Equilibrium and stability of a cylindrical linear pinch with a homogeneous temperature distribution

The equilibrium and stability of a high-current discharge have been theoretically investigated in a dense optically gray plasma. The plasma is assumed to be completely opaque to longwave photons and completely transparent to short-wave photons. The threshold frequency is determined by setting the diameter of the plasma pinch equal to the mean free path of the photons. We solve the equations of magnetohydrodynamics together with the equation of radiative transfer. We show that in a gray plasma an equilibrium state can exist with a practically homogeneous temperature distribution over the discharge cross section. Temperature homogeneity is ensured by the large radiant thermal conductivity, which is related to the longwave radiation. The radiant thermal conductivity also causes the discharge to be stable with respect to superheating. We analyze the possibility of using such a discharge for the energy pumping of a laser. We show that for discharge currents of order 10⁶ A, the efficiency of a gray discharge exceeds the efficiency of an opaque discharge by a factor of three.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 33–39, January–February, 1971.     

An alternating direction implicit method for magnetohydrodynamic heat transfer in cylindrical geometry with discontinuity in wall temperature

The temperature distribution in the magnetohydrodynamic axial flow in a circular pipe has been found by using an alternating direction implicit method which has been suitably modified for r-θ-z geometry. First the temperature distribution for from the discontinuity, which ceases to depend upon the axial coordinate, has been found. This has been used to determine the results on both sides of the discontinuity. It is found that the temperature falls as the Hartmann number is increased, and convection dominates for large values of the Peclet number. The effect of the Hartmann number is more pronounced when Peclet number is large.     

Transient temperature distribution in an internally and externally insulated cylindrical shell

This paper presents the analytical solution for unsteady state temperature distribution in a cylindrical shell having thin layer of thermal insulation coating at the inner and outer surfaces. The formula has been derived assuming different initial temperatures of shell and insulation coating while the contact between them has also been assumed to be imperfect. The internal and external surfaces of the shell and coatings are exposed to the convective boundary conditions of third kind.The generalized formula obtained has been used to obtain the warming-up-period of the cylindrical wall of a Diesel engine coated internally and externally by ceramic insulation material. A plot of Temperature-time history and heat flow rates have been obtained. The problem considered has got its application in the transient thermal analysis of an adiabatic engine. Any other similar problem in metallurgical, aeronautical, furnace design, boiler design applications may be solved by the formula obtained.Nomenclature a ₁, a ₂, a ₃ thermal diffusivity of shell, inner and outer insulation coatings - A ₁(, ) to A ₆(, ) as defined in equation (4) - B _g , B _w Biot's numbers on inner and outer surfaces - C ₁, C ₂, C ₃ Specific heat of shell, inner and outer insulation coatings - F ₀ Fourier's number, F ₀ = a ₁ t/R ₂ ² - G(s) as defined in equation (4) - h _g , h _w heat transfer coefficients at inner and outer surfaces - K ₁, K ₂, K ₃ coefficient of thermal conductivity of shell, inner and outer insulation coatings - ratio defined as, - thermal activeness ratio, - L ₁ to L ₂₁ Factors defined in equation (4) - m ₂, m ₃ thermal contact resistances at interfaces, (kcal/m² hr°C)^–1 - M ₂, M ₃ dimensionless contact coefficients, M ₂ = m ₂ K ₂/₂, M ₃ = m ₃ K ₃/₃ - P factor defined in equation (7) - Q ₁, Q ₂, Q ₃, Q ₄ heat flow rates at inner, interfaces and outer surfaces - R ₁, R ₂, R ₃, R ₄ Interfaces, inner and outer radii - r radial co-ordinate - s Laplace parameter - t time - T ₁(r, t), T ₂(r, t), T ₃(r, t) temperatures in shell, inner and outer insulation coatings - T ₁₀, T ₂₀, T ₃₀ initial temperatures in shell, inner and outer insulation coatings - T _g , T _w gaseous and water side temperatures - U _m (, x) as defined in equation (4) - V _m (, x) as defined in equation (4) - W _m (, x) as defined in equation (4) - x, x ₁ dimensionless radii, x = r/R ₂ and x ₁ = R ₁/R ₂ Greek symbols ₂, ₃ thicknesses of the insulation coatings, ₂ = (R ₁ – R ₃), = (R ₄ – R ₂) - , dimensionless radii, = (r – R ₃)/₂, = (r – R ₂)/₃ - ₁₀, ₂₀, ₃₀, _g initial temperatures ₁₀ = ( T ₁₀ – T _w ); ₂₀ = (T ₂₀ – T _w ); ₃₀ = T ₃₀ – T _w ; _g = T _g – T _w ) - ₁(x, F ₀), ₂(, F ₀), ₃(, F ₀) temperature symbols defined as ₁ = ( T ₁ (r, t) – T _w ); ₂ = (T ₂ (r, t) – T _w ); ₃ = T ₃ (r, t) – T _w ) - Laplace transformation of ₁(x, F ₀), ₂(, F ₀) and ₃(, F ₀) - defined as, - defined as - defined as, - ₁, ₂, ₃ densities of shell, inner and outer insulation coatings - angle defined in equation (5) - _n factor defined in equation (7)     

Stress distribution around a circular cylindrical cavity in a prestressed plate

A system of equilibrium equations for nonthin transversely isotropic plates with a uniform prestress field is derived by expanding the unknown functions into Fourier-Legendre series. A method of finding the general solution of this system is expounded and used to determine the stress state of a plate with a circular cylindrical cavity __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 1, pp. 28–39, January 2008.     

The sputtering temperature of a cooling cylindrical rod with an insulated core

By a standard application of Jones's method associated with the Wiener-Hopf technique an explicit solution is obtained for the temperature distribution inside a cylindrical rod with an insulated inner core when the rod is allowed to enter into a fluid of large extent with a uniform speed, and a simple integral expression is derived for the value of the sputtering temperature of the rod at the points of entry. Numerical results under certain special circumstances are also obtained and presented in the form of a table.     

Experimental investigation of the velocity of alternating jets issuing from a horizontal annular cavity with a vibrating inner cylindrical surface

The flow characteristics of a single pulsating jet and a single-row system of pulsating jets produced by the transverse vibrations of a horizontal cylinder installed coaxially in a stationary perforated shell are investigated.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 178–180, July–August, 1989.     

Determination of contact temperature in cylindrical joints

The problem of determining the contact temperatures arising due to internal friction between two coated cylinders through their coatings is considered. The case of imperfect thermal contact is treated. The contact temperatures on the coating surfaces are determined in closed form.     

Contact load distribution along the length of a cylindrical shell

Mariupol' Metallurgical Institute. Translated from Prikladnaya Mekhanika, Vol. 25, No. 4, pp. 46–50, April, 1989.     

Investigation of temperature distribution in a piecewise-homogeneous seam with pressed-in hot fluid

Temperature distribution in a piecewise-homogeneous finiteseam exposed to hot fluid and the effect of inhomogeneity in the permeability and thermal properties of separate zones of a seam on the redistribution of temperature fields for flat parallel or axial flow of a pressed-in hot liquid are studied. The differential equations which describe the process of temperature distribution in accordance with [1] are solved for various initial and boundary conditions. Exact analytic formulas are obtained which are useful in numerical computations. The problem under consideration is related to important engineering problems in hydrology, geothermy, as well as in the development of oil or gas fields [2–4, 5].     

Convection currents in a vertical layer with a space-modulated temperature distribution on the boundaries

Steady convective motions in a plane vertical fluid layer are investigated. The temperature along the boundaries of the layer varies harmonically and has different average values on each of the boundaries. Thus space-period modulation of the temperature of the walls is assigned along with average lateral heating of the layer. The form of the plane steady motions and regions of existence of through currents and currents of cellular structure are found for various values of the parameters of the problem by the finite difference grid-point method. The dependence of the main characteristics of fluid motion on the Grashof number is determined. The results presented in the article pertain to the case when the period of modulation of the temperature of the boundaries coincides with the wavelength of the critical mode of a plane-parallel current. A numerical investigation of supercritical motions in a vertical layer with plane isothermal boundaries heated to a different temperature was carried out in [1–3]. The effect of a space-periodic inhomogeneity due to curvature of walls on the form and stability of convective motions in a vertical layer with lateral heating was examined in [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 20–25, September–October, 1978.The author thanks E. M. Zhukhovitskii for formulating the problem and supervising the work and G. Z. Gershuni for discussions and useful comments.     

Magneto-thermo-elastic stresses in an infinitely long cylindrical conductor carrying a uniformly distributed axial current

A formulation of two-dimensional magneto-thermo-elastostatic boundary value problems is presented in this paper. It is found that since the Lorentz pondermotive body force is conservative in this case, a nonhomogeneous biharmonic equation for the stress function can be derived. The effects of the Lorentz body force and Joule heating on the elastic deformation can thus be easily examined. As an illustrative example, stresses induced in an infinitely long cylindrical conductor carrying a uniformly distributed axial current is analysed.     

Transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical workpiece

This paper presents the numerical solutions of the transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical hollow workpiece (steel) with conjugate heat transfer. Outer surface of the workpiece is heated partly-circumferentially heat flux as its remainder outer surface is circumferentially cooled with fluid (water). Three phenomena have been considered as; (1) conduction inside the cylinder, (2) convection from the cylinder surface to the surrounding fluid, and (3) thermal stress produced by high temperature gradient inside the cylinder. The governing flow and energy equations have been solved numerically by using a control volume approach. The PHOENICS 3.2 and HEATING7 computer codes have been used for the numerical evaluation. The transient calculations have been performed individually for four fluid inlet velocities, u_i = 0.005, 0.01, 0.015 and 0.020 m/s, until the system attains steady-state. The results of this study clearly demonstrate that the temperature contours in the low inlet velocity cases are more near to a symmetric case with respect to the y = 0 plane than that in the high inlet velocity cases, and the increment of the inlet velocity exponentially reduces the temperatures and thermally induced stresses in the workpiece. The effective thermal stress differences occurring in the workpiece can be significantly reduced by the high fluid inlet velocity.