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Ideal gas: Ilexan, heat transfer medium, Illingworth, A, Imbedded fins, Immersed bodies: Immersed tubes, in fluidized beds, heat transfer to, Immiscible liquids, condensation of vapors producing Impairment of heat transfer in combined free and forced convection in a vertical pipe, Imperfectly diffuse surfaces: Impingement damage in heat exchangers, Impingement plate: Impingement protection, in shell-and-tube heat exchangers, Impinging jets: Implicit equations, solution of Inclined enclosures, free convective heat transfer in, Inclined flow, effect of on heat transfer to cylinders, Inclined pipes: Inclined surfaces, free convective heat transfer from, Inconel, spectral characteristics of reflectance from oxidized surface of, Induced flow instabilities, in augmentation of heat transfer, Injection: Inlet effects in shell-and-tube heat exchangers, In-line tube banks: Inorganic compounds, solutions of, as heat transfer media, Inorganic substances: Instability, parallel channel, in condensers, Insulators, thermal conductivity of, Integral condensation: Integral finned tubes: Interaction coefficients in heat exchangers, Interaction parameters for binary systems, tables, Interfacial friction, in three-phase (liquid-liquid-gas) stratified flows, Interfacial resistance, in condensation, Interfacial roughness, relationships for, in annular gas-liquid flow, Interfacial shear stress, effect on filmwise condensation, on vertical surface, Intergrannular corrosion, of Intermating troughs, as corrugation design in plate heat exchangers, Intermittent flows: Internal heat sources, temperature distribution in bodies with, Internal heat transfer coefficient, use in transient conduction calculations, Internal reboilers (in distillation columns), characteristics advantages and disadvantages of, Internally finned tubes: International codes for pressure vessels, Interpenetrating continua (as representation of heat exchangers):
partial differential equations for,
Partial differential equations for interpenetrating continua
porosity in,
Intertube velocity, in tube banks, Inviscid flow, compressible, with heat addition, Iodine: Iodobenzene: Iodoethane: Iodomethane: ISO codes for mechanical design of heat exchangers, Isobutane: Isobutanol: Isobutylamine: Isobutylformate: Isobutyric acid: Isoparaffins: Isopentane: Isopentanol: Isopropanol: Isopropylacetate: Isopropylamine: Isopropylbenzene: Isopropylcyclohexane: Isothermal flow, compressible, in ducts, Isothermal gas, radiation heat transfer to walls from, Isotropic materials, elastic properties, Isotropic scattering, Italy, guide to national practice for heat exchanger mechanical design,

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A B C D E F G H I
Ideal gas: Ilexan, heat transfer medium, Illingworth, A, Imbedded fins, Immersed bodies: Immersed tubes, in fluidized beds, heat transfer to, Immiscible liquids, condensation of vapors producing Impairment of heat transfer in combined free and forced convection in a vertical pipe, Imperfectly diffuse surfaces: Impingement damage in heat exchangers, Impingement plate: Impingement protection, in shell-and-tube heat exchangers, Impinging jets: Implicit equations, solution of Inclined enclosures, free convective heat transfer in, Inclined flow, effect of on heat transfer to cylinders, Inclined pipes: Inclined surfaces, free convective heat transfer from, Inconel, spectral characteristics of reflectance from oxidized surface of, Induced flow instabilities, in augmentation of heat transfer, Injection: Inlet effects in shell-and-tube heat exchangers, In-line tube banks: Inorganic compounds, solutions of, as heat transfer media, Inorganic substances: Instability, parallel channel, in condensers, Insulators, thermal conductivity of, Integral condensation: Integral finned tubes: Interaction coefficients in heat exchangers, Interaction parameters for binary systems, tables, Interfacial friction, in three-phase (liquid-liquid-gas) stratified flows, Interfacial resistance, in condensation, Interfacial roughness, relationships for, in annular gas-liquid flow, Interfacial shear stress, effect on filmwise condensation, on vertical surface, Intergrannular corrosion, of Intermating troughs, as corrugation design in plate heat exchangers, Intermittent flows: Internal heat sources, temperature distribution in bodies with, Internal heat transfer coefficient, use in transient conduction calculations, Internal reboilers (in distillation columns), characteristics advantages and disadvantages of, Internally finned tubes: International codes for pressure vessels, Interpenetrating continua (as representation of heat exchangers):
partial differential equations for,
Partial differential equations for interpenetrating continua
porosity in,
Intertube velocity, in tube banks, Inviscid flow, compressible, with heat addition, Iodine: Iodobenzene: Iodoethane: Iodomethane: ISO codes for mechanical design of heat exchangers, Isobutane: Isobutanol: Isobutylamine: Isobutylformate: Isobutyric acid: Isoparaffins: Isopentane: Isopentanol: Isopropanol: Isopropylacetate: Isopropylamine: Isopropylbenzene: Isopropylcyclohexane: Isothermal flow, compressible, in ducts, Isothermal gas, radiation heat transfer to walls from, Isotropic materials, elastic properties, Isotropic scattering, Italy, guide to national practice for heat exchanger mechanical design,
J K L M N O P Q R S T U V W X Y Z
I Interpenetrating continua (as representation of heat exchangers): partial differential equations for,
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Partial differential equations for interpenetrating continua

DOI 10.1615/hedhme.a.000099

1.2 DEFINITIONS AND RELATIONSHIPS
1.2.6 Partial Differential Equations for Interpenetrating Continua

D. Brian Spalding

A. INTRODUCTION

The differential equations given in Section 98 are useful if the two fluids flow in parallel or counter flow, or in some combination of these. They cannot be used, however, in cross-flow situations, for these give rise to 2D or 3D temperature variations, see Section 101.

The task of the present section is to develop the differential equations that govern the temperature distribution in more complex situations. Mass transfer and phase-change effects will be neglected for simplicity; a more advanced treatment, allowing for these effects, is to be found in Spalding (1980).

It has been common practice for heat exchanger theorists to suppose that they know quantitatively the pattern of flow adopted by the fluids in the equipment, and that their task is to predict the resulting temperature distributions. This is the first level at which the differential equations can be approached: the velocities appearing in them can be regarded as known functions of position.

However, knowledge of actual flow patterns in, say, baffled shells, is in fact very unreliable; little more is known than that the common assumptions are considerably at fault. It therefore becomes desirable to be able to calculate the velocity fields on the basis of the best general information that is available concerning flows in media containing distributed resistances (such as baffles per banks of tubes).

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