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Packaged units, specification of, Packing characteristic, in cooling towers, Packings, for cooling towers Packings, for fixed beds: Packinox heat exchanger, Paints, spectral characteristics of reflectance of surfaces treated with, Palen, J W Panchal, C B, Paraffins, normal and isonormal: Paraldehyde: Parallel channel instability, in condensers, Partial boiling in subcooled forced convective heat transfer, Participating media, radiation interaction in, Particle convective component, in heat transfer from fluidized beds, Particle emissivity, Particle Reynolds number in fixed beds, Particles: Particulate fluidization, Particulate fouling, Pass arrangements, in plate heat exchangers, Passes, tube side, Passive methods, for augmentation of heat transfer, passive systems for: PD5500 mechanical design of shell-and-tube heat exchangers to, Peacock, D K, Pearson number, Peclet number Peng-Robinson equation of state, application to hydrocarbons, Penner's rule, in absorption of radiation by gases, Pentachloroethane (Refrigerant 120): Pentadecane: Pentadecene: Pentadiene 1, 2: Pentadiene 1, trans 3: Pentadiene 1, 4: Pentadiene 2-3: Pentafluoroethane (Refrigerant 125) Pentamethylbenzene: Pentane: Pentanoic acid: 1-Pentanol: 1-Pentene: cis-2-Pentene: trans-2-Pentene: Pentylacetate: Pentylbenzene: Pentylcyclohexane: Pentylcyclopentane: Pentylcyclopropane, liquid properties, Perforated fins, in plate fin heat exchangers, Perforated plates, loss coefficients in, Periodic operation, of regenerator, Periodic variations in temperature, thermal conduction in bodies with, PFR correlation, for heat transfer in high fin tube banks, Pharmaceutical industry, fouling of heat exchangers in, Phase change materials, in augmentation of heat transfer, Phase change number, Phase equilibrium: Phase inversion Phase separation, as source of corrosion problems, Phenol: Phenols: Phenylhydrazine: Phonons, in thermal conductivity of solids, Phosgene: Physical properties: Pi theorum, in dimensional analysis, Pinch analysis, for heat exchanger network design, Pioro, I L Pioro, LS, Pipe leads, Piperidine: Pipes, circular: Pipes, noncircular: Piping components: Pitting corrosion, in stainless steels, Planck's constant, Planck's law, for spectral distribution of blackbody radiation, Plane shells, steady-state thermal conduction in, Plastic deformation Plate fin heat exchangers Plate fins, efficiency, Plate heat exchangers: Plate evaporator Plates: Plug flow: Plug flow model, for furnaces, Pneumatic conveyance, Pneumatic conveying dryer, P-NTU method: Polarization, of thermal radiation, Polyglycols, as heat transfer media, Polymers: Pool boiling, Porous surfaces: Port arrangements, in plate heat exchangers, Portable fouling unit, Poskas, P, Postdryout heat transfer: Powders: Power law fluid (non-Newtonian), Power plant: Prandtl number Precipitation (crystallization) fouling, Precipitation hardening, of stainless steels, Pressure coefficient: Pressure control of condensers, Pressure drop: Pressure gradient: Pressure, specification of in mechanical design to EN13445, Pressure testing, Pressure vessels, principle codes for, Pressurised water reactor, fouling in, Printed circuit heat exchanger, Problem table algorithm, in pinch analysis, Process heaters: Progressive plastic deformation Prolate spheroids, free convective heat transfer from, Promoters, in dropwise condensation, Propadiene: Propane: 1-Propanol: 2-Propanol: Propeller agitator, Property ratio method, for temperature dependent physical property Propionaldehyde: Propionic acid: Propionic anhydride: Proprionitrile: Propyl acetate: Propylamine: Propylbenzene: Propylcyclohexane: Propylcyclopentane: Propylene: 1,3-Propylene glycol: Propylene oxide: Propyl formate: Propyl propionate: Pseudo-boiling in supercritical fluids, Pseudo-film boiling in supercritical fluids, Pseudocritical pressure, Pseudocritical tempertaure, Pugh, S F Pulp and paper industry, fouling of heat exchangers in, Pulsations, use in augmentation of heat transfer, Pulverized fuel water-tube boiler, Pumping, lost work in, Pushkina and Sorokin correlation, for flooding in vertical tubes, Pyramid, free convective heat transfer from, Pyridine:
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Goodness Factor Comparisons

DOI 10.1615/hedhme.a.000302

3.9.7 Goodness factor comparisons

Surface geometries must be selected for each fluid stream before the heat exchanger design can be undertaken. This selection will depend on mechanical design and thermal performance considerations. On a thermal performance basis alone, one desires a surface geometry that meets the required cost, size, and friction power limitations. Several “goodness factors” have been proposed to allow comparison of surface performance characteristics in this regard (LaHaye et al., 1974; Kays and London, 1951; Cox and Jallouk, 1973; Bergles et al., 1974; Soland et al., 1976). These methods compare the thermal performance of two surfaces on a friction power basis. By writing the heat transfer coefficient (α) and the friction power (P) as functions of j, f, ReDh, and Dh, one obtains

\[\label{eq1} \alpha=\frac{c_{p}\eta}\,{\mbox{Pr}^{2/3}}\frac{j\mbox{Re}_{D_{h}}}{D_{h}} \tag{1}\]

\[\label{eq2} \frac{P}{A}=\frac{\eta^{3}}{2\rho^{2}}\frac{f\,\mbox{Re}^{3}_{D_{h}}}{D^{3}_{h}} \tag{2}\]

The thermal performance of two surfaces may be compared by plotting jReDhDh versus f (ReDh /Dh)3, which compares the heat transfer coefficients for equal friction power per unit surface area. For equal P /A, or f (ReDh /Dh)3, the surface having the largest value of j ReDh /Dh will require the least heat transfer surface area for equal thermal effectiveness. Alternatively, one may modify Equation 1 and Equation 2 to allow comparison on a volume basis. Multiplying each equation by (β = A /V = 4σ /Dh) allows comparison of αA /V versus P /V. Thus, for equal friction power per unit volume (P /V), one compares the heat exchanger volumes for equal thermal effectiveness.

The application of Equation 1 and Equation 2 are illustrated in Figure 1. This figure shows the performance of the surfaces of Figure 299.1 and Figure 299.2 on a surface area goodness factor basis. The graph is prepared for the case of equal hydraulic diameter. Figure 1 shows that the offset-strip fin yields significantly higher heat transfer coefficients for equal P /A. As the Reynolds number is reduced to small values, associated with laminar flow, the offset fin loses some of its advantage.

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