Heat transfer definition

In both convective heat transfer definitions it is presumed that the solid surface is warmer than the fluid so that heat is being transferred from the solid to the fluid. Equations (5.125) and (5.127) are sometimes called Newton s law of cooling but are merely the defining equation for the hk parameters [102, 60, 15]. 

A low temperature of approach for the network reduces utihties but raises heat-transfer area requirements. Research has shown that for most of the pubhshed problems, utility costs are normally more important than annualized capital costs. For this reason, AI is chosen eady in the network design as part of the first tier of the solution. The temperature of approach, AI, for the network is not necessarily the same as the minimum temperature of approach, AT that should be used for individual exchangers. This difference is significant for industrial problems in which multiple shells may be necessary to exchange the heat requited for a given match (5). The economic choice for AT depends on whether the process environment is heater- or refrigeration-dependent and on the shape of the composite curves, ie, whether approximately parallel or severely pinched. In cmde-oil units, the range of AI is usually 10—20°C. By definition, AT A AT. The best relative value of these temperature differences depends on the particular problem under study. 

The definition of the heat-transfer coefficient is arbitrary, depending on whether bulk-fluid temperature, centerline temperature, or some other reference temperature is used for ti or t-. Equation (5-24) is an expression of Newtons law of cooling and incorporates all the complexities involved in the solution of Eq. (5-23). The temperature gradients in both the fluid and the adjacent solid at the fluid-solid interface may also be related to the heat-transfer coefficient ... 

Overall Coefficient of Heat Transfer In testing commercial heat-transfer equipment, it is not convenient to measure tube temperatures (t,3 or t4 in Fig. 5-6), and hence the overall performance is expressed as an overall coefficient of heat transfer U based on a convenient area dA, which may be dAi, oi an average of dAi and dA whence, by definition,... 

Functional Definitions Heat-transfer equipment can be designated by type (e.g., fixed tube sheet, outside packed head, etc.) or by... 

The thermal duty here is the opposite of solidification operations. The indirect heat-transfer equipment suitable for one operation is not suitable for the other because of the material-handling rather than the thermal aspects. Whether the temperature of transformation is a definite or a ranging one is of little importance in the selection of equipment for fusion. The burden is much agitated, but the beds are deep. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

Good heat transfer on the outside of the reactor tube is essential but not sufficient because the heat transfer is limited at low flow rates at the inside film coefficient in the reacting stream. The same holds between catalyst particles and the streaming fluid, as in the case between the fluid and inside tube wall. This is why these reactors frequently exhibit ignition-extinction phenomena and non-reproducibility of results. Laboratory research workers untrained in the field of reactor thermal stability usually observe that the rate is not a continuous function of the temperature, as the Arrhenius relationship predicts, but that a definite minimum temperature is required to start the reaction. This is not a property of the reaction but a characteristic of the given system consisting of a reaction and a particular reactor. 

To simplify the effects of radiation and convection on dry heat transfer, the concept of operative temperature is often used. By definition operative temperature is the temperature of a uniform environment (= MRT) that has the same total dry heat loss (convection + radiation) as the actual environment where MRT. 

B is the heat transfer from Z to the closed cycle within control surface Y, which occurs during the time interval that A/f, the mass of fuel, is supplied and [CV]q is its calorific value per unit mass of fuel for the ambient temperature (Tq) at which the reactants enter. F = A/f[CV]o is equal to the heat (0o) that would be transferred from Z if the products were to leave the control surface at the entry temperature of the reactants, taken as the temperature of the environment, Tq. Fig. 1.7 illustrates the definition of calorific value. 

If the definition of work is limited to mechanical work, an interesting simplification is possible. In this case, AE is merely the heat exchanged at constant volume. This is so because if the volume is constant, no mechanical work can be done on or by the system. Then AE = q. Thus AE is a very useful quantity in constant volume processes. However, chemical and especially biochemical processes and reactions are much more likely to be carried out at constant pressure. In constant pressure processes, AE is not necessarily equal to the heat transferred. For this reason, chemists and biochemists have defined a function that is especially suitable for constant pressure processes. It is called the enthalpy, H, and it is defined as... 

From the definition of thermal conductivity, the heat transferred per unit time through unit area at a distance v from the surface is given by ... 

Now R0 (the shear stress in the fluid at the surface) is equal and opposite to R, the shear stress acting on the surface, —q jQs is by definition the heat transfer coefficient at the surface (h), and (—NA)y=o/ CAjl - CAw) is the mass transfer coefficient ho). Then dividing both sides of equation 12.100 by pu, and of equation 12.101 by u, to make them dimensionless ... 

It should be emphasized that under conditions of energy dissipation the definition of the heat transfer coefficient as k dT/dr)/ T — T ), where T is the average fluid temperature and 7 is the wall temperature, does not characterize the acmal heat transfer properly (Kays and Crawford 1993 Schlichfing 2000). 

From this relationship it is clear that the rate of heat transfer is the product of three factors the overall heat transfer coefficient the area of the hot surface and the temperature drop. If instead of Sj either S2 or Sm had been chosen, one would have obtained the heat transfer coefficients based on these areas, namely, U2 or Um. It follows that a definite area must be chosen and that the overall heat transfer coefficient is automatically based on the chosen area. The choice is, in general, arbitrary. 

The transfer of heat by radiation in general can be said to occur simultaneously with heat transfer by convection and conduction. Transfer by radiation tends to become more important than that by the other two mechanisms as the temperature increases. It is useful to gain an appreciation of the basic definitions of the energy flux terms, the surface property terms and their relationships while discussing radiative heat transfer. With this objective, reference may be made to Table 3.4 in which these are presented. 

Equations (8) are based on the assumption of plug flow in each phase but one may take account of any axial mixing in each liquid phase by replacing the molecular thermal conductivities fc, and ku with the effective thermal conductivities /c, eff and kn eff in the definition of the Peclet numbers. The evaluation of these conductivity terms is discussed in Section II,B,1. The wall heat-transfer terms may be defined as... 

The lack of hydrodynamic definition was recognized by Eucken (E7), who considered convective diffusion transverse to a parallel flow, and obtained an expression analogous to the Leveque equation of heat transfer (L5b, B4c, p. 404). Experiments with Couette flow between a rotating inner cylinder and a stationary outer cylinder did not confirm his predictions (see also Section VI,D). At very low rotation rates laminar flow is stable, and does not contribute to the diffusion process since there is no velocity component in the radial direction. At higher rotation rates, secondary flow patterns form (Taylor vortices), and finally the flow becomes turbulent. Neither of the two flow regimes satisfies the conditions of the Leveque equation. 

For the conditions cited, it was shown that jD was 0.235 and, by the Chilton-Colburn analogy Jh = 0.235. From the definition of the heat transfer factor jH, it follows that... 

With this definition, a heat transfer efficiency of 100% implies that the temperature of the off-gas will be the same as the temperature of the bath. The HTE reported in the literature are in the 80-90% range (Ibaraki et al., 1990 Takahashi et al., 1992 Katayama et al., 1993b). Several authors (i.e., Gou et al., 1993, and Gudenau et al., 1993) have indicated that this definition has limitations because the heat losses to the furnace walls... 

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