Convection defined

Parker, J. D., Convection Defined, Classified to Aid Problem Solving, Heat Trans., Update—Part 3, Pennwell Publishing Company, July (1980). 

Figure 4.19 shows the kinetics of transfer of the contaminant in the food, under the same conditions as shown in Figure 4.18 (L = 0.03 cm 1 litre liquid), for various values of the coefficient of convection defined by the dimensionless number R.

Heat transfer (e.g., free or forced convection) Defined as boundary condition Correct heat transfer coefficients must be used (analytically calculated)... 

The scan rate, u = EIAt, plays a very important role in sweep voltannnetry as it defines the time scale of the experiment and is typically in the range 5 mV s to 100 V s for nonnal macroelectrodes, although sweep rates of 10 V s are possible with microelectrodes (see later). The short time scales in which the experiments are carried out are the cause for the prevalence of non-steady-state diflfiision and the peak-shaped response. Wlien the scan rate is slow enough to maintain steady-state diflfiision, the concentration profiles with time are linear within the Nemst diflfiision layer which is fixed by natural convection, and the current-potential response reaches a plateau steady-state current. On reducing the time scale, the diflfiision layer caimot relax to its equilibrium state, the diffusion layer is thiimer and hence the currents in the non-steady-state will be higher. 

The solution flow is nomially maintained under laminar conditions and the velocity profile across the chaimel is therefore parabolic with a maximum velocity occurring at the chaimel centre. Thanks to the well defined hydrodynamic flow regime and to the accurately detemiinable dimensions of the cell, the system lends itself well to theoretical modelling. The convective-diffiision equation for mass transport within the rectangular duct may be described by... 

The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

Keeping all of the flow regime conditions identical to the previous example, we now consider a finite element model based on treating silicon rubber as a viscoelastic fluid whose constitutive behaviour is defined by the following upper-convected Maxwell equation... 

The convective heat-transfer coefficient and friction factor for laminar flow in noncircular ducts can be calculated from empirically or analytically determined Nusselt numbers, as given in Table 5. For turbulent flow, the circular duct data with the use of the hydrauhc diameter, defined in equation 10, may be used. 

The time constants characterizing heat transfer in convection or radiation dominated rotary kilns are readily developed using less general heat-transfer models than that presented herein. These time constants define simple scaling laws which can be used to estimate the effects of fill fraction, kiln diameter, moisture, and rotation rate on the temperatures of the soHds. Criteria can also be estabHshed for estimating the relative importance of radiation and convection. In the following analysis, the kiln wall temperature, and the kiln gas temperature, T, are considered constant. Separate analyses are conducted for dry and wet conditions. 

In fossil fuel-fired boilers there are two regions defined by the mode of heat transfer. Fuel is burned in the furnace or radiant section of the boiler. The walls of this section of the boiler are constmcted of vertical, or near vertical, tubes in which water is boiled. Heat is transferred radiatively from the fire to the waterwaH of the boiler. When the hot gas leaves the radiant section of the boiler, it goes to the convective section. In the convective section, heat is transferred to tubes in the gas path. Superheating and reheating are in the convective section of the boiler. The economizer, which can be considered as a gas-heated feedwater heater, is the last element in the convective zone of the boiler. 

The mathematical principles of convective heat transfer are complex and outside the scope of this section. The problems are often so complicated that theoretical handling is difficult, and full use is made of empirical correlation formulas. These formulas often use different variables depending on the research methods. Inaccuracy in defining material characteristics, experimental errors, and geometric deviations produce noticeable deviations between correlation formulas and practice. Near the validity boundaries of the equations, or in certain unfavorable cases, the errors can be excessive. 

First the dimensionless characteristics such as Re and Pr in forced convection, or Gr and Pr in free convection, have to be determined. Depending on the range of validity of the equations, an appropriate correlation is chosen and the Nu value calculated. The equation defining the Nusselt number is... 

The kind of convective heat transfer—forced convection or natural (at floor, wall, or ceiling)—must be considered and taken into account by selecting appropriate values for the convective heat transfer coefficient see Eq. (11.14)). Thus, the heat transfer coefficient implicitly assumes the flow situation at the surface. Normally, coefficients for convective heat transfer are considered as a preset constant parameter (the coefficient may be defined as variable, however, depending on other parameters). Therefore, the selection of appropriate values is crucial. Values for heat transfer coefficients can be found in several references a comprehensive summary is given in Daskalaki. ... 

In the simulation, the time dependency of the energy release of such sources is defined in so-called schedules. The heat sources transfer energy to the room air by convection and to the surfaces by long-wave radiation. In principle, heat sources can be modeled by two kinds of parameterization ... 

The dimensionless numbers are important elements in the performance of model experiments, and they are determined by the normalizing procedure ot the independent variables. If, for example, free convection is considered in a room without ventilation, it is not possible to normalize the velocities by a supply velocity Uq. The normalized velocity can be defined by m u f po //ao where f, is the height of a cold or a hot surface. The Grashof number, Gr, will then appear in the buoyancy term in the Navier-Stokes equation (AT is the temperature difference between the hot and the cold surface) ... 

Zone electrophoresis is defined as the differential migration of a molecule having a net charge through a medium under the influence of an electric field (1). This technique was first used in the 1930s, when it was discovered that moving boundary electrophoresis yielded incomplete separations of analytes (2). The separations were incomplete due to Joule heating within the system, which caused convection which was detrimental to the separation. 

Convective heat transfer occurs when a fluid (gas or liquid) is in contact with a body at a different temperature. As a simple example, consider that you are swimming in water at 21°C (70°F), you observe that your body feels cooler than it would if you were in still air at 21°C (70°F). Also, you have observed that you feel cooler in your automobile when the air-conditioner vent is blowing directly at you than when the air stream is directed away from you. Both ot these observations are directly related to convective heat transfer, and we might hypothesize that the rate of energy loss from our body due to this mode of heat transfer is dependent on not only the temperature difference but also the typie of surrounding fluid and the velocity of the fluid. We can thus define the unit heat transfer for convection, q/A, as follows ... 

Radiative heat transfer is perhaps the most difficult of the heat transfer mechanisms to understand because so many factors influence this heat transfer mode. Radiative heat transfer does not require a medium through which the heat is transferred, unlike both conduction and convection. The most apparent example of radiative heat transfer is the solar energy we receive from the Sun. The sunlight comes to Earth across 150,000,000 km (93,000,000 miles) through the vacuum of space. FIcat transfer by radiation is also not a linear function of temperature, as are both conduction and convection. Radiative energy emission is proportional to the fourth power of the absolute temperature of a body, and radiative heat transfer occurs in proportion to the difference between the fourth power of the absolute temperatures of the two surfaces. In equation form, q/A is defined as ... 

At a convection heat transfer surface the heat flux (heat transfer rate per unit area) is related to the temperature difference between fluid and surface by a heat transfer coefficient. Newton s law of cooling defines this ... 

Overall, the RDE provides an efficient and reproducible mass transport and hence the analytical measurement can be made with high sensitivity and precision. Such well-defined behavior greatly simplifies the interpretation of the measurement. The convective nature of the electrode results also in very short response tunes. The detection limits can be lowered via periodic changes in the rotation speed and isolation of small mass transport-dependent currents from simultaneously flowing surface-controlled background currents. Sinusoidal or square-wave modulations of the rotation speed are particularly attractive for this task. The rotation-speed dependence of the limiting current (equation 4-5) can also be used for calculating the diffusion coefficient or the surface area. Further details on the RDE can be found in Adam s book (17). 

As shown in Fig. 21, in this case, the entire system is composed of an open vessel with a flat bottom, containing a thin layer of liquid. Steady heat conduction from the flat bottom to the upper hquid/air interface is maintained by heating the bottom constantly. Then as the temperature of the heat plate is increased, after the critical temperature is passed, the liquid suddenly starts to move to form steady convection cells. Therefore in this case, the critical temperature is assumed to be a bifurcation point. The important point is the existence of the standard state defined by the nonzero heat flux without any fluctuations. Below the critical temperature, even though some disturbances cause the liquid to fluctuate, the fluctuations receive only small energy from the heat flux, so that they cannot develop, and continuously decay to zero. Above the critical temperature, on the other hand, the energy received by the fluctuations increases steeply, so that they grow with time this is the origin of the convection cell. From this example, it can be said that the pattern formation requires both a certain nonzero flux and complementary fluctuations of physical quantities. 

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