Heat transfer multidimensional

A recent review relating the pyrotechnic reaction mechanism, particle size, stoichiometry, temp and compaction density to burning rate is Ref 66, and a study of the effect of multidimensional heat transfer on the rate of flame propagation is Ref 120, which showed that the material of the delay body has no effect on the performance of most delay compns, a finding which agrees with test data... 

To rationalize the isothermal assumption, Dykhuizen 39() discussed two related physical phenomena. First, heat may be drawn out of the substrate from an area that is much larger than that covered by asplat. Thus, the 1 -D assumption in the Stefan problem becomes invalid, and a solution of multidimensional heat conduction may make the interface between a splat and substrate closer to isothermal. Second, the contact resistance at the interface is deemed to be the largest thermal resistance retarding heat removal from the splat. If this resistance does not vary much with substrate material, splat solidification should be independent of substrate thermal properties. Either of the phenomena would result in a heat-transfer rate that is less dependent on the substrate properties, but not as high as that calculated by Madej ski based on the... 

More sophisticated, computerized heat transfer calculation techniques are available where specific scenarios require detailed analysis (Idling et al., 1977 Paulsson, 1983). These techniques involve the use of multidimensional finite element programs. 

It has been demonstrated that kg can be estimated by analogy with the Graetz-Nusselt problem governing heat transfer to a fiuid in a duct with constant wall temperature (SH= Nut) [30] and that the axial concentration profiles of NO and of N H 3 provided by the 1D model are equivalent and almost superimposed with those of a rigorous multidimensional model of the SCR monolith reactor in the case of square channels and of ER kinetics, which must be introduced to comply with industrial conditions for steady-state applications characterized by substoichiometric NH3 NO feed ratio, that is, a[Pg.401]

Langston, L. S. Heat Transfer from Multidimensional Objects Using One-Dimensional Solutions for Heat Loss, Int. J. Heat Mass Transfer, vol. 25, p. 149, 1982. 

In order to size the compressor of a new refrigerator, it is desired to determine the rate of heat transfer from the kitchen air into the refrigerated space through the walls, door, and the top and bottom section of the refrigerator (Fig. 2-11). In your analysis, would you treat this as a transient or steady-state heat transfer problem Also, would you consider the heat transfer to be one-dimensional or multidimensional Explain. 

SOLUTION Heat transfer from the kitchen air to a refrigerator is considered. It is to be determined whether this heat transfer is steady or transient, and whether it is one- or multidimensional. 

In the last section we considered one-dimensional heat conduction and assumed heat conduction in other directions to be negligible. Most heat transfer problems encountered iu practice can be approximated as being onedimensional, and we mostly deal with such problems in tliis text. However, this is not always the case, and sometimes we need to consider heat transfer in other directions as well. In such cases heal conduction is said to be multidimensional, and in this section we develop the governing differential equation in such systems in rectangular, cylindrical, and spherical coordinate systems. 

Two assumptions commonly used in solving complex multidimensional heat transfer problems by treating them as one-dimensional (say,- in the... 

Certain multidimensional heat transfer problems involve two surfaces maintained at constant temperatures 7 and 7j. The steady rate of beat transfer between these two surfaces is expressed as... 

Tlie total heat transfer to or from a multidimensional geometry can also be determined by using the one-dimensional values. The transient heat transfer for a two-diiuensioiial geometry formed by the intersection of two one-dimensional geometries 1 and 2 is... 

L.A. Sphaier and R.M. Cotta, Integral Transform Analysis of Multidimensional Eigenvalue Problems Within Irregular Domains, Num. Heat Transfer, Part B-Fundamentals, Vol. 38, pp. 157-175 (2000). 

The basic solutions for the infinite plates and infinitely long cylinders can be used to obtain solutions for multidimensional systems such as long rectangular plates, cuboids, and finite circular cylinders with end cooling. The texts on conduction heat transfer [4,11, 23, 29, 38, 49,56, 87] should be consulted for the proofs of the method and other examples. 

W. A. Fiveland and J. P. Jessee, A Finite Element Formulation of the Discrete-Ordinate Method For Multidimensional Geometries, in Radiative Heat Transfer Current Research, ASME HTD no. 244, New York, 1993. 

S. H. Chan, Numerical Methods for Multidimensional Radiative Transfer Analysis in Participating Media, Annual Review of Numerical Fluid Mechanics and Heat Transfer, vol. 1, Hemisphere, New York, pp. 305-350,1987. 

Z.-Q. Tan, Radiative Heat Transfer in Multidimensional Emitting, Absorbing, and Anisotropic Scattering Media—Mathematical Formulation and Numerical Method, ASME Journal of Heat Transfer, 111, pp. 141-147,1989. 

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