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Cabin heater, Caetano, EF Calcium carbonate, fouling of heat exchangers by, Calcium sulphate, fouling of heat exchangers by, CALFLO, heat transfer media, Calorically perfect gas, CANDU Reactor, fouling problems in, Carbon dioxide: Carbon disulfide: Carbon monoxide: Carbon steel: Carbon-manganese steels Carbon-molybdenum steels, Carbon tetrachloride: Carbonyl sulfide: Carboxylic acids: Carnot cycle in refrigeration, Carnot factor, Carreau fluid (non-Newtonian), Carryover of solids in fluidized beds, Cashman, B L, Cast iron, thermal and mechanical properties, Cavitation as source of damage in heat exchangers, Cell method, for heat exchanger effectiveness, Cement kilns, CEN code for pressure vessels, Centrifugal dryer, Ceramics Certification of heat exchangers, Chan, S H, Channel emissivity, Chapman-Rubescin formula for viscosity variation with temperature, Chemical exergy, Chemical formulas of commonly used fluids Chemical industry, fouling of heat exchangers in, Chemical reactions, exergy analysis of, Chemical reaction fouling, Chen correlation for forced convective boiling, Chen method, for enthalpy of vaporisation, Chenoweth, J M, Chevron troughs as corrugation design in plate heat exchangers, Chillers, construction features of, Chilton-Colburn analogy, Chisholm, D Chisholm correlations: Chlorine: Chloroacetic acid: Chlorobenzene: Chlorobutane: Chlorodifluoromethane (see Refrigerant 22) 1-Chloro-1,1-difluoroethane (Refrigerant 142b): Chloroethane (Refrigerant 160): Chloromethane (Refrigerant 40): Chloropentane: 1,2-Chloropentafluoroethane (Refrigerant 115): Chloroprene (2-Chloro-1,3-butadiene): 1-Chloropropane: 2-Chloropropane: m-Chlorotoluene: o-Chlorotoluene: Chlorotrifluoroethylene: Chlorotrifluoromethane (see Refrigerant 13) Chromium-molybdenum steels, Chudnovsky, Y, Chugging flow (gas-liquid), in shell-and-tube heat exchangers, Chung et al method, for viscosity of low pressure gases, Church and Prausnitz methods: Churchill, S W, Churchill and Chu correlations for free convective heat transfer: Churn flow, regions of occurrence of, Circles, radiative heat transfer shape factors between parallel coaxial, Circular girth flanges, design according to ASME VIII code, Circulating fluidized beds, Circulation, modes of in free convection: in enclosures heated from below, CISE correlations for void fractions, Clausius-Clapeyron relationship: Cleaning: Climbing film evaporator, Closed circuit cooling towers, Coalescence of bubbles in fluidized beds, Coatings for corrosion protection Cocurrent flow: Codes, mechanical design: Cogeneration Colburn and Drew method for binary vapor condensation, Colburn and Hougen method for condensation in presence of noncondensable gases Colburn equation for single-phase heat transfer outside tube banks, Colburn j factor: Colebrook-White equation for friction factor in rough circular pipe, Coles, law of the wake, Collier, J G, Combined free and forced convection heat transfer: Combined heat and mass transfer, Combining flow, loss coefficients in, Combustion model for furnaces, Compact heat exchangers (see Plate fin heat exchangers) Compartment dryers, Composite curves, in the pinch analysis method for heat exchanger network analysis: Compressed liquids, density of: Compressible flow: Compression, exergy analysis of Compressive stress, in heat exchanger tubes, Computer-aided design, of evaporators, Computer program for Monte Carlo calculations of radiative heat transfer, Computer simulation, of fouling, Computer software for mechanical design, Concentration, choice of evaporator type for, Concentric spheres, free convective heat transfer in, Concurrency corrections in plate heat exchangers, Condensation: Concrete, lightweight, submerged combustion system for, Condensation curves: Condenser/preheater tubes, in multistage flash evaporation, Condensers: Conduction, heat: Conductors, thermal conductivity of, Cones, under internal pressure, EN13445 guidelines for, Cones, vertical: Conical shells, mechanical design of: Conjugate radiation interactions Connors equation for fluid elastic instability, Conservation equations: Constantinon and Gani method, for estimating normal boiling point, Contact angle, Contact resistance: Continuity equation: Continuum model, for fluids, Continuum theories, for non-Newtonian fluids, Contraction, sudden, pressure drop in: Control: Control volume method, in finite difference solutions for conduction, Convection, interaction of radiation with, Convection effects, on heat transfer in kettle reboilers, Convective heat transfer, single-phase: Conversion factors: Conveyor, gravity: Cooling curves, in condensation, Cooling towers: Cooling water fouling, Cooper correlation, for nucleate boiling, Cooper, Anthony, Copper, thermal and mechanical properties, Copper alloys, Correlation, general nature of, Corresponding states principle Corrosion: Corrugation design, for plate heat exchangers Costing of heat exchangers: Countercurrent flow: Coupled thermal fields, in transient conduction, Cowie, R C, Crank-Nicolson differencing scheme, in finite difference method, Creeping flow, in combined free and forced convection around immersed bodies, m-Cresol: o-Cresol: p-Cresol: Crevice corrosion, in stainless steels, Critical constants Critical density, of commonly used fluids, Critical flow, in gas-liquid systems, Critical heat flux: Critical pressure: Critical Rayleigh number, in free convection, Critical temperature: Critical velocity, in stratification in bends and horizontal tubes, Critical volume (see also Critical density) Cross counterflow heat exchangers, Crossflow: Crude oil, fouling of heat exchangers: Cryogenic plant, entropy generation in, Crystallization Crystallization fouling, Curved ducts: Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers, C-value method for heat exchanger costing, Cycling, of expansion bellows, Cyclobutane: Cyclohexane: Cyclohexanol: Cyclohexene: Cyclopentane: Cyclopentene: Cyclopropane: Cylinders: Cylindrical contacts, thermal contact resistance in, Cylindrical coordinates, finite difference equations for conduction in, Cylindrical shell, analytical basis of code rules for,

Index

HEDH
A B C
Cabin heater, Caetano, EF Calcium carbonate, fouling of heat exchangers by, Calcium sulphate, fouling of heat exchangers by, CALFLO, heat transfer media, Calorically perfect gas, CANDU Reactor, fouling problems in, Carbon dioxide: Carbon disulfide: Carbon monoxide: Carbon steel: Carbon-manganese steels Carbon-molybdenum steels, Carbon tetrachloride: Carbonyl sulfide: Carboxylic acids: Carnot cycle in refrigeration, Carnot factor, Carreau fluid (non-Newtonian), Carryover of solids in fluidized beds, Cashman, B L, Cast iron, thermal and mechanical properties, Cavitation as source of damage in heat exchangers, Cell method, for heat exchanger effectiveness, Cement kilns, CEN code for pressure vessels, Centrifugal dryer, Ceramics Certification of heat exchangers, Chan, S H, Channel emissivity, Chapman-Rubescin formula for viscosity variation with temperature, Chemical exergy, Chemical formulas of commonly used fluids Chemical industry, fouling of heat exchangers in, Chemical reactions, exergy analysis of, Chemical reaction fouling, Chen correlation for forced convective boiling, Chen method, for enthalpy of vaporisation, Chenoweth, J M, Chevron troughs as corrugation design in plate heat exchangers, Chillers, construction features of, Chilton-Colburn analogy, Chisholm, D Chisholm correlations: Chlorine: Chloroacetic acid: Chlorobenzene: Chlorobutane: Chlorodifluoromethane (see Refrigerant 22) 1-Chloro-1,1-difluoroethane (Refrigerant 142b): Chloroethane (Refrigerant 160): Chloromethane (Refrigerant 40): Chloropentane: 1,2-Chloropentafluoroethane (Refrigerant 115): Chloroprene (2-Chloro-1,3-butadiene): 1-Chloropropane: 2-Chloropropane: m-Chlorotoluene: o-Chlorotoluene: Chlorotrifluoroethylene: Chlorotrifluoromethane (see Refrigerant 13) Chromium-molybdenum steels, Chudnovsky, Y, Chugging flow (gas-liquid), in shell-and-tube heat exchangers, Chung et al method, for viscosity of low pressure gases, Church and Prausnitz methods: Churchill, S W, Churchill and Chu correlations for free convective heat transfer: Churn flow, regions of occurrence of, Circles, radiative heat transfer shape factors between parallel coaxial, Circular girth flanges, design according to ASME VIII code, Circulating fluidized beds, Circulation, modes of in free convection: in enclosures heated from below, CISE correlations for void fractions, Clausius-Clapeyron relationship: Cleaning: Climbing film evaporator, Closed circuit cooling towers, Coalescence of bubbles in fluidized beds, Coatings for corrosion protection Cocurrent flow: Codes, mechanical design: Cogeneration Colburn and Drew method for binary vapor condensation, Colburn and Hougen method for condensation in presence of noncondensable gases Colburn equation for single-phase heat transfer outside tube banks, Colburn j factor: Colebrook-White equation for friction factor in rough circular pipe, Coles, law of the wake, Collier, J G, Combined free and forced convection heat transfer: Combined heat and mass transfer, Combining flow, loss coefficients in, Combustion model for furnaces, Compact heat exchangers (see Plate fin heat exchangers) Compartment dryers, Composite curves, in the pinch analysis method for heat exchanger network analysis: Compressed liquids, density of: Compressible flow: Compression, exergy analysis of Compressive stress, in heat exchanger tubes, Computer-aided design, of evaporators, Computer program for Monte Carlo calculations of radiative heat transfer, Computer simulation, of fouling, Computer software for mechanical design, Concentration, choice of evaporator type for, Concentric spheres, free convective heat transfer in, Concurrency corrections in plate heat exchangers, Condensation: Concrete, lightweight, submerged combustion system for, Condensation curves: Condenser/preheater tubes, in multistage flash evaporation, Condensers: Conduction, heat: Conductors, thermal conductivity of, Cones, under internal pressure, EN13445 guidelines for, Cones, vertical: Conical shells, mechanical design of: Conjugate radiation interactions Connors equation for fluid elastic instability, Conservation equations: Constantinon and Gani method, for estimating normal boiling point, Contact angle, Contact resistance: Continuity equation: Continuum model, for fluids, Continuum theories, for non-Newtonian fluids, Contraction, sudden, pressure drop in: Control: Control volume method, in finite difference solutions for conduction, Convection, interaction of radiation with, Convection effects, on heat transfer in kettle reboilers, Convective heat transfer, single-phase: Conversion factors: Conveyor, gravity: Cooling curves, in condensation, Cooling towers: Cooling water fouling, Cooper correlation, for nucleate boiling, Cooper, Anthony, Copper, thermal and mechanical properties, Copper alloys, Correlation, general nature of, Corresponding states principle Corrosion: Corrugation design, for plate heat exchangers Costing of heat exchangers: Countercurrent flow: Coupled thermal fields, in transient conduction, Cowie, R C, Crank-Nicolson differencing scheme, in finite difference method, Creeping flow, in combined free and forced convection around immersed bodies, m-Cresol: o-Cresol: p-Cresol: Crevice corrosion, in stainless steels, Critical constants Critical density, of commonly used fluids, Critical flow, in gas-liquid systems, Critical heat flux: Critical pressure: Critical Rayleigh number, in free convection, Critical temperature: Critical velocity, in stratification in bends and horizontal tubes, Critical volume (see also Critical density) Cross counterflow heat exchangers, Crossflow: Crude oil, fouling of heat exchangers: Cryogenic plant, entropy generation in, Crystallization Crystallization fouling, Curved ducts: Cut-and-twist factor, in enhancement of heat transfer in double pipe heat exchangers, C-value method for heat exchanger costing, Cycling, of expansion bellows, Cyclobutane: Cyclohexane: Cyclohexanol: Cyclohexene: Cyclopentane: Cyclopentene: Cyclopropane: Cylinders: Cylindrical contacts, thermal contact resistance in, Cylindrical coordinates, finite difference equations for conduction in, Cylindrical shell, analytical basis of code rules for,
D E F G H I J K L M N O P Q R S T U V W X Y Z

Combined Free and Forced Convection in Passages

DOI 10.1615/hedhme.a.000177

2.5.10 Combined free and forced convection in passages

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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