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McNaught, J M,
Macdonald equation, for fixed-bed pressure drop,
Mach number,
Macleod-Sugden method for surface tension
Macrolayer consumption model for critical heat flux in pool boiling,
Maddox, R N
Magnetic fields, effect on properties of rheologically complex materials,
Magnetic devices, for fouling mitigation,
Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems,
Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for,
Marlotherm, heat transfer media,
Martensitic stainless steels,
Martin, H
Martinelli and Boelter equations for combined free and forced convection,
Martinelli and Nelson correlations:
Mass absorption coefficient,
Mass extinction coefficient,
Mass fraction, in multicomponent mixtures,
Mass scattering coefficient,
Mass transfer:
Mass transfer coefficient:
Materials of construction, for heat exchangers,
Low temperature operation, ASME VIII code guidelines for,
Matovosian, Robert,
Matrix inversion techniques, in radiative heat transfer,
Maximum drag reduction
Maximum velocities (in shell-and-tube heat exchangers)
Maxwell model, for non-Newtonian fluid,
Maxwell-Stefan equations, for multicomponent diffusion,
Maxwell's equations, for electromagnetic radiation,
Mean beam length concept, in radiative heat transfer:
Mean phase content,
Mean temperature difference:
application in shell-and-tube heat exchangers,
effective, in kettle reboilers,
F-factor correction method for,
in condensers,
in double pipe heat exchangers,
Measurement of fouling resistance,
Mechanical design of heat exchangers:
Mechanical draft cooling towers,
Mechanical loads, specifications in EN13445,
Mechanical vapour compression cycles in refrigeration,
Mediatherm, heat transfer medium,
Melo, L F,
Melting, thermal conduction in,
Melting point:
Mercury:
Merilo correlation, for critical heat flux in horizontal tubes,
Merkel's equation, in cooling tower design,
Mertz, R,
Metais and Eckert diagrams, for regimes of convection:
Metals:
Metallurgical industry, kilns and furnaces for,
Metastable equilibrium, of vapor and liquid,
Methane:
Methanol:
Methyl acetate:
Methylacetylene:
Methyl acrylate:
Methyl amine
n-Methylaniline:
Methyl benzoate:
2-Methyl-1,3-Butadiene (Isoprene):
2-Methylbutane (isopentane):
Methylbutanoate:
2-Methyl-2-butene:
Methylcyclohexane:
Methylcyclopentane:
Methylethylketone:
Methyl formate:
Metallurgical slag, use of submerged combustion in reprocessing of,
Methyl fluorate:
2-Methylhexane:
Methylisobutylketone:
Methylmercaptan:
1-Methylnaphthalene:
2-Methylnaphthalene:
2-Methylpentane:
3-Methylpentane:
2-Methylpropane (isobutane):
2-Methylpropene:
Methyl propionate:
Methylpropylether:
Methylpropyl ketone:
Methyl salicylate:
Methyl-t-butyl ether:
Microbubbles, for drag reduction,
Microchannels (see also microfluidics)
Micro-fin tubes:
Microfluidics, enhancement of heat transfer in,
Mie scattering, in pulverized coal combustion,
Miller, C J
Miller, E R
Mineral oils, as heat transfer media, physical properties of,
Mineral wool production, submerged combustion systems for,
Minimum fluidization velocity,
Minimum heat flux in pool boiling:
Minimum tubeside velocity, in shell-and-tube heat exchangers,
Minimum velocity for fluidization,
Minimum wetting rate, for binary mixtures,
Mirror-image concept, in radiative heat transfer,
Mirrors, spectral characteristics of reflectance from,
Mishkinis, D,
Mist flow:
Mitigation of fouling,
Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for,
Mixing (shell-side), in twisted tube heat exchangers,
Mixing length, in turbulent flow,
Mixtures:
Modelling, of fouling:
Models, theory of,
Modulus of elasticity:
Moffat, R S M,
Molecular gas radiation properties,
Molecular weight:
Mollier chart, for humid air,
Momentum equation:
Monitoring, on line, of fouling,
Monochloroacetic acid:
Monte Carlo methods, in radiative heat transfer,
Moody chart:
Morris, M
Mostinski correlations:
Moving bed, heat transfer to,
Muchowski, E,
Mueller, A C
Muller-Steinhagen, H
Multicomponent mixtures:
Multidimensional systems, heat conduction in,
Multiflux methods, for radiative heat transfer in nonisothermal gases,
Multipass shell-and-tube heat exchangers,
Multiphase fluid flow and pressure drop:
Multiple duties, in plate heat exchangers,
Multiple effect evaporation,
Multiple hairpin heat exchanger,
Multistage flash evaporation (MSF)
Multizone model, for furnaces,
Index
HEDH
A
B
C
D
E
F
G
H
I
J
K
L
M
McNaught, J M,
Macdonald equation, for fixed-bed pressure drop,
Mach number,
Macleod-Sugden method for surface tension
Macrolayer consumption model for critical heat flux in pool boiling,
Maddox, R N
Magnetic fields, effect on properties of rheologically complex materials,
Magnetic devices, for fouling mitigation,
Magnetohydrodynamcs, inaugmentation of heat transfer in microfluidic systems,
Margarine manufacture, crystallization of edible oils and fats in, scraped surface heat exchangers for,
Marlotherm, heat transfer media,
Martensitic stainless steels,
Martin, H
Martinelli and Boelter equations for combined free and forced convection,
Martinelli and Nelson correlations:
Mass absorption coefficient,
Mass extinction coefficient,
Mass fraction, in multicomponent mixtures,
Mass scattering coefficient,
Mass transfer:
Mass transfer coefficient:
Materials of construction, for heat exchangers,
Low temperature operation, ASME VIII code guidelines for,
Matovosian, Robert,
Matrix inversion techniques, in radiative heat transfer,
Maximum drag reduction
Maximum velocities (in shell-and-tube heat exchangers)
Maxwell model, for non-Newtonian fluid,
Maxwell-Stefan equations, for multicomponent diffusion,
Maxwell's equations, for electromagnetic radiation,
Mean beam length concept, in radiative heat transfer:
Mean phase content,
Mean temperature difference:
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
application in shell-and-tube heat exchangers,
effective, in kettle reboilers,
F-factor correction method for,
in condensers,
in double pipe heat exchangers,
Measurement of fouling resistance,
Mechanical design of heat exchangers:
Mechanical draft cooling towers,
Mechanical loads, specifications in EN13445,
Mechanical vapour compression cycles in refrigeration,
Mediatherm, heat transfer medium,
Melo, L F,
Melting, thermal conduction in,
Melting point:
Mercury:
Merilo correlation, for critical heat flux in horizontal tubes,
Merkel's equation, in cooling tower design,
Mertz, R,
Metais and Eckert diagrams, for regimes of convection:
Metals:
Metallurgical industry, kilns and furnaces for,
Metastable equilibrium, of vapor and liquid,
Methane:
Methanol:
Methyl acetate:
Methylacetylene:
Methyl acrylate:
Methyl amine
n-Methylaniline:
Methyl benzoate:
2-Methyl-1,3-Butadiene (Isoprene):
2-Methylbutane (isopentane):
Methylbutanoate:
2-Methyl-2-butene:
Methylcyclohexane:
Methylcyclopentane:
Methylethylketone:
Methyl formate:
Metallurgical slag, use of submerged combustion in reprocessing of,
Methyl fluorate:
2-Methylhexane:
Methylisobutylketone:
Methylmercaptan:
1-Methylnaphthalene:
2-Methylnaphthalene:
2-Methylpentane:
3-Methylpentane:
2-Methylpropane (isobutane):
2-Methylpropene:
Methyl propionate:
Methylpropylether:
Methylpropyl ketone:
Methyl salicylate:
Methyl-t-butyl ether:
Microbubbles, for drag reduction,
Microchannels (see also microfluidics)
Micro-fin tubes:
Microfluidics, enhancement of heat transfer in,
Mie scattering, in pulverized coal combustion,
Miller, C J
Miller, E R
Mineral oils, as heat transfer media, physical properties of,
Mineral wool production, submerged combustion systems for,
Minimum fluidization velocity,
Minimum heat flux in pool boiling:
Minimum tubeside velocity, in shell-and-tube heat exchangers,
Minimum velocity for fluidization,
Minimum wetting rate, for binary mixtures,
Mirror-image concept, in radiative heat transfer,
Mirrors, spectral characteristics of reflectance from,
Mishkinis, D,
Mist flow:
Mitigation of fouling,
Mixed convection occurrence in horiozntal circular pipe, Metais and Eckert diagram for,
Mixing (shell-side), in twisted tube heat exchangers,
Mixing length, in turbulent flow,
Mixtures:
Modelling, of fouling:
Models, theory of,
Modulus of elasticity:
Moffat, R S M,
Molecular gas radiation properties,
Molecular weight:
Mollier chart, for humid air,
Momentum equation:
Monitoring, on line, of fouling,
Monochloroacetic acid:
Monte Carlo methods, in radiative heat transfer,
Moody chart:
Morris, M
Mostinski correlations:
Moving bed, heat transfer to,
Muchowski, E,
Mueller, A C
Muller-Steinhagen, H
Multicomponent mixtures:
Multidimensional systems, heat conduction in,
Multiflux methods, for radiative heat transfer in nonisothermal gases,
Multipass shell-and-tube heat exchangers,
Multiphase fluid flow and pressure drop:
Multiple duties, in plate heat exchangers,
Multiple effect evaporation,
Multiple hairpin heat exchanger,
Multistage flash evaporation (MSF)
Multizone model, for furnaces,
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Mean Temperature Difference
DOI 10.1615/hedhme.a.000267
3.4.8 Mean temperature difference
A. C. Mueller
For the simple case of condensation at constant temperature and constant overall coefficient in a singlepass arrangement, the logarithmic mean temperature difference is used. When stepwise calculations are made, the local temperature difference is used with the local overall coefficients and is integrated numerically. In a multipass arrangement it is necessary to use the local overall coefficient and local temperature difference for each pass. Iterative calculations are required in order to have the stream temperatures match at the turn-around. Computers can be programmed to perform such calculations. For shell-side condensation and assuming that the overall coefficient is constant for each pass at a given location along the shell, Butterworth (1977) has proposed the following calculation procedure.
The presentation assumes that temperature-enthalpy curves for the two fluid streams are already available. Capital letters are used to denote the shell-side stream and lowercase letters denote the tube side. Figure 1 shows a typical T-H curve for the shell-side stream. The tube-side temperatures may be plotted on this diagram by integrating numerically the equation
\[\label{eq1} \frac{dh^{II}}{dh^{I}} = \frac{T - t^{II}}{T - t^{I}}\tag{1}\]
A simple numerical form of this is
\[\label{eq2} {h^{II}_{\rm new}} = {h^{II}_{\rm old}} - \Delta h^{I} \frac{T - t^{II}}{T - t^{I}}\tag{2}\]
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