Heat-transfer coefficients for fluids

HEAT-TRANSFER COEFFICIENTS FOR FLUIDS FLOWING INSIDE TUBES FORCED CONVECTION, SENSIBLE HEAT 7.26... 

Select the appropriate heat-transfer coefficient equation. Heat-transfer coefficients for fluids flowing inside tubes or ducts can be calculated using these equations ... 

Select the appropriate heat-transfer coefficient equation. Heat-transfer coefficients for fluids flowing inside helical coils can be calculated with modifications of the equations for straight tubes. The equations presented in Example 7.18 should be multiplied by the factor 1 + 3.5/1, /D,. where Di is the inside diameter and Dc is the diameter of the helix or coil. In addition, for laminar flow, the term (Dc/Dj)1/6 should be substituted for the term (L/Zl)1 3. The Reynolds number required for turbulent flow is 2100[1 + I2(/1,//1C)I/2. ... 

Helical Coils Heat transfer coefficients for fluids flowing inside helical coils can be calculated with modifications of the equations for straight tubes. The equations for straight tubes should be corrected as below ... 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

Estimation of the heat transfer coefficients for forced convection of a fluid in pipes is usually based on empirical expressions. The most well known expression for this purpose is ... 

A software package (MIXER) was developed to determine the heat transfer coefficient for any type of agitator and surface using the value in Table 7-16, fluid physical properties, agitator speed, and diameter. 

Figure 10-50C. Tube-side (inside tubes) liquid film heat transfer coefficient for Dowtherm . A fluid inside pipes/tubes, turbulent flow only. Note h= average film coefficient, Btu/hr-ft -°F d = inside tube diameter, in. G = mass velocity, Ib/sec/ft v = fluid velocity, ft/sec k = thermal conductivity, Btu/hr (ft )(°F/ft) n, = viscosity, lb/(hr)(ft) Cp = specific heat, Btu/(lb)(°F). (Used by permission Engineering Manual for Dowtherm Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

Figure 10-50D. Tube-side (inside pipes or tubes) liquid film heat transfer coefficient for Dowtherm A and E at various temperatures. (Used by permission Engineering Manual for Heat Transfer Fluids, 1991. The Dow Chemical Co.)...

The outer and inner tubes extend from separate stationary tube sheets. The process fluid is heated or cooled by heat transfer to/from the outer tube s outside surface. The overall heat transfer coefficient for the O.D. of the inner tube is found in the same manner as for the double-pipe exchanger. The equivalent diameter of the annulus uses the perimeter of the O.D. of the inner tube and the I.D. of the inner tube. Kem presents calculation details. 

The calculation of every heat transfer coefficient for a refrigeration or air-conditioning system would be a very time-consuming process, even with modern methods of calculation. Formulas based on these factors will be found in standard reference works, expressed in terms of heat transfer coefficients under different conditions of fluid flow [1, 4-8]. 

This expression is applicable only to the region of fully developed flow. The heat transfer coefficient for the inlet length can be calculated approximately, using the expressions given in Chapter 11 for the development of the boundary layers for the flow over a plane surface. It should be borne in mind that it has been assumed throughout that the physical properties of the fluid are not appreciably dependent on temperature and therefore the expressions will not be expected to hold accurately if the temperature differences are large and if the properties vary widely with temperature. 

Obtain by dimensional analysis a functional relationship for the wall heat transfer coefficient for a fluid flowing through a straight pipe of circular cross-section. Assume that the effects of natural convection can be neglected in comparison with those of forced convection. 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy between momentum transfer and mass transfer (equimolecular counterdiffusion) for the turbulent flow of a fluid over a surface. Write down the corresponding analogy for heat transfer. State clearly the assumptions which are made. For turbulent flow over a surface, the film heat transfer coefficient for the fluid is found to be 4 kW/m2 K. What would the corresponding value of the mass transfer coefficient be. given the following physical properties ... 

Optimized microfabrication and advanced assembly led to the use of thin platelets, in an original version 100 pm thick with a 80 pm micro channel depth, so that very thin walls (20 pm in the case sketched) remain for separating the fluids. Therefore, also the total inner reaction volume with respect to the total construction volume or the active internal surface area is very large. The latter surface amounts to 300 cm (for both the heat transfer and reaction sides) at a cubic volume of 1 cm. Indeed, the micro heat exchangers exhibited high heat transfer coefficients for gas [46] and liquid (Figure 3.10) [47, 48] flows. 

The overall heat transfer coefficient for thermal energy exchange between the tube wall and the reacting fluid may be taken as 1.0 x 10 3 cal/cm2-sec-°K. The effective thermal conductivity of the catalyst pellets may be taken as equal to 6.5 x 1CT4 cal/(sec-cm-°C). 

The heat transfer characteristics of liquid-solid fluidised systems, in which the heat capacity per unit volume of the solids is of the same order as that of the fluid are of considerable interest. The first investigation into such a system was carried out by Lemlich and Caldas193, although most of their results were obtained in the transitional region between streamline and turbulent flow and are therefore difficult to assess. Mitson194 and Smith(20) measured heat transfer coefficients for systems in which a number of different solids were fluidised by water in a 50 mm diameter brass tube, fitted with an annular heating jacket. 

De Wasch and Froment (1971) discuss the calculation of the wall heat transfer coefficients for the fluid and gas phases based on a lumped wall heat transfer coefficient. Furthermore, radial heat conduction in the thermal well is neglected since it should be of minor importance for a thin solid well. 

This second method does not lend itself to the development of quantitative correlations which are based solely on true physical properties of the fluids and which, therefore, can be measured in the laboratory. The prediction of heat transfer coefficients for a new suspension, for example, might require pilot-plant-scale turbulent-flow viscosity measurements, which could just as easily be extended to include experimental measurement of the desired heat transfer coefficient directly. These remarks may best be summarized by saying that both types of measurements would have been desirable in some of the research work, in order to compare the results. For a significant number of suspensions (four) this has been done by Miller (M13), who found no difference between laboratory viscosities measured with a rotational viscometer and those obtained from turbulent-flow pressure-drop measurements, assuming, for suspensions, the validity of the conventional friction-factor—Reynolds-number plot.11 It is accordingly concluded here that use of either type of measurement is satisfactory use of a viscometer such as that described by Orr (05) is recommended on the basis that fundamental fluid properties are more readily determined under laminar-flow conditions, and a means is provided whereby heat transfer characteristics of a new suspension may be predicted without pilot-plant-scale studies. 

Equation (46) may lead to predictions of zero or even negative heat transfer coefficients for the authors fluids within the range of Reynolds numbers for which the equation is claimed to be applicable. The parameter y, which is included to account for the deviation from non-Newtonian behavior, has a value of zero for Newtonian fluids and increases gradually toward infinity as the non-Newtonian character increases in the direction of pseudoplasticity. However, the peculiar form of the chosen function of this parameter does not uniquely characterize non-Newtonian behavior it has been shown by Branch (B7) that the term 1 — yv first increases as po/pa increases, then goes through a maximum, and finally decreases, reaching negative values for po/pa > 2.0. 

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