Method of mass-average quantities for the boundary layer in an outer flow with transverse nonuniformity

An engineering method is proposed for calculating the friction and heat transfer through a boundary layer in which a nonuniform distribution of the velocity, total enthalpy, and static enthalpy is specified across the streamlines at the initial section x₀. Such problems arise in the vortical interaction of the boundary layer with the high-entropy layer on slender blunt bodies, with sudden change of the boundary conditions for an already developed boundary layer (temperature jump, surface discontinuity), and in wake flow past a body, etc.Notation x, y longitudinal and transverse coordinates - u,, H, h gas velocity, stream function, total and static enthalpy - p,,, pressure, density, viscosity, Prandtl number - , q friction and thermal flux at the body surface - r(x), (x) body surface shape and boundary layer thickness - V, M freestream velocity and Mach number - u⁽⁰⁾(x₀,), H⁽⁰⁾(x₀,), h⁽⁰⁾(x₀,) parameter distributions at initial section - u⁽⁰⁾(x,), h⁽⁰⁾(x,), h⁽⁰⁾(x,) profiles of quantities in outer flow in absence of friction and heat transfer at the surface of the body The indices v=0, 1 relate to plane and axisymmetric flows - , w, b, relate to quantities at the outer edge of the inner boundary layer, at the body surface in viscid and nonviscous flows, and in the freestream, respectively. The author wishes to thank O. I. Gubanov, V. A. Kaprov, I. N. Murzinov, and A. N, Rumynskii for discussions and assistance in this study.     

Eine analytische Näherungslösung für die eingefrorene laminare Grenzschichtströmung eines binären Gemisches

Zusammenfassung Für die eingefrorene laminare Grenzschichtströmung eines teilweise dissoziierten binären Gemisches entlang einer stark gekühlten ebenen Platte wird eine analytische Näherungslösung angegeben. Danach läßt sich die Wandkonzentration als universelle Funktion der Damköhler-Zahl der Oberflächenreaktion angeben. Für das analytisch darstellbare Konzentrationsprofil stellt die Damköhler-Zahl den Formparameter dar. Die Wärmestromdichte an der Wand bestehend aus einem Wärmeleitungs- und einem Diffusionsanteil wird angegeben und diskutiert. Das Verhältnis beider Anteile läßt sich bei gegebenen Randbedingungen als Funktion der Damköhler-Zahl ausdrücken.

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An analytical approximation for the frozen laminar boundary layer flow of a binary mixture

An analytical approximation is derived for the frozen laminar boundary layer flow of a partially dissociated binary mixture along a strongly cooled flat plate. The concentration at the wall is shown to be a universal function of the Damkohler-number for the wall reaction. The Damkohlernumber also serves as a parameter of shape for the concentration profile which is presented in analytical form. The heat transfer at the wall depending on a conduction and a diffusion flux is derived and discussed. The ratio of these fluxes is expressed as a function of the Damkohler-number if the boundary conditions are known.

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Formelzeichen A Atom - A₂ Molekül - C Konstante in Gl. (20) - c₁=1/(2C) Konstante in Gl. (35) - c_p spezifische Wärme bei konstantem Druck - D binärer Diffusionskoeffizient - Ec=u ² /(2h_f) Eckert-Zahl - h spezifische Enthalpie - h_t=h+u²/2 totale spezifische Enthalpie - h _A ⁰ spezifische Dissoziationsenthalpie - K_w Reaktionsgeschwindigkeitskonstante der heterogenen Wandreaktion - 1= /( ) Champman-Rubesin-Parameter - Le=Pr/Sc Lewis-Zahl - M Molmasse - p statischer Druck - Pr= c_pf/ Prandtl-Zahl - q_w Wärmestromdichte an der Wand - q_cw, q_dw Wärmeleitungsbzw. Diffusionsanteil der Wärmestromdichte an der Wand - universelle Gaskonstante - R=/(2M_a) individuelle Gaskonstante der molekularen Komponente - Re_x= u x/ Reynolds-Zahl - Sc=/( D) Schmidt-Zahl - T absolute Temperatur - T_d=h _A ⁰ /R charakteristische Dissoziationstemperatur - u, v x- und y-Komponenten der Geschwindigkeit - U=u/u normierte x-Komponente der Geschwindigkeit - x, y Koordinaten parallel und senkrecht zur Platte Griechische Symbole - =A/ Dissoziationsgrad - Grenzschichtdicke - ₂ Impulsverlustdicke - Damköhler-Zahl der Oberflächenreaktion - =T/T normierte Temperatur - =y/ normierter Wandabstand - Wärmeleitfähigkeit - dynamische Viskosität - , ^* Ähnlichkeitskoordinaten - Dichte - Schubspannung Indizes A auf ein Atom bezogen - M auf ein Molekül bezogen - f auf den eingefrorenen Zustand bezogen - w auf die Wand bezogen - auf den Außenrand der Grenzschicht bezogen     

Exact Solutions of the Hydrodynamic Equations Derived from Partially Invariant Solutions

The paper proposes a heuristic approach to constructing exact solutions of the hydrodynamic equations based on the specificity of these equations. A number of systems of hydrodynamic equations possess the following structure: they contain a reduced system of n equations and an additional equation for an extra function w. In this case, the reduced system, in which w = 0, admits a Lie group G. Taking a certain partially invariant solution of the reduced system with respect to this group as a seed:rdquo; solution, we can find a solution of the entire system, in which the functional dependence of the invariant part of the seed solution on the invariants of the group G has the previous form. Implementation of the algorithm proposed is exemplified by constructing new exact solutions of the equations of rotationally symmetric motion of an ideal incompressible liquid and the equations of concentrational convection in a plane boundary layer and thermal convection in a rotating layer of a viscous liquid.     

Chaos and integrability in a nonlinear wave equation

We consider the parametrized family of equations _tt ,u- _xx u-au+u ₂ ² u=O,x(0,L), with Dirichlet boundary conditions. This equation has finite-dimensional invariant manifolds of solutions. Studying the reduced equation to a four-dimensional manifold, we prove the existence of transversal homoclinic orbits to periodic solutions and of invariant sets with chaotic dynamics, provided that =2, 3, 4,.... For =1 we prove the existence of infinitely many first integrals pairwise in involution.     

Saint-Venant's principle in linear two-dimensional elasticity for non-striplike domains

Let be a simply connected domain in the x ₁-x ₂ plane which lies within the strip 0<x ₂, is a simple closed piecewise smooth curve. Let l= [(x ₁, x ₂): (x ₁, x ₂) and x ₁>0], _l = [(x ₁ x ₂): (x ₁ ,x ₂) and x ₁>1>0].Suppose that a two-dimensional homogeneous isotropic elastic body occupies , that a self-equilibrated stress loading is applied to - l, and that l is stress-free. Knowles [2] and Flavin [6] showed that the elastic energy in _l decays exponentially with respect to l with an exponential decay constant of the form k/b, where k is a universal constant. It is shown here that a decay constant of the form c/ may be obtained where c is a universal constant and is a characteristic dimension of , which is more appropriate than b for general non-striplike domains. In addition, an appropriate decay theorem is obtained for coil-like domains.     

Anwendung des Übertragungsverfahrens bei stark abklingenden Lösungsfunktionen

Übersicht Bei stark abklingenden Funktionen wird die Übertragungsmatrix U() aufgespalten in die Anteilc U ₁() e^– und U ₂() e. Der zweite Term spielt am Rand = 0 keinc Rolle. Die unbekannten Anfangswerte sind über die Matrix U ₁(0) an die bekannten gebunden und eindeutig bestimmbar.

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Summary For strongly decaying solution functions the transfer matrix U() is splitted into the parts U ₁() e^– and U ₂() e. The second term does not influence at the boundary = 0. The unknown initial values are related by the matrix U ₁(0) to the known values and they can be uniquely determined.

     

Optical co-ordinates in general relativity 2 — the problem of distance

Summary Let denote the congruence of null geodesics associated with a given optical observer inV ₄. We prove that determines a unique collection of vector fieldsM₍₎ ( =1, 2, 3) and ₍₀₎ overV ₄, satisfying a weak version of Killing's conditions.This allows a natural interpretation of these fields as the infinitesimal generators of spatial rotations and temporal translation relative to the given observer. We prove also that the definition of the fieldsM₍₎ and ₍₀₎ is mathematically equivalent to the choice of a distinguished affine parameter f along the curves of, playing the role of a retarded distance from the observer.The relation between f and other possible definitions of distance is discussed.

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Sommario Sia la congruenza di geodetiche nulle associata ad un osservatore ottico assegnato nello spazio-tempoV ₄. Dimostriamo che determina un'unica collezione di campi vettorialiM₍₎ ( =1, 2, 3) e ₍₀₎ inV ₄ che soddisfano una versione in forma debole delle equazioni di Killing. Ciò suggerisce una naturale interpretazione di questi campi come generatori infinitesimi di rotazioni spaziali e traslazioni temporali relative all'osservatore assegnato. Dimostriamo anche che la definizione dei campiM₍₎, ₍₀₎ è matematicamente equivalente alla scelta di un parametro affine privilegiato f lungo le curve di, che gioca il ruolo di distanza ritardata dall'osservatore. Successivamente si esaminano i legami tra f ed altre possibili definizioni di distanza in grande.

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Work performed in the sphere of activity of: Gruppo Nazionale per la Fisica Matematica del CNR.     

Supersonic air flow past a sphere with account for vibrational relaxation

A numerical solution is obtained for the problem of air flow past a sphere under conditions when nonequilibrium excitation of the vibrational degrees of freedom of the molecular components takes place in the shock layer. The problem is solved using the method of [1]. In calculating the relaxation rates account was taken of two processes: 1) transition of the molecular translational energy into vibrational energy during collision; 2) exchange of vibrational energy between the air components. Expressions for the relaxation rates were computed in [2]. The solution indicates that in the state far from equilibrium a relaxation layer is formed near the sphere surface. A comparison is made of the calculated values of the shock standoff with the experimental data of [3].Notation uV_max, vV_max velocity components normal and tangential to the sphere surface - V_max maximal velocity - P V _max ² pressure - density - TT temperature - e_viRT vibrational energy of the i-th component per mole (i=–O₂, N₂) - =rb–1 shock wave shape - a _f the frozen speed of sound - HRT/m gas total enthalpy     

A turbulent immersed air wall jet on a burning graphite surface

The turbulent boundary layer in an immersed air jet traveling along a burning graphite wall is analyzed. In order to study the heat and mass transfer and the friction in the boundary layer, a method of calculation based on the solution of the integrated energy and momentum relations is employed, allowing for the conservative properties of the turbulent boundary layer at the wall [1].Notation x longitudinal coordinate - y transverse coordinate - s height of slot - thickness of boundary layer - * displacement thickness - ** momentum-loss thickness - velocity - j transverse mass flow (flux) - density - T temperature - i total enthalpy - temperature factor - ₁ enthalpy factor - k reduced concentration of the i-th component - tangential stress - b permeability parameter - C₁ form (shape) parameter - dynamic viscosity coefficient - c _f friction coefficient - relative friction coefficient Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 60–67, January–February, 1971.     

The Thermodynamic Significance of the Local Volume Averaged Temperature

Since the temperature is not an additive function, the traditional thermodynamic point of view suggests that the volume integral of the temperature has no precise physical meaning. This observation conflicts with the customary analysis of non-isothermal catalytic reactors, heat pipes, driers, geothermal processes, etc., in which the volume averaged temperature plays a crucial role. In this paper we identify the thermodynamic significance of the volume averaged temperature in terms of a simple two-phase heat transfer process. Given the internal energy as a function of the point temperature and the density

Flow Structure in the Separation Zone in the Interaction between Shock Waves and the Boundary Layer on a Plate with Slip

A model which makes it possible to calculate the reverse-flow parameters in the separation zone is constructed on the basis of the results of an integrated experimental study of the characteristics of the separated flow developed in the transition from free to non-free interaction between plane shock waves and the boundary layer on a plate with slip. The effect of the Mach number of the reverse flow in the separation zone on the properties of inner boundary layer separation is analyzed. Features of the interference flow due to boundary layer transition are described. The present study is a continuation of investigations [1–3] devoted to the study of a new steady-state type of interaction between shock waves and the boundary layer on a plate with slip in which the separation line formed would propagate upstream beyond the sharp leading edge if no leading edge was present, i.e., so-called non-free interaction.     

The dynamic performance of the Weissenberg rheogoniometer III. Large amplitude oscillatory shearing — harmonic analysis

The harmonic content of the nonlinear dynamic behaviour of 1% polyacrylamide in 50% glycerol/water was studied using a standard Model R 18 Weissenberg Rheogoniometer. The Fourier analysis of the Oscillation Input and Torsion Head motions was performed using a Digital Transfer Function Analyser.In the absence of fluid inertia effects and when the amplitude of the (fundamental) Oscillation Input motion _I is much greater than the amplitudes of the Fourier components of the Torsion Head motion _Tn empirical nonlinear dynamic rheological propertiesG _n (, ⁰),G _n (, ⁰) and/or _n (, ⁰), _n (, ⁰) may be evaluated without a-priori-knowledge of a rheological constitutive equation. A detailed derivation of the basic equations involved is presented.Cone and plate data for the third harmonic storage modulus (dynamic rigidity)G ₃ (, ⁰), loss modulusG ₃ (, ⁰) and loss angle ₃ (, ⁰) are presented for the frequency range 3.14 × 10^–2 1.25 × 10² rad/s at two strain amplitudes, _CP ⁰ = 2.27 and 4.03. Composite cone and plate and parallel plates data for both the third and fifth harmonic dynamic viscosities ₃ (, ⁰), _S (, ⁰) and dynamic rigiditiesG ₃ (, ⁰),G ₅ (, ⁰) are presented for strain amplitudes in the ranges 1.10 _CP ⁰ 4.03 and 1.80 _PP ⁰ 36 for a single frequency, = 3.14 × 10^–1 rad/s. Good agreement was obtained between the results from both geometries and the absence of significant fluid inertia effects was confirmed by the superposition of the data for different gap widths.     

Analysis of turbulent boundary layer interaction with an external supersonic flow behind a step

An integral method of analyzing turbulent flow behind plane and axisymmetric steps is proposed, which will permit calculation of the pressure distribution, the displacement thickness, the momentum-loss thickness, and the friction in the zone of boundary layer interaction with an external ideal flow. The characteristics of an incompressible turbulent equilibrium boundary layer are used to analyze the flow behind the step, and the parameters of the compressible boundary layer flow are connected with the parameters of the incompressible boundary layer flow by using the Cowles-Crocco transformation.A large number of theoretical and experimental papers devoted to this topic can be mentioned. Let us consider just two [1, 2], which are similar to the method proposed herein, wherein the parameter distribution of the flow of a plane nearby turbulent wake is analyzed. The flow behind the body in these papers is separated into a zone of isobaric flow and a zone of boundary layer interaction with an external ideal flow. The jet boundary layer in the interaction zone is analyzed by the method of integral relations.The flow behind plane and axisymmetric steps is analyzed on the basis of a scheme of boundary layer interaction with an external ideal supersonic stream. The results of the analysis by the method proposed are compared with known experimental data.Notation x, y longitudinal and transverse coordinates - X, Y transformed longitudinal and transverse coordinates - , ^*, ^** boundary layer thickness, displacement thickness, momentum-loss thickness of a boundary layer - , ^*, ^** layer thickness, displacement thickness, momentum-loss thickness of an incompressible boundary layer - u, velocity and density of a compressible boundary layer - U, velocity and density of the incompressible boundary layer - , stream function of the compressible and incompressible boundary layers - , dynamic coefficient of viscosity of the compressible and incompressible boundary layers - r₁ radius of the base part of an axisymmetric body - r radius - R transformed radius - M Mach number - friction stress - p pressure - a speed of sound - s enthalpy - v Prandtl-Mayer angle - P Prandtl number - P_t turbulent Prandtl number - r₂ radius of the base sting - b step depth - =0 for plane flow - =1 for axisymmetric flow Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 33–40, May–June, 1971.In conclusion, the authors are grateful to M. Ya. Yudelovich and E. N. Bondarev for useful comments and discussions.     

Influence of vorticity on the heat transfer to blunt bodies in hypersonic flight

When blunt bodies are in hypersonic flight, a high-entropy layer of gas with nonzero vorticity is formed near their surface. The transverse gradients of the entropy, density, and gas velocity in the layer are high, which makes it necessary to take into account its absorption by the boundary layer of finite thickness . This vortex interaction is usually accompanied by an increase in the heat flux q and the frictional stress on the wall compared with their values as calculated in accordance with the classical scheme of a thin boundary layer, when the parameters on the outer edge of the boundary layer are set equal to the inviscid parameters on the body. This effect has been investigated on the side surface of slender (with angle 1 to the undisturbed flow) blunt bodies in a hypersonic stream [1–3]. It is shown in the present paper that the effect can have a stronger and even qualitative influence on the flow over blunt bodies with 1 if the radius of curvature R_s of the detached shock wave on the axis is small compared with the midsection radius R of the body. It is shown that the distributions of the heat fluxes with allowance for the vorticity of the inviscid shock layer are similar in the case of slightly blunt (r₀/R 0) cones with half-angles less than a critical _*.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 50–57, March–April, 1981.     

On nonlinear problems of mixed type: A qualitative theory using infinite-dimensional center manifolds

We consider the equation a(y)u_xx+div_y(b(y)_yu)+c(y)u=g(y, u) in the cylinder (–l,l)×, being elliptic where b(y)>0 and hyperbolic where b(y)<0. We construct self-adjoint realizations in L₂() of the operatorAu= (1/a) div_y(b_yu)+(c/a) in the case ofb changing sign. This leads to the abstract problem u_xx+Au=g(u), whereA has a spectrum extending to + as well as to –. For l= it is shown that all sufficiently small solutions lie on an infinite-dimensional center manifold and behave like those of a hyperbolic problem. Anx-independent cross-sectional integral E=E(u, u_x) is derived showing that all solutions on the center manifold remain bounded forx ±. For finitel, all small solutionsu are close to a solution on the center manifold such that u(x)-(x) Ce ^-(1-|x|) for allx, whereC and are independent ofu. Hence, the solutions are dominated by hyperbolic properties, except close to the terminal ends {±1}×, where boundary layers of elliptic type appear.     

Laminar assisting mixed convection heat transfer from a vertical isothermal plate to water with variable physical properties

The steady laminar boundary layer flow, with an external force, along a vertical isothermal plate is studied in this paper. The external force may be produced either by the motion of the plate or by a free stream. The fluid is water whose density-temperature relationship is non-linear at low temperatures and viscosity and thermal conductivity are functions of temperature. The results are obtained with the numerical solution of the boundary layer equations with , k and variable across the boundary layer. Both upward and downward flow is considered. It was found that the variation of , k and with temperature has a strong influence on mixed convection characteristics.Nomenclature c_p water specific heat - f dimensionless stream function - g gravitational acceleration - Gr_x local Grashof number - k thermal conductivity - Nu_x local Nusselt number - Pr Prandtl number - Pr_a ambient Prandtl number - Re_x local Reynolds number - s salinity - T water temperature - T_a ambient water temperature - T_o plate temperature - u vertical velocity - u_a free stream velocity - u_o plate velocity - v horizontal velocity - x vertical coordinate - y horizontal coordinate - pseudo-similarity variable - nondimensional temperature - dynamic viscosity - _f film dynamic viscosity - _o dynamic viscosity at plate surface - kinematic viscosity - buoyancy parameter - water density - _a ambient water density - _f film water density - _o water density at plate surface - physical stream function     

The effect of background particulates on the delayed transition of a heated 9:1 ellipsoid

An experimental study was done to quantify the effects of a variety of background particulates on the delayed laminar-turbulent transition of a thermally stabilized boundary layer in water. A Laser-Doppler Velocimeter system was used to measure the location of boundary layer transition on a 50 mm diameter, 9:1 fineness ratio ellipsoid. The ellipsoid had a 0.15 m RMS surface finish. Boundary layer transition locations were determined for length Reynolds numbers ranging from 3.0 × 10⁶ to 7.5 × 106. The ellipsoid was tested in three different heating conditions in water seeded with particles of four distinct size ranges. For each level of boundary layer heating, measurements of transition were made for clean water and subsequently, water seeded with 12.5 m, 38.9 m, 85.5 m and 123.2 m particles, alternately. The three surface heating conditions tested were no heating, T = 10°C and T = 15°C where T is the difference between the inlet model heating water temperature, T _i, and free stream water temperature, T . The effects of particle concentration were studied for 85.5 m and 123.2 m particulates.The results of the study can be summarized as follows. The 12.5 m and 38.9 m particles has no measurable effect on transition for any of the test conditions. However, transition was significantly affected by the 85.5 m and 123.2 m particles. Above a length Reynolds number of 4 × 10⁶ the boundary layer transition location moved forward on the body due to the effect of the 85.5 m particles for all heating conditions. The largest percentage changes in transition location from clean water, were observed for 85.5 m particles seeded water.Transition measurements made with varied concentrations of background particulates indicated that the effect of the 85.5 m particles on the transition of the model reached a plateau between 2.65 particulates/ml concentration and 4.2 particles/ml. Measurements made with 123.3 m particles at concentrations up to 0.3 part/ml indicated no similar plateau.     

Theoretical derivation of tangential velocity profiles in a flat vortex chamber-influence of turbulence and wall friction

Summary As part of a study on the hydrodynamics of a cyclone separator, a theoretical investigation of the flow pattern in a flat box cyclone (vortex chamber) has been carried out. Expressions have been derived for the tangential velocity profile as influenced by internal friction (eddy viscosity) and wall friction. The most important parameter controlling the tangential velocity profile is = –u ₀ R/(v+ ), where u ₀ is the radial velocity at the outer radius R of the cyclone, the kinematic liquid viscosity and is the kinematic eddy viscosity. For values of greater than about 10 the tangential velocity profile is nearly hyperbolic, for smaller than 1 the tangential velocity even decreases towards the centre. It is shown how and also the wall friction coefficient may be obtained from experimental velocity profiles with the aid of suitable graphs. Because of the close relation between eddy viscosity and eddy diffusion, measurements of velocity profiles in flat box cyclones will also provide information on the eddy motion of particles in a cyclone, a motion reducing its separation efficiency.List of symbols A cross-sectional area of cyclone inlet - h height of cyclone - p static pressure in cyclone - p static pressure difference in cyclone between two points on different radius - r radius in cyclone - r ₁ radius of cyclone outlet - R radius of cyclone circumference - u radial velocity in cyclone - u ₀ radial velocity at circumference of flat box cyclone - v tangential velocity - v ₀ tangential velocity at circumference of flat box cyclone - w axial velocity - z axial co-ordinate in cyclone - friction coefficient in flat box cyclone (for definition see § 5) - ₁ value of friction coefficient for ₁<< ₂ - ₂ value of friction coefficient for ₂<<1 - = - ₁ value of for ₁<< ₂ - ₂ value of for ₂<<1 - thickness of laminar boundary layer - =/h - turbulent kinematic viscosity - ratio of z to h - k ratio of height of cyclone to radius R of cyclone - parameter describing velocity profile in cyclone =–u ₀ R/(+) - kinematic viscosity of fluid - density of fluid - ratio of r to R - ₁ value of at outlet of cyclone - ₂ value of at inner radius of cyclone inlet - _w shear stress at cyclone wall - angular momentum in cyclone/angular momentum in cyclone inlet - ₁ value of at = ₁ - ₂ value of at = ₂     

Stability of Thermal Vibrational Flow in an Inclined Liquid Layer Against Finite‐Frequency Vibrations

Stability of the flow that arises under the action of a gravity force and streamwise finitefrequency vibrations in a nonuniformly heated inclined liquid layer is studied. By the Floquet method, linearized convection equations in the Boussinesq approximation are analyzed. Stability of the flow against planar, spiral, and threedimensional perturbations is examined. It is shown that, at finite frequencies, there are parametricinstability regions induced by planar perturbations. Depending on their amplitude and frequency, vibrations may either stabilize the unstable ground state or destabilize the liquid flow. The stability boundary for spiral perturbations is independent of vibration amplitude and frequency.     

Development of magnetohydrodynamic boundary layers

Many authors have studied the problem of the development of a hydrodynamic boundary layer when a body is suddenly set in motion. The results obtained are presented most fully in the monographs of H. Schlichting [1] and L. G. Loitsyanskii [2]. In magnetohydrodynamics the development of the boundary layer over the surface of an infinite flat plate for uniform oncoming flow has been closely studied (for example [3, 4]). Below, the problem of the development of a plane magnetohydrodynamic boundary layer is considered in a different formulation. We shall suppose that the distributions of velocity U(x) and enthalpy h(x) are given along the body contour for t=0. At that moment the viscosity and thermal conductivity mechanisms are instantaneously switched on. Viscous and thermal boundary layers begin to grow in a direction normal to the body. The medium in the boundary layer interacts with the magnetic field. This formulation corresponds to the development of a magnetohydrodynamic boundary layer on a body which is set in motion with a jerk, in the case where the rate of establishment of magnetohydrodynamic flow of the inviscid, thermally nonconducting fluid around the body is much less than the rate of development of the boundary layer. Then U(x) and h(x) are found by solving the problem of stationary magnetohydrodynamic flow of an inviscid thermally nonconducting fluid around a body, or simply the hydrodynamic flow if the medium interacts with the field only in the boundary layer.