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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:
augmentation of heat transfer in, boiling of binary and multicomponent mixtures in, combined free and forced convection in,
Combined Free and Forced Convection in Passages in condensers, horizontal channels, vertical pipes,
flow boiling in: horizontal pipes, free convective heat transfer from outside of, heat transfer to, in fluidized beds, heat transfer to liquid metals in, laminar heat transfer in, pneumatic conveyance (gas solids flow) in, radiative heat transfer along, roughened surface, radiative heat transfer along, single-phase fluid flow and pressure drop in fully developed transition between laminar and turbulent flows, heat transfer in turbulent heat transfer in, two-phase gas-liquid flow in, use in shell-and-tube heat exchangers for single-phase flow,
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:

Index

HEDH
A B C D E F G H I J K L M N O P
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:
augmentation of heat transfer in, boiling of binary and multicomponent mixtures in, combined free and forced convection in,
Combined Free and Forced Convection in Passages in condensers, horizontal channels, vertical pipes,
flow boiling in: horizontal pipes, free convective heat transfer from outside of, heat transfer to, in fluidized beds, heat transfer to liquid metals in, laminar heat transfer in, pneumatic conveyance (gas solids flow) in, radiative heat transfer along, roughened surface, radiative heat transfer along, single-phase fluid flow and pressure drop in fully developed transition between laminar and turbulent flows, heat transfer in turbulent heat transfer in, two-phase gas-liquid flow in, use in shell-and-tube heat exchangers for single-phase flow,
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:
Q R S T U V W X Y Z
P Pipes, circular: combined free and forced convection in,
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Combined Free and Forced Convection in Passages

DOI 10.1615/hedhme.a.000177

2.5.10 Combined free and forced convection in passages

J. D. Jackson

General introduction

The term “combined forced and free convection” is used to describe the process of heat transfer in fluids where the flow field is modified significantly by the action of non-uniformity of gravitational body force as a consequence of the temperature dependence of fluid density. The influence of free convection is usually thought of in terms of the concept of fluid buoyancy. Another term commonly used to describe heat transfer under such conditions is “mixed convection”.

The effectiveness of heat transfer by forced convection as characterised by the Nusselt number NuF depends on Reynolds number and Prandtl number. In the case of free convection the corresponding parameter NuN depends on Grashof number and Prandtl number. Thus, for combined free and forced it is not surprising that Nusselt number depends on Reynolds number, Grashof number and Prandtl number.

In the early studies of convective heat transfer the forced and free convection modes were considered independently with only passing reference being made to any possible interaction between them. When combined free and forced convection did eventually begin to be investigated, attention was at first restricted to laminar and transitional flows. Later, it became clear that measurable influences of free convection could also be present in turbulent flows and that in some circumstances they were a dominant factor in determining the effectiveness of heat transfer under such conditions.

In the following review of combined free and forced convection in passages, attention is focussed on heat transfer in vertical and horizontal pipes. Clearly, the orientation of the pipe is an important parameter under conditions of buoyancy-influenced convective heat transfer. In the vertical case, the flow can be either aided by buoyancy (upward flow in a pipe with heating/ downward flow with cooling) or opposed by buoyancy (downward flow in a pipe with heating/upward flow with cooling). In the horizontal case buoyancy causes secondary, transverse motion to be superimposed on the axial flow. If a horizontal pipe is heated, the fluid tends to have an upward component of velocity over the sides and a downward component in the central region and the secondary flow pattern takes the form of two counterrotating vortices. Cooling, rather than heating, produces similar buoyancy-induced secondary circulation but with rotation in the opposite sense.

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