Steady-state heat transfer through a wall with longitudinal rectangular fins and variable thermal conductivity

A method is examined of solving steady-state problems of heat transfer through a surface with longitudinal rectangular fins in the case when the thermal conductivity depends on temperature.Notation T temperature - T₀ temperature of coolant - T₁ temperature at base of fin - T_N some characteristic temperature - (T) thermal conductivity of fin material - heat transfer coefficient; F-cross-sectional area of fin - fin perimeter - h fin height - L fin length - fin thickness - Q heat flux - O_i change of temperature in i-th section - T_i mean temperature at i-th section     

Study of flow on the surface of fins on cross-finned tubes

The visualization method was used to study the washing of a flow of air over the surface of fins on tubes with external fins in an annular arrangement.Notation S₁ transverse spacing of tubes in bundle - S₂ lengthwise spacing of tubes in bundle - d diameter of tube bearing the fins - h fin height - t fin spacing - fin thickness - finning coefficient - Re Reynolds number calculated from the velocity of the incoming flow U and the diameter d - x_os size of the separation zone A on the OX axis - heat-transfer coefficient Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 47, No. 1, pp. 28–34, July, 1984.     

Mixed convection flow of micropolar fluid over an isothermal plate with variable spin gradient viscosity

Summary A steady two-dimensional mixed convection flow of viscous incompressible micropolar fluid past an isothermal horizotal heated plate with uniform free stream and variable spin-gradient viscosity is considered. With appropriate transformations the boundary layer equations are transformed into nonsimilar equations appropriate for three distinct regimes, namely, the forced convection regime, the free convection regime and the mixed convection regime. Solutions of the governing equations for these regimes are obtained by an implicit finite difference scheme developed for the present problem. Results are obtained for the pertinent parameters, such as the buoyancy parameter, in the range of 0 to 10 and the vortex viscosity parameters, =0.0, 1.0, 3.0, 5.0 and 10.0 for fluid with Prandtl number Pr=0.7 and are presented in terms of local shear-stress and the local rate of heat transfer. Effects of these parameters are also shown graphically on the velocity, temperature and the couple stress distributions. From the present analysis, it is observed that both the momentum boundary layer and the thermal boundary layer increase due to an increase in the vortex viscosity of the fluid.List of symbols f, F, dimensionless stream function for forced convection free convection and mixed convection, respectively - g acceleration due to gravity - Gr_x local Grashof number - j micro-inertia density - m ₂₃ distribution of couple stress - N microrotation component normal to (x, y)-plane - p pressure of the fluid - q dimensionless rate of heat transfer - Re_x local Reynolds number - T temperature of the fluid in the boundary layer - T temperature of the ambient fluid - T temperature at the surface - u, v thex andy-components of the velocity field - U free stream velocity - x, y axis in direction along and normal to the plate Greek thermal diffusivity - coefficient of volume expansion - vortex viscosity parameter - stream function - , , nondimensional similarity variables - buoyancy parameter (=Gr _x Re _x ^/5/2 ) - vortex viscosity - density of the fluid - v kinematic coefficient of viscosity - spin-gradient viscosity - stream function - dimensionless skin-friction - fluid viscosity     

Numerical modeling of thermal regimes during the assembly of a multicomponent system

Results are presented from a numerical modeling of the solution of a problem involving optimization of the thermal regime in the assembly of integrated circuits. The modeling was performed on array processors of hybrid computers.Notation T_g gas temperature - heat-transfer coefficient - c_V specific heat capacity - thermal conductivity - time - q heat flux - L internal heat of phase transformations or other internal transformations - c_Ve effective volumetric heat capacity - density - q_V power of internal heat sources Indices g gas - c convection, contact - sp spectral - r radiative - L phase transformation - V volumetric - 0 initial - e environment - liquidus - s solidus - s surface - total Abbreviations R-R resistance circuit - Liebmann method - T Gel'perin method Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 56, No. 5, pp. 793–798, May, 1989.     

Excess energy in quenchedβ-Cu-Zn-Al alloys: relation to the martensitic transformation

The disorder-induced excess energy,L , of a-Cu_1– x)(ZnAl) _x (0.30 x 0.35) alloy, which shows a martensitic transformation at low temperature, after quenching from different initial temperatures,T _i, is calculated. Ordering-energi-es for the different nearest and next-nearest neighbour atom pairs, obtained by fitting mean field expressions of order-disorder critical temperatures to experimental data, are used. The excess energy is related to the changes of the latent heat of the martensitic transformation,L, observed just after quenching from T_i. It was found that the shift in latent heat correlates linearly with the calculated excess energy of the-phase. Calorimetric measurements justify the results.     

Use of adjoint functions in investigations of heat conduction and transfer processes

An examination is made of the use of adjoint functions in heat conduction and convection theory. Formulas of perturbation theory are obtained for steady and unsteady cases, an interpretation of the physical meaning of adjoint temperature is given, and some applications of the theory are discussed.Notation (r,) thermal conductivity - t(r,) temperature - t *(r,) adjoint temperature - q_V(r,) density of heat release sources - p(r,) a parameter of adjoint equation - r generalized coordinate - time - (r_s, ) heat transfer coefficient - I linear functional of temperature - (r,;r₀,₀) and *(r,; r₀,₀) Green's function for t(r, ) and t *(r, ) - C(r,) volume specific heat - W(r, ) vector distribution of flow velocities - V, S volume and surface areas of body - R radius of HRE - r, radial and angular coordinates - F_in, F_out inlet and outlet flow areas of channel     

Optical thermophysical characteristics of the condensed phase of combustion products and heatproof materials

An unconventional unit for experimentally studying the optical thermophysical properties of materials over a wide temperature range is described. Results are presented of studying the temperature function and dispersion of the absorption index for the condensed phase of the combustion products of a metalbearing fuel and of the emittance of fiber fireproof materials.Notation K spectral absorption coefficient - D spectral transmission coefficient - spectral absorption index - wavelength - d sample thickness - d_s surface layer thickness - I spectral intensity of radiation - , spectral and total emittances Kirov Polytechnical Institute. Kazan Chemical Engineering Institute, Russia. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 3, pp. 330–336. March, 1993     

Dynamic characteristics of thermoanemometers with glass-covered transducers

This study deals with the frequency characteristics of a glass-covered thermistor serving as transducer in a thermoanemometer and of a constant-resistance thermoanemometer with such probes.Notation A average-in-time coefficient of heat transfer at the glass-fluid boundary, W/m²· °C - A_tot coefficient of steady-state heat transfer at a bare probe (a fictitious quantity introduced for gauging the heat transfer between a glass-covered probe with the moving fluid), W/m²· °C - a thermal diffusivity of glass which insulated the heat sensitive element from the fluid, m²/sec - C_T total thermal capacity of transducer, W· sec/m²· °C - H₁ ratio of moduli in the expressions for current and resistance fluctuations in the transducer, dB - H₂ ratio of moduli in the expressions for heat transfer and resistance fluctuations in the transducer, dB - I quiescent current through thermistor, A - i transform of fluctuation current through thermistor, A - K_v voltage gain of feedback amplifier - k frequency parameter, 1/m - l thickness of glass layer, m - N intrinsic time constant of thermistor, sec - N time constant of constant-resistance thermoanemometer, sec - M intrinsic time constant of thermistor, sec - M time constant of constant-resistance thermoanemometer, sec - p complex variable in the Laplace transformation - Q average-in-time thermal flux from the transducer, W/m² - q transform of thermal flux fluctuations in the transducer, W/m² - R average-in-time operating resistance of thermistor, - R₁ constant resistance in series with the thermistor in the thermoanemometer circuit, - r transform of resistance fluctuations in the thermistor, - S effective surface area of heat transfer from the transducer, m² - T_D steady-state temperature of hot film, °K - T steady-state temperature of insulating glass layer, °K - T_L temperature of fluid, °K - u velocity of oncoming fluid, m/sec - W_T relation between resistance fluctuations and current in the thermistor, in operator form - y space coordinate in the mathematical model of the transducer, m - fluctuation component of heat transfer coefficient, W/m²· °C - temperature coefficient of resistance, 1/°C - thermal conductivity of insulating material, W/m· °C - _d transform of temperature fluctuations in the hot film, °K - transform of temperature fluctuations in the insulating glass layer, °K - coefficient in the transfer function of a thermistor at high frequencies Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 22, No. 6, pp. 1042–1048, June, 1972.     

Nonstationary process of heat transfer in a tube with longitudinal fins

An analytical solution to the problem of nonstationary thermal interaction of a flow of a heat-transfer agent and a thin-walled tube with longitudinal fins is constructed for variable parameters of heat transfer.Notation u, temperatures of the fins - ,w temperatures of the tube walls - temperature of the flow of the heat-transfer agent - _i ,i= coefficients of heat transfer from the ambient medium to the fins and the tube walls, respectively - _i ,i= temperature distributions for the ambient medium - coefficients of heat transfer from the flow of the heat-transfer agent to the tube walls - q _i density of the heat flux to the corresponding portions of the tube - heat capacity, thermal conductivity, density, and thickness of the fin and tube material - c _p , ,G, F heat capacity, density, and flow rate of the heat-transfer agent, cross-sectional area of the tube - dimensions of the tube Bauman Moscow State Technical University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66, No. 6, pp. 673–680, June, 1994.     

Computational thermography: Numerical modeling of the thermal regimes of building structures

We consider numerical methods of simulating thermal regimes of building structures that make it possible to create optimum structures as regards power consumption by using more accurate calculations than those available in existing construction specifications and regulations. Possible means of reducing energy expenditures for formation of an optimum microclimate in living quarters are described.Notation R thermal resistance to heat transfer - _i thermal conductivity - c _i heat capacity - _i moisture content - i number of a layer - S thermal inertia of the material - density of the substance - frequency of harmonic vibrations - t time - Fo Fourier number - thermal diffusivity - t time step - x spatial step - Bi Biot number - h _c coefficient of convective heat transfer - k thermal conductivity - T ambient temperature - T _w wall temperature - Nu Nusselt number - Ra _l Rayleigh number - Gr _l Grashof number - Pr Prandtl number - g free fall acceleration - coefficient of thermal volumetric expansion of air - l characteristic length - coefficient of kinematic viscosity of air - determining temperature - thermal conductivity of the material - q heat flux - s area of the heat transfer surface - perimeter of the heat transfer surface - T free stream velocity - air viscosity Academic Scientific Complex A. V. Luikov Heat and Mass Transfer Institute of the Academy of Sciences of Belarus, Minsk. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 66 No. 6, pp. 733–738, June, 1994.     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

Structure of thermal stresses arising in a viscoelastic half-space with thermal “memory”

We develop the structure of thermal stresses arising in a viscoelastic half-space owing to the thermal impact of a heat flux at the boundary.Notation z coordinate normal to the surface of the half-space - t time - =T–T_o temperature of the half-space - (t) relaxation function of the heat flux - (t) relaxation function of the internal energy - c_v specific heat at constant volume - q_o heat flux acting on the boundary of the half-space - _xx, _yy, _zz normal stresses - density of the material - _t coefficient of linear thermal expansion - u=[(0)/c_v]^1/2 heat-propagation velocity - _t coefficient of thermal conductivity - _r relaxation time of the heat flux - relaxation time of the stresses Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 894–897, November, 1979.     

Joule-Thompson effect in a disperse medium

An expression for the Joule-Thompson coefficient of a polydisperse medium subject to throttling is derived in the relaxation approximation of thermodynamics of irreversible processes, with both temperature and velocity relaxation in the phases taken into account.Notation A_qk, A_fk thermal and momentum interphase exchange affinities - _qk, _fk relaxation parameters - T, w temperature and velocity of a phase relaxation in the mixture - density of the mixture - T_o, T_k temperature of the carrier phase and of the k-th group of solid particles - p pressure of the carrier phase - h enthalpy of the mixture - W _o ² /2 specific kinetic energy of the carrier phase - _o, _k volume concentration of the carrier phase and of the k-th group of solid particles - _o, _k true density of the carrier phase and of the k-th group of solid particles - c_v and c_p constant-volume and constant-pressure specific heats of the mixture - c_k specific heat of the k-th group of solid particles - c_v, c_p constant-volume and constant-pressure specific heats, respectively, of the mixture referred to volume - _qk, _fk temperature and velocity relaxation times, respectively, of the k-th group of solid particles - t times - frequency in the Fourier series expansion - differential Joule-Thompson coefficient (adiabatic throttle effect) - N number of groups of particles in the mixture Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 5, pp. 825–829, November, 1979.     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

Precipitation phenomena in the Mg-31 at% Li-1 at% Al alloy

Precipitation phenomena produced in the -phase (b c c) of the Mg-31 at% Li-1 at%Al alloy subjected to different heat treatments have been studied by sensitive single-crystal X-ray diffraction techniques. The variation of the hardness values of specimens quenched and then aged was also examined. It was confirmed that AlLi is a stable phase at room temperature for the examined Al content; AlLi precipitation is only produced for very slow cooling rates from the -field. Phase reactions for specimens quenched and then aged can be summarized as follows: ++ after ageing at room temperature; + ++ AlLi after ageing at 473 K. A considerable increase of the hardness, which attains its maximum value after about 30 h ageing at room temperature, was observed. Neither the -phase nor the AlLi-phase precipitation can account for the observed hardening process. The presence of the -metastable phase when the hardness reaches its maximum value is verified.     

Systematic derivation of contour integration formulae for laplace and elastostatic gradient BIE's

A complete set of contour integrands is derived for the primary BIE's of elastostatics and potential flow. Because of surface-independent properties of vector potentials, these apply to nonplanar surfaces and can be differentiated at the fixed point, producing contour integrands for both the so-called hypersingular and Cauchy singular parts of the gradient BIE. The results are applicable to far field, near field and on surface cases. Numerical examples demonstrate exact agreement with surface quadrature, and contour plots are given showing variation of the hypersingular integrands in on surface cases.     

Effect of the elastic factor on the hydrodynamic stability of a structurally viscous medium

The effect of relaxation phenomena on the hydrodynamic stability of the plane gradient flow of a structurally viscous medium is investigated using linear theory.Notation _ij stress tensor deviator - U_i components of the velocity vector - x_i coordinates - t time - P pressure - =₀L/^*V plasticity parameter - _o limiting shear stress - andc dimensionless wave number and the perturbation frequency - Re=VL/* Reynolds number - density - F_ij deformation rate tensor Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 35, No. 5, pp. 868–871, November, 1978.     

Rheological behaviour of fresh cement paste as measured by squeeze flow

A method is proposed for measuring the rheology of cement paste under conditions that suppress shear flow, i.e. squeezing. This method is based on squeezing samples in a servohydraulic compression-tension testing machine, and is different from the commonly used shear flow experiments. Possible artefacts such as the buoyancy of the piston that penetrates the paste, sedimentation of cement paste, geometry of the container, and friction at the interface between the top plate (or piston) and sample are investigated. Plots of stress versus apparent strain were obtained and compared with results from standard shear flow experiments. Because cement paste has both viscoelastic and viscoplastic characteristics, results are analysed in terms of both solid-like deformation and liquid-like flow behaviour. A first-approximation theoretical analysis is developed, based on the assumption that cement paste behaves as a non-Newtonian liquid, and results are compared with the experimental results.Nomenclature Shear strain rate in power law fluid model - _zr Shear strain converted from _zr - Shear strain rate - Normal strain rate - _zr Component of shear strain - _zr Component of shear strain rate - _zz Component of normal strain - Viscosity - Density of cement paste (3.2 g cm^–3) - _Cav Calculated average normal stress of cement paste - _Nav Calculated average normal stress of power law fluid - _m Measured normal stress of cement paste - _zz Normal stress in z direction - _eq Equivalent shear stress converted from normal stress - _rz Shear stress in momentum equation - a _i Coefficients in polynomial function of geometric factor for cement paste - B Buoyancy force - CGF Geometric factor for cement paste - d _o Amplitude of squeeze motion - F _N Load in normal direction - g Gravitational constant - h Sample height - h _o Initial sample height - Velocity of platen - k Order of polynomial function of geometric factor for cement paste - m Consistency in power-law fluid model - n Power index in power-law fluid model - P Pressure - P _a Atmospheric pressure - PGF Geometric factor for power-law fluid model - r Radial direction in cylindrical coordinates - R Radius of sample - s 1/n - V Volume of the top platen submerged into cement paste - v _r Velocity inr direction - v _z Velocity in z direction - z Vertical direction in cylindrical coordinates     

Paramagnetic resonance in a “dirty” spin-glass

For a spin-glass with nonmagnetic defects (n _m ^1/3l 1, where n _m is the magnetic impurity concentration and l is the mean free path) an absorption function () is derived. Three ranges of temperature and external magnetic field are considered. In the vicinity of the transition the value of () d is estimated as a function of temperature and field.     

Microstructural evolution in rapidly solidified Al-Cu-Si ternary alloys

Several Al-Cu-Si alloys were melt spun to produce stable, fine scale microstructures suitable for superplastic deformation and consolidation. Scanning electron microscopy of the ribbon cross-sections reveal two distinct alternating microstructural morphologies, suggesting transitions in solidification behavior. One structure consists of intimately interlocked -Al and (Al₂Cu) phases with dispersed spheroids of (Si). The other structure consists of equiaxed or cellular-dendritic -Al with interdendritic and (Si). The latter was found in the middle portion of the ribbon cross-section when cast at a low speed, and throughout the ribbon cross-section when cast at high speed. The dendritic structure appears to result from independent nucleation events in the undercooled liquid ahead of the solid-liquid interface. The solidification mechanism for the interlocked structure appears to involve multiple nucleation of the phase followed by its cooperative growth with the -Al phase. This cooperative growth is unlike that which forms a lamellar structure, as it results in a branched, randomly oriented network. We postulate that the (Si) phase is the first phase to form from the undercooled liquid, and it is uniformly dispersed throughout the undercooled melt. The (Si) spheroids provide nucleation sites for the phase because of its observed association with the phase. The -Al grain size varies from 1 m near the wheel side surface of the ribbon to 8 m with sub-grains near the free surface. The size of the and (Si) phases is on the order of a m and less. The microstructural size scale appears to be small enough for this material to exhibit superplastic behavior when deformed.