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CHAPTER 4 1965 Guide And Data Book Hed* Transfer*'' 59 ^rron hv EauatioD 1 of Table 6, the heat transfer is deterby the flow conditions, as indicated by the Reynolds number, and by the`fluid properties, as indicated by the prandtl number. Equation 1 of Table 6 may be modified to the form given by Equation 4 (Table 6) so as to present the heat transferfactor, j. The heat transfer factor is related to the frictionfactorf, due to theinterrelationship between the trans port of momentum and heat, and approximately equals //2 for turbulent flow in straight ducts. These factors are plotted in Fig- 4. The characteristic length d is the diameter of the tube, out side or inside, or the length of the plane plate. For other shapes, thehydraulic diameter Dt, is used, where D, = 4r* = 4 (cross-sectional area for flow)/(total wetted perimeter). This reduces to twice the distance between surfaces in the case of parallel plates or_an annulus. For convenience, a number of simplified equations appli cable to common fluids under normal operating conditions have been presented in Equations 8 to 24 of Table 6. Graphi cal solutions for water and liquid refrigerants appear in Figs. 5 and 6. An excellent introduction to the theoretical founda tions of forced convection heat transfer will be found in Ref ence 12. BOILING Beat transfer by boiling occurs in a wide variety of re frigeration equipment. Examples are flooded shell-aod-tube evaporators, where refrigerants boil outside bundles of plain or finned .horizontal tubes, flooded vertical or inclined tube evaporators, where - boiling occurs inside^.tubes, and dry expansion evaporators, where the refrigerant flows ingiHo tubes and is vaporised completely before being recirculated.. A detailed description of various types of evaporators may be found in Chapters 34 and 43. Forms of Baiting Boding from a submerged heated surface with movement of the liquid generated by free convection or the stirring ac tion of bubbles is called pool boiling. Boiling on a surface past which liquid flows with a significant velocity is called forced . convection boiling. If the bulk liquid is at or near the boiling point, vapor generated at the heated surface will move through the liquid and be released at the liquid interface. However, if the bulk liquid is below the boiling point, the 1 vapor bubbles generated at the heated surface will reoondense iu tiie liquid. The former process is called boiling isiih net evaporation; the latter is termed subcooled, surface, or local boiling. Hie discussion which follows deals only with boiling with net evaporation. As originally^described by Nukiyama,*8 and later elucidated by'Drew and Mueller,* boiling may take place in several radically different forms. The forms or regimes of boiling de pend primarily on the difference, At, between the surface temperature and the boiling temperature of the fluid, as illus trated in Fig. 7 for pool boiling of water. When At is very small, the liquid in contact with the warmer surface becomes slightly superheated and rises to the liquid-vapor interface, where the evaporation takes place. This is called natural con vection boiling. When At increases, the familiar form of bubble formation fakra place. The bubble formation, and fluid agita tion due to the movement of- bubbles, result in high heat transfer coefficients. Since this is based primarily on the nuclei on which bubbles are formed, it is called nucleate boiling. The coefficient increases rapidly with At until a limit is readied, called the critical temperature difference. Beyond this, the coefficient is actually reduced by further increases of At. The third form of boiling, called film boiling, occurs when the temperature difference is so large that either the surface or the drops of fluid are covered by a vapor film, causing vapor binding. The coefficient continues to decrease in spite of in creasing At, until a lower limit is reached. In the fourth stage, radiation heat transfer from the film becomes significant, and the coefficient again increases with At. The change from one form of boiling to another is generally separated by a transi tion region where both forms are mixed. The heat flux corresponding to the critical At is sometimes called the peak heat flux or burnout flux. From Fig. 7, it can be seen that if the energy input to the heated surface is increased beyond this peak value, there will be a sudden transition from the nucleate boiling to film boiling regime, and a corresponding jump in surface temperature. The term burnout originates from the fact that, with water boiling at atmospheric pressure, this jump in.surface temperature can carry most common metals past their melting point. The critical At for water is about 45 F, for ^propanol about 80 F, and for n-butanol about 70 F.* It is unknown for most refrigerants. Natural Convection Boiling When the temperature difference between the heated stirface and the liquid is low, heat transfer take* place by natural convection since few, if any, bubbles are generated. As a consequence, correlations of experimental data in this regime are based on equations of the form of Equation 1, Table 5. ... Equations 1 and 2 of Table 7, for heat transfer from sub merged vertical and horizontal surfaces, are based on the experiments of King and others conducted at atmospheric pressure.. Simplified equations for Refrigerants 12 and 22/'"' outside a submerged horizontal.tube,nJand water from a hori zontal plate, are given in Equations 3, 4, and 5, Table 7. fig. 7 ...Basic Concepts'of Boiling' Mechanisms and Their Dependence on Temperature Difference Nucleate Boiling For nucleate, boiling, factors affecting bubble formation, growth,,detachment from the surface, .and rise through the liquid will influence heat transfer rates. Bubbles originate from cavities on the heated surface.' The initial bubble di` ameter, which equals the diameter of the cavity from which it originates', caa be estimated from Equation 6, Table 7. When the buoyant forces on the bubble exceed the adhesive force II