can be viewed as the primary impact factor of shock stand-off distance under hypersonic condition. The theoretical model in this work can rapidly evaluate the effect of MHD control, and it can provide theoretical guidance to the design of experiment scheme and the analysis of results.