Surface Energy Balance

Because densification occurs via tire shrinkage of tliennodynamically unstable pores, densification and microstmcture development can be assessed on tire basis of tire dihedral angle, 0, fonned as a result of tire surface energy balance between tire two solid-vapour and one solid-solid interface at tire pore-grain boundary intersection [, 78, 79 and 80],... 

It should be stressed that although these symmetry considerations may allow one to anticipate barriers on reaction potential energy surfaces, they have nothing to do with the thermodynamic energy differences of such reactions. Symmetry says whether there will be symmetry-imposed barriers above and beyond any thermodynamic energy differences. The enthalpies of formation of reactants and products contain the information about the reaction s overall energy balance. 

An equation representing an energy balance on a combustion chamber of two surface zones, a heat sink Ai at temperature T, and a refractory surface A assumed radiatively adiabatic at Tr, inmost simply solved if the total enthalpy input H is expressed as rhCJYTv rh is the mass rate of fuel plus air and Tp is a pseudoadiabatic flame temperature based on a mean specific heat from base temperature up to the gas exit temperature Te rather than up to Tp/The heat transfer rate out of the gas is then H— — T ) or rhCp(T f — Te). The... 

Though this is a quartic equation, it is capable of explicit solution because of the absence of second and third degree terms. Trial-and-error enters, however, because (GSi)r and are mild functions of Tg and related Te, respectively, and aprehminary guess of Tg is necessaiy. An ambiguity can exist in interpretation of terms. If part of the enclosure surface consists of screen tubes over the chamber-gas exit to a convection section, radiative transfer to those tubes is included in the chamber energy balance, but convection is not, because it has no effect on chamber gas temperature. 

A common process task involves heating a slurry by pumping it through a well-stirred tank. It is useful to know the temperature profile of the slurry in the agitated vessel. This information can be used to optimize the heat transfer process by performing simple sensitivity studies with the formulas presented below. Defining the inlet temperature of the slurry as T, and the temperature of the outer surface of the steam coil as U then by a macroscopic mass and energy balance for the system, a simplified calculation method is developed. 

The room model consists of nodes, which are interconnected by heat exchange paths (Fig. 11.36). The nodes represent either surface temperatures of the individual walls or the zone air temperature. For each node, an energy balance is formulated. From the resulting set of equations, the temperatures and heat fluxes can be determined. 

Summerfield writes the energy balance at the propellant surface as... 

For the more complex case of a multi-sided enclosure formed from n surfaces, the radiosities may be obtained from an energy balance for each surface in turn in the enclosure. Thus the energy falling on a typical surface i in an enclosure formed from... 

The value of the integral in the energy balance (equation 11.55) is again given by equation 11.60 [substituting (6S - 8o) for 0 ]. The heat flux q0 at the surface is now constant, and the right-hand side of equation 11.55 may be expressed as (—qa/Cf,p). Thus, for constant surface heat flux, equation 11.55 becomes ... 

Evapotranspiration (ET) is the collective term for land surface evaporation and plant transpiration, which are difficult to isolate in practice. Transpiration refers to the process in which water is transported through plants and returned to the atmosphere through pores in the leaves called stomata, and is distinct from direct evaporation of intercepted precipitation from leaf surfaces. Some land surface processes and the roles of vegetation in the water and energy balances are illustrated in Fig. 6-5. Due to... 

Eor saturated surfaces, the Bowen ratio can then be used to calculate evapotranspiration as a residual of the surface energy balance (Penman, 1948). Since direct measurement of ET is difficult and expensive, the energy balance method is fairly common. 

This section is concerned with the UA xtiT — Text) term in the energy balance for a stirred tank. The usual and simplest case is heat transfer from a jacket. Then A xt refers to the inside surface area of the tank that is jacketed on the outside and in contact with the fluid on the inside. The temperature difference, T - Text, is between the bulk fluid in the tank and the heat transfer medium in the jacket. The overall heat transfer coefficient includes the usual contributions from wall resistance and jacket-side coefficient, but the inside coefficient is normally limiting. A correlation applicable to turbine, paddle, and propeller agitators is... 

Among the components of our atmosphere, the concentration of carbon dioxide is a mere 325 parts per million (ppm). In other words, 999,675 of every million molecules in the air are not CO2. (Almost all the molecules are N2 or O2.) At such a low concentration, how could CO2 possibly cause a measurable change in the Earth s surface temperature The answer lies in the role that minor atmospheric species play in the global energy balance. 

Heat losses. For the majority of cases, heat losses to the environment from hot surfaces will be small compared to other heat duties and can be neglected. Occasionally, it might be necessary to accept a significant heat loss and to account for it in the energy balance. If the heat loss is from a cold stream, then it should be included with the process duty, as the heat loss must be serviced either from heat recovery or hot utility. If the loss is from a hot stream, the heat loss can be accounted for by splitting the stream from which the heat loss is occurring into two components the process duty and the heat loss. The heat loss should then be left out of the analysis if the heat loss from the hot stream is to be accepted. 

In order to use these equations, however, the local temperatures and pressures must be known. Equation 13.2.16 can be used to evaluate the latter parameter, while an energy balance on the reacting fluid gives the temperature. If the temperature difference between the bulk fluid and the external surface of the catalyst pellets is neglected for the reasons noted earlier, the energy balance on the reacting fluid can be written as ... 

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