An analytical model for the transfer has been development and applied for calculating the shape of the solid thickness profile for continuous casting of a thin plate as an example. The stationary solidification front relative to the crystallizer was received from the superposition of the motions of the liquid metal flow in the axial direction and the solidifying metal in the perpendicular direction. The shape of the solidified crust was analyzed for different casting forms. The results are compared and graphically shown for different selected forms.
Z. Lipnicki, K. Pantoł and B. Weigand
An analytical heat transfer model has been development and applied for calculating the shape of the solid thickness profile for continuous casting of thin metal rods. The stationary solidification front relative to the crystallizer was received from superposition of the motions of the liquid metal flow in the axial direction and the solidifying metal in the radial direction. The shape of the solidified crust depends on several parameters. The influence of the contact layer between the frozen crust and the internal surface of a crystallizer on the solidification process is also studied. The results are presented as an analytical model and are graphically shown for different selected parameters.
W. Wołczyński, Z. Lipnicki, A.W. Bydałek and A.A. Ivanova
Some metallographic studies performed on the basis of the massive forging steel static ingot, on its cross-section, allowed to reveal the following morphological zones: a/ columnar grains (treated as the austenite single crystals), b/ columnar into equiaxed grains transformation, c/ equiaxed grains at the ingot axis. These zones are reproduced theoretically by the numerical simulation. The simulation was based on the calculation of both temperature field in the solidifying large steel ingot and thermal gradient field obtained for the same boundary conditions. The detailed analysis of the velocity of the liquidus isotherm movement shows that the zone of columnar grains begins to disappear at the first point of inflection and the equiaxed grains are formed exclusively at the second point of inflection of the analyzed curve. In the case of the continuously cast brass ingots three different morphologies are revealed: a/ columnar structure, b/ columnar and equiaxed structure with the CET, and c/ columnar structure with the single crystal formation at the ingot axis. Some forecasts of the temperature field are proposed for these three revealed morphologies. An analysis / forecast of the behavior of the operating point in the mold is delivered for the continuously cast ingot. A characteristic delay between some points of breakage of the temperature profile recorded at the operating point and analogous phenomena in the solidifying alloy is postulated.
P. Kwapisiński, Z. Lipnicki, A. A. Ivanova and W. Wołczyński
The Structural Peclet Number has been estimated experimentally by analyzing the morphology of the continuously cast brass ingots. It allowed to adapt a proper development of the Ivantsov’s series in order to formulate the Growth Law for the columnar structure formation in the brass ingots solidified in stationary condition. Simultaneously, the Thermal Peclet Number together with the Biot, Stefan, and Fourier Numbers is used in the model describing the heat transfer connected with the so-called contact layer (air gap between an ingot and crystallizer). It lead to define the shape and position of the s/l interface in the brass ingot subjected to the vertical continuous displacement within the crystallizer (in gravity). Particularly, a comparison of the shape of the simulated s/l interface at the axis of the continuously cast brass ingot with the real shape revealed at the ingot axis is delivered. Structural zones in the continuously cast brass ingot are revealed: FC - fine columnar grains, C - columnar grains, E - equiaxed grains, SC - single crystal situated axially.
Zygmunt Lipnicki, Hanna Lechów and Katarzyna Pantoł
In this paper the problem of cooling a component, in the interior of which heat is generated due to its work, was solved analytically. the problem of cooling of a processor with the use of a heat pump was solved based on a earlier theoretical analysis of authors of external surface cooling of the cooled component by using the phenomenon of liquid evaporation. Cases of stationary and non-stationary cooling were solved as well. The authors of the work created a simplified non-stationary analytical model describing the phenomenon, thanks to which heat distribution within the component, contact temperature between the component and liquid layer, and the evaporating substance layer thickness in relation to time, were determined. Numerical calculations were performed and appropriate charts were drawn. The resulting earlier analytical solutions allowed conclusions to be drawn, which might be of help to electronics engineers when designing similar cooling systems. Model calculations for a cooling system using a compressor heat pump as an effective method of cooling were performed.
Zygmunt Lipnicki, Marta Gortych, Anna Staszczuk and Tadeusz Kuczyński
The goal of the paper was to simplify the designing process for mass and energy flow through solar collector - chimney system. Theoretical analysis allowed to get involved system of three nonlinear analytical equations in dimensionless forms that have been saved. Dimensionless numbers for the problem are well known in the literature on fluid mechanics and thermodynamics: Reynolds, Grashof, Galileo, Biot and Prandtl. In the analyzed equations are also dimensionless geometric parameters expressing the ratios of basic geometrical dimensions of the collector system-chimney: the radius disc collector to the thickness gap, the height and radius of the chimney. In the system of equations, the Reynolds number is treated as the determined number, which is a novelty of the method used.