Heat transfer coefficients definition

A direct numerical relationship between heat and momentum fluxes, as for the simple Reynolds analogy for a single phase, is not obtained in this case because of a basic and significant difference in heat transfer coefficient definitions. For singlephase flow in pipes, the mixed mean or integrated average temperature is used in... 

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 ... 

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... 

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 problem of burn-out prediction is a difficult one, and one on which a great deal of experimental work is being carried out, particularly in connection with nuclear-reactor development. Much of the earlier literature is rather confused, due to the fact that the mechanics of the burn-out were not carefully defined. Silvestri (S8) has discussed the definitions applicable to burn-out heat flux. It appears possible to define two distinctly different kinds of burn-out, one due to a transition from nucleate to film boiling, and one occurring at the liquid deficient point of the forced-convection region. The present discussion treats only the latter type of burn-out fluxes. The burn-out point in this instance is usually determined by the sudden rise in wall temperature and the corresponding drop in heat flux and heat-transfer coefficient which occur at high qualities. 

Unlike Fourier s Law, Eq. (4.62) is purely empirical—it is simply the definition for the heat transfer coefficient. Note that the units of he (W/m -K) are different from those for thermal conductivity. Under steady-state conditions and assuming that the heat transfer area is constant and h is not a function of temperature, the following form of Eq. (4.62) is often employed ... 

Earlier it,was noted that a definite relationship exists between the heat transfer coefficient and the mass transfer coefficient. Chilton and Colburn [10] developed Equation 3.31, which will be restated here ... 

Thermal resistance due to fouling has to be included in the calculation of the overall heat transfer coefficient. By definition, the overall heat transfer coefficient is the reciprocal of the overall thermal resistance. Thus, including the thermal resistance due to fouling, it follows... 

The heat transfer rate, q, is taken as positive in the direction wall-to-fluid so that it will have the same sign as(Tw -T/) and h will always, therefore, be positive. A number of names have been applied to h including convective heat transfer coefficient , heat transfer coefficient , film coefficient , film conductance , and unit thermal convective conductance . The heat transfer coefficient, h, has the units W/m2-K or, since its definition only involves temperature differences, W/m2oC, in the SI system of units. In the imperial system of units, h has the units Btu/ft2-hr-°F. 

Solution. The definition of the mean heat transfer coefficient gives ... 

This relation immediately suggests the definition of the heat-transfer coefficient for the case where viscous heating is important by the relation... 

In Eq. (5-37), W is defined in terms of the heat-transfer coefficient across the wall instead of an over-all coefficient to the average temperature in the cross section of the tube. The definition is... 

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