Document 7OyQMYqzxvmZeL7R6XNvGMeDj

54 CHAPTER 4 1965 Guide And Data Book Ai, At A,,.-The fraction of W\A\ absorbed at Aj due to direct radiation from A\ is Fyaj. The fraction >of W\Ai ab sorbed at Aj because of reflection and re-reflection off-the other surfaces A, is BoF&i. It follows, therefore, that the total fraction of IFiAj absorbed at A/is: - 'By * F\j<ij + ' 21 P\sPjBij. i-i , Radiation emitted from the other surfaces may be treated similarly: ' By -- Pyaj + 2 PtiPiBy Bu TM F4- 23 PuPiBij <_1 - (14) *-! - B*j = F,jaj + ^F*nnBij There are n simultaneous equations for the n values of B^required in Equation 13 for a given <jj, that is,* for-a given sur face A//Equations 14 are simply solved on a modern com puter. For calculating the q for other enclosure surfaces, one merely changes the first term on the right hand side of each equation. There is only one set of Fr4>, for an enclosure. Sev eral additional useful relations are as follows: By 1; uBijAi - *jBjiA,\ and qj = 0 (15), (16), (17) All of the calculation methods which have been applied to multisurface enclosures assume that each surface uniformly irradiates each other surface. Only a limited number of special arrangements have this characteristic. Subdividing the vari ous surfaces will improve the approximation, but the work required to obtain a solution increasea rapidly with each sub division. A balance must be found which is consistent with the importance of the problem. Special Surfaces in Enclosures All types of diffuse-radiation processes are included M"der the enclosure method discussed above, and surfaces having special characteristics are treated by being assigned consistent Heat Transfer - nroDerties An opening is treated as an equivalent area A,' 1-th a reflectivity of zero. If energy, enters the .enclosure . densely through the opening, A, is assigned an equivalent temperature; otherwise its temperature is taken as zero. If the . loss through the opening is desired, q. is found. A window in the enclosure is assigned its actual properties. A surface in radiant balance is one for which radiant emis sion is balanced by radiant absorption. Such a surface, sometimes called a no-flux surface, may be simulated for the calculation of the rate of loss for any other surface by assigning to it a reflectivity of 1.0 and an emissivity of 0. The absorption factors are then found from Equation 14 by using these values. If the temperature of this surface is desired, the actual values of emissivity and reflectivity are used to determine the ab sorption factors. They are then substituted into Equation 13, with 5/ = 0, to find Wj and Tj. The calculation of surface temperatures in radiant surroundings has been treated in de tail by Gebhart.u This general method may also be applied to enclosures con taining grey absorbing and emitting media. 55 ^ i NATURAL CONVECTION Heat transfer involving motion in a fluid due to a difference in density and the action of gravity is called natural convec tion. It is called forced convection if the motion is due to ex ternal means, such as a blower or pump. Heat transfer coeffi cients for natural convection are generally much,lower than for forced convection and, as a consequence, it is important not to ignore radiation in calculating the total heat loss or gain from a body. Radiant heat transfer may be of the same order of magnitude as natural convection, even at room tem peratures, as'evidenced by the fact that wall temperatures in a room can affect human comfort. (See Chapter 7.) Natural or free convection b important in a wide variety of heating and refrigeration equipment. Examples are the socalled gravity coils used in high-humidity cold storage rooms and in roof-mounted refrigerant condensers, the evaporator and condensefof household refrigerators, baseboard radi ators and-convectors for space heating, and cooling panels for air conditioning. Natural convection b also involved in the I. General Relationships Toble 5____Natural Convection Heat Transfer Coefficients :Nir. 'e(Nar-AW fkc' (f LVgg(A0t) 'y / MC,y or h e' L V , //- V k )/ Characteristic Length, L, for Vertical Plates, or Pipes Horizontal Plates Horizontal Pipes Spheres Rectangular Block, with horizontal length I* and vertical length L, L ~ height L * length L -- diameter L -- J (diameter) ~l Tk + T. (1) (2) II. Planes and Pipes Horizontal or Vertical Planes, Pipes, Rectangular Blocks, and Spheres (excluding horizontal plates facing downward for heating and facing upward for cooling). (a) laminar Range (Nor-Npr) between 10* and 10* (b) Turbulent Range (Nor-Nfr) between 10* and 10" iV*. - 0.56(Nor-Nrr)U4 = 0.13(N*.-N,r)u* (3) (4) III. Wires . For horizontal or vertical wires use L * dia, for (NofNn) between 10"* and 1. IV. With Atr (Nor-Nn) - 1.6 X 10L*(Af), (70 F, L in ft, 6t in F deg) (a) Cylinders Small Cylinder, Laminar Range . Large Cylinder, Turbulent Range 8mall Plates, laminar Range large Plates, Turbulent Range. (c) Horizontal Plates, facing upward when heated or downward' when cooled Small Plates, laminar Range large Plates, Turbulent Range(d) Horizontal Plates, facing downward when heated, or upward when cooled Small Plates = (No,-N*)'-' 1 " 027(t) . .... h - 0.18(Af)1'*. `-""(tT . h - 0.19(AI) ' - K -- 0.27 (/--A)\1/.4 : - h <= 0.22(Af)* . *_ -l2.( i) ` (5) " (6) (7) (8) (9) ' (10) (11) (12)