Rectangular enclosures

Other chaia-type ea-masse coaveyors use flight coafiguratioas made up from plates or bars welded to standard forged chain and mounted ia a rectangular enclosure. 

Figure 7. Preparation of synthetic lignin 16, ethylated copolymer of coniferyl alcohol 7 and arylglycerol-/ -syringaresinol ether 6. In 16, the rectangular enclosure represents an assumed structure of the moiety derived from 7.

NATURAL CONVECTIVE HEAT TRANSFER ACROSS A RECTANGULAR ENCLOSURE... 

Attention will here be restricted here to flow in a rectangular enclosure as shown in Fig. 8.24. In general, the enclosure is inclined to the vertical as illustrated in Fig. 8.24. For simplicity, in order to illustrate how enclosure flows can be analyzed, it will be assumed that one wall of the enclosure (AB in Fig. 8.24) is at a uniform high temperature, Th, and that the opposite wall (CD in Fig. 8.24) is at a uniform low temperature, Tc Two boundary conditions on temperature are usually considered on the two remaining end walls (BC and DA in Fig. 8.24). If these walls are made from a material that has a low thermal conductivity, it is usual to assume that these walls are adiabatic, i.e., that there is no net heat transfer to or from the wall at any point on the wall. Alternatively, if these walls are made from a material that has a relatively high thermal conductivity, it is usual to assume that these walls are perfectly conducting and that the temperature on these end walls varies linearly with distance from the hot wall from T to Tc-... 

The above discussion was concerned with enclosures in which the heated and cooled walls were at aft angle to the horizontal. In the present section, the concern is with rectangular enclosures in which the hot and cold walls are horizontal and in which the hot wall is at the bottom, see [68] to [83]. The flow situation being considered is therefore as shown in Fig. 8.32. 

Some of the more commonly used methods of obtaining solutions to problems involving natural convective flow have been discussed in this chapter. Attention has been given to laminar natural convective flows over the outside of bodies, to laminar natural convection through vertical open-ended channels, to laminar natural convection in a rectangular enclosure, and to turbulent natural convective boundary layer flow. Solutions to the boundary layer forms of the governing equations and to the full governing equations have been discussed. 

Newell, M.E. and Schmidt, F.W., Heat Transfer by Laminar Natural Convection Within Rectangular Enclosures , J. Heat Transfer, Vol. 92, pp. 159-168, 1970. 

Rubel, A. and Landis, R., Numerical Study of Natural Convection in a Vertical Rectangular Enclosure , Phys. Fluids, Suppl. II, Vol. 12-11, pp. 208-213, 1969. 

Wirtz, R. A. and Tseng, W.F., Natural Convection Across Tilted. Rectangular Enclosures of Small Aspect Ratio , Natural Convection in Enclosures, ASME publication HTD-Vol. 8, pp. 47-54, 1980. 

Oosthuizen. P.H. and Paul, J.T.. "Natural Convection in a Rectangular Enclosure with a Partially Heated Wall and Partly Filled with a Porous Medium", Proc. Eighth Int. Conf. on Numerical Methods in Thermal Problems. Vol. VIII. Part I, Pineridge Press, Swansea, U.K., 1993, pp. 467-478. 

Mass How Rate ttirougn ttie Space beLV, een Plates 519 9-5 Natural Convection Inside Enclosures 521 effective Thermal Conductivity 522 Horizontal Rectangular Enclosures 523 Inclined Rectangular Enclosures 523 Vertical Rectangular Enclosures 524 Concentric Cylinders 524 Concentric Spheres 525 Combined Natural Convection and Radiation 525... 

Enclosures arc frequently encountered in practice, and heal transfer through them is of practical interest. Heat transfer in enclosed spaces is complicated by the fact that the fluid in the enclosure, in general, does not remain stationary. In a vertical enclosure, the fluid adjacent to the hotter surface rises and the fluid adjacent to the cooler one falls, setting off a rolationary motion within the enclosure that enhances heat transfer through the enclo.surc. Typical flow patterns in vertical and horizontal rectangular enclosures are shown in Figs. 9-21 and 9-22. 

FIGURE 9-21 Convective currents in a vertical rectangular enclosure. 

An inclined rectangular enclosure with isothermal surfaces. 

Analysis We have a rectangular enclosure filled with air. The characteristic length in this case is the distance between the two glasses, = t = 0.02 m. Then the Rayleigh number becomes... 

In a horizontal rectangular enclosure with the hotter plate at tlie top. heat transfer is by pure conduction and Nu = 1, When the hotter plate is at the bottom, the Niisselt niltnber is... 

Show that the thermal resistance of a rectangular enclosure can be expressed as iJ = LJ Ak Nu), where k is the thermal conductivity of the fluid in the euclosure. 

Let us now analyze the more complex shielding application of Figure 7.12(a), which illustrates a rectangular enclosure partitioned by two equal horizontal PEC walls. In the front plane, there is a centered (20 x 5) cm horizontal aperture. The dimensions are a = b = 60 cm, d = 120 cm, / = 70 cm, w = 2 cm, and the excitation is launched by a vertical coaxially fed monopole. Due to the nonstandard operators of (3.43), the domain is discretized into the coarse grid of30 x 60 x 30 cells with Ax = Ay = Az = 2 cm and At = 30.567 ps. In the area of the aperture, spatial derivatives are computed by the fictitious-point technique of Section 2.4.5, whereas the DRP schemes of Section 2.5.3 are also utilized. Figure 7.12(b) displays the shielding efficiency defined as the ratio of the electric field amplitude evaluated in front of... 

Note that the extension of the DO approximation to three-dimensional rectangular enclosures was attempted by a number of researchers (see, e.g., Refs. 65 and 85). Even though the formulation of the three-dimensional model will not be given here, its governing equations can be derived with little difficulty. As shown in Refs. 65 and 85, the original SN quadratures yield accurate results in three-dimensional solutions they are listed in Table 7.4 for S2,S4, S6, and S approximations. 

M. H. N. Naraghi and M. Kassemi, Radiative Transfer in Rectangular Enclosures A Discretized Exchange Factor Solution, ASME Proceedings, vol. 1, pp. 259-267,1988. 

M. P. Mengtt and R. Viskanta, Radiative Transfer in Three-Dimensional Rectangular Enclosures Containing Inhomogeneous, Anisotropically Scattering Media, Journal of Quantitative Spectroscopy and Radiative Transfer, 33, pp. 533-549,1985. 

R. K. Iyer and M. P. Mengii , Quadruple Spherical Harmonics Approximations for Radiative Transfer in Two-Dimensional Rectangular Enclosures, AIAA Journal of Thermophysics and Heat Transfer, 3, p. 266,1989. 

W. A. Fiveland, Discrete-Ordinate Solutions of the Radiative Transfer Equation for Rectangular Enclosures, ASME Journal of Heat Transfer, 106, p. 699,1984. 

A. S. Jamaluddin and P. J. Smith, Predicting Radiative Transfer in Rectangular Enclosures Using the Discrete Ordinates Method, Combustion Science and Technology, 62, p. 173,1988. 

T.-K. Kim and H. Lee, Effect of Anisotropic Scattering on Radiative Heat Transfer in Two-Dimensional Rectangular Enclosures, International Journal of Heat and Mass Transfer, 31(8), pp. 1711-1721,1988. 

M. M. Razzaque, D. E. Klein, and J. R. Howell, Finite Element Solution of Radiative Heat Transfer in a Two-Dimensional Rectangular Enclosure with Gray Participating Media, ASME Journal of Heat Transfer, vol. 105, pp. 933-934,1983. 

C. Kasper, The theory of the potential and the technical practice of electrodeposition V. The two-dimensional rectangular enclosures, Trans. Electrochem. Soc. 82 (1942) 153-185. 

Hideo, I. Yanlai, Z. Akihiko, H. Naoto, H. Numerical simulation of natural convection of latent heat phase-change-material microcapsulate slurry packed in a horizontal rectangular enclosure heated from below and cooled from above. Heat Mass Transfer 43 (2007) 459-470. 

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