Heat transfer in the fluid

Convection is the heat transfer in the fluid from or to a surface (Fig. 11.28) or within the fluid itself. Convective heat transport from a solid is combined with a conductive heat transfer in the solid itself. We distinguish between free and forced convection. If the fluid flow is generated internally by density differences (buoyancy forces), the heat transfer is termed free convection. Typical examples are the cold down-draft along a cold wall or the thermal plume upward along a warm vertical surface. Forced convection takes place when fluid movement is produced by applied pressure differences due to external means such as a pump. A typical example is the flow in a duct or a pipe. 

Bi very large. The resistance to heat transfer in the fluid is then low compared with that in the solid with the temperature of the surface of the particle being approximately equal to the bulk temperature of the fluid, and the heat transfer rate is independent of the Biot number. Equation 9.44 then simplifies to ... 

The effect of axial conduction on heat transfer in the fluid in the micro-channel can be characterized by a dimensionless parameter... 

FIGURE 11 Cross section of a heat exchanger tube, with convective heat transfer in the fluids and fouling deposits on the surfaces. 

Now, if the longitudinal heat transfer in the fluid is neglected, the energy equation for fully developed constant fluid property turbulent pipe flow can be written as ... 

Conjugate Heat Transfer to Moving Materials. In the previous two subsections, the thickness of the material was assumed to be small, so that the controlling resistance was on the fluid side therefore, the thermal coupling between heat transfer within the moving material and the convective flow and heat transfer in the fluid could be neglected. However, in many... 

Some analytical solutions of boundary layer flows have been used to deduce the relationships between the heat transfer coefficient and the flow properties. For example, fluid flow over heated surfaces develops two boundary layer thicknesses, that is, the hydrodynamic boundary layer and the thermal boundary layer. When these two layers coincide, then, Pr = 1. For flow over a flat surface the condition of "no slip" at the wall suggests that the heat transfer in the fluid directly contacting the wall, that is, in the thin layer adjacent to the wall, occurs by pure conduction. Therefore the heat flux is given by... 

In this analysis F will be constant but it could be described more accurately as a function of parameters influencing heat transfer in the condenser (temperature, pressure, flow rate, fluid thermodynamical, and thermophysical characteristics. . . ). 

Where heat transfer is taking place at the saturation temperature of a fluid, evaporation or condensation (mass transfer) will occur at the interface, depending on the direction of heat flow. In such cases, the convective heat transfer of the fluid is accompanied by conduction at the surface to or from a thin layer in the liquid state. Since the latent heat and density of fluids are much greater than the sensible heat and density of the vapour, the rates of heat transfer are considerably higher. The process can be improved by shaping the heat exchanger face (where this is a solid) to improve the drainage of condensate or the escape of bubbles of vapour. The total heat transfer will be the sum of the two components. 

For the common problem of heat transfer between a fluid and a tube wall, the boundary layers are limited in thickness to the radius of the pipe and, furthermore, the effective area for heat flow decreases with distance from the surface. The problem can conveniently be divided into two parts. Firstly, heat transfer in the entry length in which the boundary layers are developing, and, secondly, heat transfer under conditions of fully developed flow. Boundary layer flow is discussed in Chapter 11. 

Virtual prototyping will be the future method to develop new reactors and chemical processes. With a good description of the fluid dynamics, and mass and heat transfer in the reactor, the specific chemical reactions and physical properties of the fluid can be changed and a process optimization can be performed in virtual... 

In addition to simply solving the differential equation, we seek to use the solution to understand and quantify the heat transfer between the fluid and the duct walls. The heat flux q" (W/m2) can be described in terms of a heat-transfer coefficient h (W/m2 K), with the thermal driving potential being the difference between the wall temperature and the mean fluid temperature ... 

A distinctive feature of fluidized beds is a high rate of heat transfer between the fluid and immersed surfaces. Some numerical values are shown on Figure 17.37. For comparison, air in turbulent flow in pipelines has a coefficient of about 25 Btu/(hr)(sqft)(°F). (a) is of calculations from several correlations of data for the conditions identified in Table 17.19 (b) shows the effect of diameters of quartz particles and (c) pertains to 0.38 mm particles of several substances. 

Ya.B. s early works (4, 5) were strikingly deep and far ahead of their time. It is difficult to imagine that their author was a young man of 23. In the first of these papers (4) he established the extremum property of heat transfer in a fluid at rest, analogous to the well-known extremum property of dissipation for viscous fluid flows. But what is remarkable here is not only the classically simple result. In this paper a very important physical quantity appeared for the first time— the rate of decay of temperature inhomogeneities —which plays for the temperature field exactly the same role as does the rate of energy dissipation for the velocity field in a viscous fluid. 

Fluid dynamics in a tubular fuel cell has significant effects on different other phenomena such as the electrochemical reactions, which need species to be transported to the reaction site, and mass and heat transfer. In the porous structures, an equation that accounts for the fluid flowing in the pores - such as Brinkman s or Darcy s equations (Equation (3.4)) - must be used usually the velocities are low. Fluid-dynamic is modelled through Navier-Stokes equation in the channels (Equation (3.3)). 

S. Syrjala, On the Analysis of Fluid Flow and Heat Transfer in the Melt Conveying Section of a Single Screw Extruder, Num. Heat Trans., Part A, 35, 25-4-1 (1999). 

The performance of a fluidized bed combustor is strongly influenced by the fluid mechanics and heat transfer in the bed, consideration of which must be part of any attempt to realistically model bed performance. The fluid mechanics and heat transfer in an AFBC must, however, be distinguished from those in fluidized catalytic reactors such as fluidized catalytic crackers (FCCs) because the particle size in an AFBC, typically about 1 mm in diameter, is more than an order of magnitude larger than that utilized in FCC s, typically about 50 ym. The consequences of this difference in particle size is illustrated in Table 1. Particle Reynolds number in an FCC is much smaller than unity so that viscous forces dominate whereas for an AFBC the particle Reynolds number is of order unity and the effect of inertial forces become noticeable. Minimum velocity of fluidization (u ) in an FCC is so low that the bubble-rise velocity exceeds the gas velocity in the dense phase (umf/cmf) over a bed s depth the FCC s operate in the so-called fast bubble regime to be elaborated on later. By contrast- the bubble-rise velocity in an AFBC may be slower or faster than the gas-phase velocity in the emulsion... 

Regarding mass transfer, the slowest step is normally pore diffusion rather than external mass transfer, whilst for heat transfer the slowest step is the interphase heat transfer between the particle and the fluid phase rather than the internal heat transfer in the solid particle. 

When a fluid is present in contact with each solid wall, there will be an additional resistance to heat transfer in each fluid boundary layer or film . The combined mechanism of heat transfer from a hot fluid through a dividing wall to a cold fluid has many similarities to conduction through a composite slab reviewed earlier. 

The increase in enthalpy of the thermometer is equal to the rate of heat transfer from the fluid, or ... 

Because there is no heat transfer in the initial portion of the duct flow, the fluid will have a uniform temperature, Te at the point at which heat transfer starts, i.e. ... 

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