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Inverse Solution to the Vertical Plate Cooling by Radiation and Convection in Air

Hadała Beata, Malinowski Zbigniew, Gołdasz Andrzej, Cebo-Rudnicka Agnieszka

Archives of Metallurgy and Materials

2022

Vol. 67, iss. 3

1167--1178

The inverse solution to the heat flux identification during the vertical plate cooling in air has been presented. The developed solution allowed to separate the energy absorbed by the chamber due to radiation from the convection heat losses to air. The uncertainty tests were carried out and the accuracy of the solution has been estimated at a level of 1%-5% depending on the boundary condition model. The inverse solution was obtained for the temperature measurements in the vertical plate. The stainless-steel plate was heated to 950°C and then cooled in the chamber in air only to about 30°C. The identified heat transfer coefficient was compared with the Churchill and Chu model. The solution has allowed to separate the radiation heat losses and to determine the Nusselt number values that stay in good agreement with the Churchill and Chu model for a nearly steady-state air flow for the plate temperature below 100°C.

Analytical solution of forced-convective boundary-layer flow over a flat plate

Mirgolbabaei H., Barari A., Ibsen L. B., Esfahani M. G.

Archives of Civil and Mechanical Engineering

2010

Vol. 10, no 2

43-51

In this letter, the problem of forced convection heat transfer over a horizontal flat plate is investigated by employing the Adomian Decomposition Method (ADM). The series solution of the nonlinear differential equations governing on the problem is developed. Comparison between results obtained and those of numerical solution shows excellent agreement, illustrating the effectiveness of the method. The solution obtained by ADM gives an explicit expression of temperature distribution and velocity distribution over a flat plate.

W artykule przedstawiono zastosowanie metody dekompozycji Adomiana do wymuszonego, konwekcyjnie przepływu ciepła w poziomej, płaskiej płycie. Rozwiązania nieliniowych równań różniczkowych opisujących zagadnienie poszukiwana w postaci szeregów Adomiana. Z porównania otrzymanych wyników z wynikami innych metod numerycznych wynika doskonała ich zgodność, która potwierdza skuteczność zastosowanej metody. Otrzymane rozwiązanie pozwoliło jednoznacznie wyznaczyć rozkład i prędkości mian temperatury w analizowanej płycie.

Finite element solutions for two-phase magneto-heat transfer in a particle-suspension through a non-Darcian porous channel with heat source and buoyancy effects

Bhargava R., Rawat S., Takhar H. S., Beg T. A., Anwar Beg o.

International Journal of Applied Mechanics and Engineering

2008

Vol. 13, no 2

325-357

We consider the steady, laminar natural convection heat transfer of a particulate suspension in an electrically-conducting fluid through a two-dimensional channel containing a non-Darcian porous material in the presence of a transverse magnetic field. The transport equations for both fluid and particle phases are formulated using a two-phase continuum model and a heat source term is included which simulates either absorption or generation. A set of transformations are implemented to reduce the partial differential equations for momentum and energy conservation (for both phases) from a two-dimensional coordinate system to a one-dimensional system. Finite element solutions are obtained for the transformed model. A comprehensive parametric study of the effects of the heat source parameter (E), Prandtl number (Pr), Grashof number (Gr), momentum inverse Stokes number (Skm), Darcy number (Da), Forchheimer number (Fs), particle loading parameter (PL), buoyancy parameter (B), Hartmann number (Ha), temperature inverse Stokes number (SkT), viscosity ratio [...], specific heat ratio [...], dimensionless particle-phase wall slip parameter [...] on the dimensionless fluid phase velocity (U), dimensionless particle phase velocity ( ), dimensionless fluid phase temperature [...] and the dimensionless temperature of particle phase [...] are presented graphically. In addition, we also describe numerical solutions for several special cases of the model, for example, the inviscid hydromagnetic two phase non-Darcian free convection, heat transfer [...], forced convection case (GrŽ0) etc. Fluid phase velocities are found to be strongly reduced by the magnetic field, Darcian drag and also Forchheimer drag; a lesser reduction is observed for the particle phase velocity field. The Prandtl number is shown to depress both the fluid temperature and particle phase temperature in the left hand side of the channel but to boost both temperatures at the right hand side of the channel [...]. The inverse momentum Stokes number is seen to reduce fluid phase velocities and increase particle phase velocities. The influence of other thermophysical parameters is discussed in detail and computations compared with previous studies. The model finds applications in MHD plasma accelerators, astrophysical flows, geophysics, geothermics and industrial materials processing.