Calculation of heat transfer

This result suggests the heat transfer coefficient a can be defined by 

The local Nusselt number formed with this heat transfer coefficient 

Example 3.16 Air at pressure 0.1 MPa and temperature 20 °C flows at a velocity of 600 m/s over aim long and lm wide, flat plate whose temperature is maintained at 60 °C. Calculate the heat transferred. 

First of all we calculate the Reynolds number at the end of the plate, to ascertain whether the flow there is laminar or turbulent. The reference temperature for the material properties is ( 0 + As)/2 = (60 + 20) °C/2 = 40 °C. With that 

The flow at the end of the plate is turbulent, at the start of the plate it is laminar. Furthermore 

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Liquid viscosity is one of the most difficult properties to calculate with accuracy, yet it has an important role in the calculation of heat transfer coefficients and pressure drop. No single method is satisfactory for all temperature and viscosity ranges. We will distinguish three cases for pure hydrocarbons and petroleum fractions ... 

Pressure losses due to pipe friction can be calculated from the basic formulas established by Reynolds and others. However, as with the calculation of heat transfer factors, this would be a time-consuming process and some of the parameters are not known accurately. Recourse is usually made to simplified estimates or tables published in works of reference [32, 33]. 

The calculation of heat transfer film coefficients in an air-lift bioreactor is more complex, as small reactors may operate under laminar flow conditions whereas large-scale vessels operate under turbulent flow conditions. It has been found that under laminar flow conditions, the fermentation broths show non-Newtonian behaviour, so the heat transfer coefficient can be evaluated with a modified form of the equation known as the Graetz-Leveque equation 9... 

At the conceptual stage for heat exchanger network synthesis, the calculation of heat transfer coefficients and pressure drops should depend as little as possible on the detailed geometry. However, some assumptions must be made regarding the geometry. 

At the conceptual stage for heat exchanger network synthesis, the calculation of heat transfer coefficient and pressure drop should depend as little as possible on the detailed geometry. Simple models will be developed in which heat transfer coefficient and pressure drop are both related to velocity1. It is thus possible to derive a correlation between the heat transfer coefficient, pressure drop and the surface area by using velocity as a bridge between the two1. 

Heat transfer mechanisms in dense fluids calculation of heat-transfer coefficients in different arrangements... 

A knowledge of the thicknesses of flowing liquid films is of importance in a wide range of practical problems involving film flow. Such problems include the calculation of heat transfer in evaporators and condensers, mass transfer in film-type equipment, the design of overflows and downcomers, etc. 

Extensive data on liquid metals are given in Ref. 13, and the heat-transfer characteristics are summarized in Ref. 23. Lubarsky and Kaufman [14] recommended the following relation for calculation of heat-transfer coefficients in fully developed turbulent flow of liquid metals in smooth tubes with uniform heat flux at the wall ... 

All properties for use in Eq. (6-45) are evaluated at the bulk temperature. Equation (6-45) is valid for 102 < Pe < 104 and for Lid > 60. Seban and Shi. mazaki [16] propose the following relation for calculation of heat transfer to liquid metals in tubes with constant wall temperature ... 

How do you solve heat energy problems using Q = mcATl Go back to the ThoughtLab. Some of the data in this ThoughtLab can be used to illustrate the calculation of heat transfer, as shown below. 

Since the velocity profile in bubble columns is known, the procedure for the calculation of heat transfer coefficient can be developed on a more rational basis. Substitution of Equation (4) in (1) gives ... 

The discussions above on the local heat transfer coefficients arc insightful however, they are of limited value in heal transfer calculations since the calculation of heat transfer requires the average heat transfer coefficient over the entire. surface. Of the several such relations available in the literature for the average Nusselt number for cross flow over a cylinder, we present the one proposed by Churchill and Bernstein ... 

In 1916, Nusselt [4.2] had already put forward a simple theory for the calculation of heat transfer in laminar film condensation in tubes and on vertical or inclined walls. This theory is known in technical literature as Nusselt s film condensation theory. It shall be explained in the following, using the example of condensation on a vertical wall. 

In the calculation of heat transfer in the transition region between laminar and turbulent film condensation, empirical interpolation formulae are well established. One of these types of formulae is... 

Several theories on dropwise condensation have been developed for the calculation of heat transfer. One of the oldest theories, that from Eucken [4.33], starts with the concept that the first droplets arise from an adsorbed monomolecular condensate layer, this layer is favoured by nuclei, and that the new condensate flows to the droplets by means of surface diffusion which primarily occurs at the edge of the drop. This theory was taken on later by other authors [4.34],... 

Whilst heat transfer in convection can be described by physical quantities such as viscosity, density, thermal conductivity, thermal expansion coefficients and by geometric quantities, in boiling processes additional important variables are those linked with the phase change. These include the enthalpy of vaporization, the boiling point, the density of the vapour and the interfacial tension. In addition to these, the microstructure and the material of the heating surface also play a role. Due to the multiplicity of variables, it is much more difficult to find equations for the calculation of heat transfer coefficients than in other heat transfer problems. An explicit theory is still a long way off because the physical phenomena are too complex and have not been sufficiently researched. 

Calculation of heat transfer coefficients for boiling in free flow... 

Richter, W. "Parametric Screening Studies for the Calculation of Heat Transfer in Combustion Chambers" Topical Report, prepared for Pittsburgh Energy Technology Center, Department of Energy, Under Contract No. DE-AC22-80PC30297, 1982. 

Mostinski, I. L., Calculation of Heat Transfer and Critical Heat Eluxes in Liquids, Teploenergetika 10 (4), 66 (1963). 

For calculation of heat transfer coefficients, the Chilton-Colburn analogy is applied. From Figure 9.22 it can be concluded that jr/ju O.l and consequently from eq. (9.327) the heat transfer coefficient is obtained... 

Conductivity (Thermal) - This is a positive constant, k, that is a property of a substance and is used in the calculation of heat transfer rates for materials. It is the amount of heat that flows through a specified area and thickness of a material over a specified period of time when there is a temperature difference of one degree between the surfaces of the material. 

The following example illustrates the calculation of heat transfer area for different flow arrangements. 

Hepworth Refractories Limited, Calculation of heat transfer through refractory structures by GR Stein Refractories using ASTM calculation procedure. 

Chlorine is produced as a hot, wet cell gas. Its temperature leaving the cells usually is greater than 85°C, and it is saturated with water at its vapor pressure over the anolyte. Nearly all applications require cooling of this gas, which causes partial condensation of the contained water vapor. Two basically different methods of cooling are in common use, based on direct and indirect contact with the coolant. These are dealt with in Sections 9.1.3.3 and 9.1.3.4. Before considering these techniques, we review methods of calculation of heat-transfer rates and the effects of simultaneous mass transfer on the heat transfer process (Sections 9.1.3.1 and 9.1.3.2). 

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