Flow and heat transfer in a micropolar fluid past a flat plate with suction and heat sources

The laminar boundary layer flow of a micropolar fluid past a flat plate subject to uniform suction has been examined. The heat transfer study has been made in the presence of both constant as well as temperature dependent heat sources. The governing equations of momentum, first stress momentum and energy have been solved using numerical integration and Gauss-Seidel iterative procedure. For a particular value of suction parameter λ, as compared to the Newtonian fluid, the velocity decreases on increasing the value of micropolar parameter R. The skin friction and the Nusselt number have been calculated and presented in tables.     

Calculation of the temperature field in a plate with internal heat sources

We present a method for calculating the stationary temperature field in a long thin plate with internal heat sources, the plate surface being washed over by a flow of gas. The solution is obtained in the form of a Fourier series with strong convergence.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 3, pp. 411–414, March, 1971.     

Temperature field in a plate containing a system of heat sources

The temperature field is determined in a circular plate with a system of thin extrinsic heat sources.Notation T temperature in the plate with the inclusions - r polar radius - polar angle - time - (r,) coefficient of thermal conductivity - (r,) heat transfer coefficient - C(r,) volume heat capacity - W(r,, ) specific intensity of the heat sources - half thickness of the plate - (x) Dirac's delta function - ¯T finite Fourier cosine transform of the temperature - p parameter for this transformation - T Laplace transform of the temperature - s its parameter - Iv(x) Bessel function with imaginary argument of order - K _v (x) the MacDonald function of order - and dimensionless temperature - Po Pomerantz number - Bi Biot number - Fo Fourier's number - dimensionless polar radius - b₁ ^* dimensionless radius of the circle on which the inclusions are placed - R^* dimensionless radius of the plate Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 3, pp. 495–502, March, 1981.     

Heating of a cylindrical body with internal heat sources and a variable heat transfer coefficient

An approximate method is described for solution of the problem of the temperature distribution In an infinite cylinder when the coefficient of external heat transfer is a function of time. A constant power heat source acts in the body during the entire period of heating.     

Investigation of heat transfer in the entrance region of a flat plate parallel to the flow with a leading edge in the form of a one-sided wedge

Relations are given for calculating the local heat transfer in the dynamic initial section of a longitudinally washed generator of a one-sided wedge for the case of constant wall temperature and turbulent boundary layer.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 2, pp. 202–207, August, 1976.     

Heat transfer in a bed of lump materials in a counterflow with heat sources

The process of heating or cooling of spherical lumps moving in a gas counterflow is analyzed for cases when the strength of the heat sources (sinks) is a linear function of the material temperature. By making a simple substitution, the formulas obtained can be used to calculate the heating of lump materials in a parallel gas flow.     

A frequency analysis of nonsteady heat transfer in a layer of disperse material with heat sources

In this paper we consider the possibility of solving problems of nonsteady heat transfer in a layer by a frequency method which makes it possible, comparatively simply, to automate the calculations by means of a digital computer, skipping the stage of an analytical determination of the unknown functions in the time domain.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 16, No. 1, pp. 72–76, January, 1969.     

Heat transfer in a layer in the presence of moving heat sources

The problem regarding the distribution of temperatures is solved for the case of a layer in which a combustion front is moving at a constant speed, said front caused by the burnout of a fuel uniformly distributed through the layer.     

Effects of mass transfer and heat sources on the flow past an accelerated infinite vertical plate

An exact solution of the flow of an incompressible viscous fluid past an accelerated vertical infinite plate is carried out on taking into account the presence of foreign mass and temperature dependent heat source. Solutions are derived for the velocity profile, skin-friction. It is observed that the skin-friction increases with an increase in the Schmidt number Sc, heat source parameter S, but decreases with increasing the Grashof number G and the buoyancy force parameter N. The velocity profiles become of oscillatory nature when the heat source parameter S increases.     

Numerical investigation of heat transfer enhancement in a square ventilated cavity with discrete heat sources using nanofluid

A numerical study of a laminar mixed convection problem in a ventilated square cavity partially heated from bellow is carried out. The fluid in the cavity is a water-based nanofluid containing Cu nanoparticles. The effects of monitoring parameters, namely, Richardson number, Reynolds number, and solid volume fraction on the streamline and isotherm contours as well as average Nusselt number along the two heat sources are analyzed. The computation is performed for Richardson number ranging from 0.1 to 10, Reynolds number from 10 to 500, and the solid volume fraction from 0 to 0.1. The results show that by adding nanoparticles to the base fluid and increasing both Reynolds and Richardson numbers the heat transfer rate is enhanced. It is also found, regardless of the Richardson and Reynolds numbers, and the volume fraction of nanoparticles, the highest heat transfer enhancement occurs at the left heat source surface.     

Use of finite-penetration-depth method to calculate the heating of a plane plate under the action of a radiant heat flux

Using the finite-penetration-depth method, a solution is obtained to the problem of plate heating a radiant flux. The results are compared with a numerical solution.Notation t temperature - T absolute temperature - ,a thermal conductivity and diffusivity of plate material - _re reduced emissivity - x coordinate - q specific heat flux - time Deceased.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 39, No. 1, pp. 138–142, July, 1980.     

Free convective heat transfer at a vertical semiinfinite plate

The effect of the boundary layer at the leading edge on heat transfer near a vertical semiinfinite heated plate is determined by means of matched asymptotic expansions. The criterial relation for air is in good agreement with existing experimental data.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 1, pp. 32–39, July, 1977.     

Thermal stress state of a bimetallic plate subjected to pulsed electromagnetic action

We formulate a problem of thermomechanics for an infinite bimetallic plate of constant thickness subjected to nonstationary electromagnetic action and present a relationship for the evaluation of the load-carrying capacity of the plate. A procedure of approximate determination of the parameters of the electromagnetic fields, temperature, and stresses by using the quadratic approximation of the distribution of key functions over the thickness of layers of the plate is proposed. The solution of this problem is obtained for the electromagnetic action in the mode with pulsed modulating signal. We present the results of numerical investigation of the components of the stress tensor and stress intensities in the plane of contact of the constituent layers for a frequency of the carrier signal lying outside the neighborhood of the resonance frequencies and for the first resonance frequency. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 30–40, November–December, 2008.     

One-dimensional model of heat transfer in cryogenic vacuumshield thermal insulation with radiant heat sources

The heat-transfer problem in an insulation consisting of layers which receive heat from external source through radiation is numerically solved in the one-dimensional approximation.Notation T temperature - x coordinate in the direction normal to the stack - stack thickness - thermal conductivity of the vacuum-shield thermal insulation along the x-coordinate - q_v amount of heat released in a unit volume of vacuum-shield thermal insulation as a result of the incidence of radiation on the face of the shield layers - emissivity - B density of effective radiant flux - Stefan-Boltzmann constant - N number of surfaces - S_ins surface of a vacuum-shield thermal insulation stack - d_di-dj angular coefficient between elementary areas i and j of a surface - Q_o thermal flux through the insulation without a hole - Q_T thermal flux through the insulation with a hole Q_rad thermal flux through the insulation with radiative heat transfer to the bottom base of the hole - Q_s thermal flux reaching the insulation with a hole - Q_rad thermal flux through the insulation with radiative heat transfer to the bottom base of the hole - Q_s thermal flux reaching the stack face by radiative heat transfer through the hole (channel) - x thickness of the i-th insulation layer including one or more shields - _eff effective emissivity of the gap face - q_rad amount of heat reaching a unit area of the bottom base of the hole - T₀ and T₀ boundary temperatures - length of the gap between layers of the insulation stack and the length of the vacuum-shield thermal insulation stack - h width of the gap between layers of the insulation stack - longitudinal thermal conductivity of the vacuum-shield thermal insulation Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 42, No. 1, pp. 78–85, January, 1982.