Heat transfer energy diffusion

The engineering science of transport phenomena as formulated by Bird, Stewart, and Lightfoot (1) deals with the transfer of momentum, energy, and mass, and provides the tools for solving problems involving fluid flow, heat transfer, and diffusion. It is founded on the great principles of conservation of mass, momentum (Newton s second law), and energy (the first law of thermodynamics).1 These conservation principles can be expressed in mathematical equations in either macroscopic form or microscopic form. 

What we know as a flame involves a large chemical reaction network through which energy is produced, resulting in steep gradients of both molecular concentrations and temperature but the reaction rates and mechanistic paths of that network are sensitively dependent on those parameters. Thus, the chemistry is woven inextricably with heat transfer and diffusion of reactive species through the gas flow. 

The application of an exact analytical approach to frosted systems would be of great value in the study of both the heat transfer and diffusion associated with such systems. An approach of this t3rpe would involve equations of motion, energy equations and continuity equations to describe the mechanisms taking place. A large number of variables would result the use of several assumptions would be necessary to provide a means of simplification and subsequent solution. 

The term e/(e — 1), which appears in equations 1 and 2, was first developed to account for the sensible heat transferred by the diffusing vapor (1). The quantity S represents the group ratio of total transported energy to convective heat transfer. Thus it may be thought of as the fractional... 

In addition to the Burke and Schumann model (34) and the Displacement Distance theory, a comprehensive laminar diffusion flame theory can be written using the equations of conservation of species, energy, and momentum, including diffusion, heat transfer, and chemical reaction. 

An analogy exists between mass transfer by diffusion and heat transfer by conduction. Each involves coHisions between molecules and a gradient as the driving force which causes flow. Eor diffusion, this is a concentration gradient for conduction, the driving force is an energy gradient. Eourier s... 

The input and output terms of equation 1.5-1 may each have more than one contribution. The input of a species may be by convective (bulk) flow, by diffusion of some kind across the entry point(s), and by formation by chemical reaction(s) within the control volume. The output of a species may include consumption by reaction(s) within the control volume. There are also corresponding terms in the energy balance (e.g., generation or consumption of enthalpy by reaction), and in addition there is heat transfer (2), which does not involve material flow. The accumulation term on the right side of equation 1.5-1 is the net result of the inputs and outputs for steady-state operation, it is zero, and for unsteady-state operation, it is nonzero. 

Mass evaporation rate = diffusion transport rate to the air Heat transfer rate = energy required to vaporize... 

Rapid evaporation introduces complications, for the heat and mass transfer processes are then coupled. The heat of vaporization must be supplied by conduction heat transfer from the gas and liquid phases, chiefly from the gas phase. Furthermore, convective flow associated with vapor transport from the surface, Stefan flow, occurs, and thermal diffusion and the thermal energy of the diffusing species must be taken into account. Wagner 1982) reviewed the theory and principles involved, and a higher-order quasisteady-state analysis leads to the following energy balance between the net heat transferred from the gas phase and the latent heat transferred by the diffusing species ... 

One other measurement technique that has been used to measure Kl over a shorter time period, and is thus more responsive to changes in wind velocity, is the controlled flux technique (Haupecker et al., 1995). This technique uses radiated energy that is turned into heat within a few microns under the water surface as a proxy tracer. The rate at which this heat diffuses into the water column is related to the liquid film coefficient for heat, and, through the Prandtl-Schmidt number analogy, for mass as well. One problem is that a theory for heat/mass transfer is required, and Danckwert s surface renewal theory may not apply to the low Prandtl numbers of heat transfer (Atmane et al., 2004). The controlled flux technique is close to being viable for short-period field measurements of the liquid film coefficient. 

Just as diffusive momentum transfer depends on a transport property of the fluid called viscosity, diffusive heat transfer depends on a transport property called thermal conductivity. This section provides a brief discussion on the functional forms of thermal conductivity, with the intent of facilitating the understanding of the heat-transfer discussions in the subsequent sections on the conservation of energy. 

The next task is to develop expressions for the heat-transfer and work terms in Eq. 3.148. We consider two contributions to the heat that crosses the surfaces of a control volume. The first is thermal conduction via Fourier s law, which behaves in the same way for a fluid as it does for a solid. The second contribution is associated with energy that crosses the control surfaces as chemical species diffuse into and out of the control volume. In... 

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