Transport phenomena heat conduction

The transfer of heat in a fluid may be brought about by conduction, convection, diffusion, and radiation. In this section we shall consider the transfer of heat in fluids by conduction alone. The transfer of heat by convection does not give rise to any new transport property. It is discussed in Section 3.2 in connection with the equations of change and, in particular, in connection with the energy transport in a system resulting from work and heat added to the fluid system. Heat transfer can also take place because of the interdiffusion of various species. As with convection this phenomenon does not introduce any new transport property. It is present only in mixtures of fluids and is therefore properly discussed in connection with mass diffusion in multicomponent mixtures. The transport of heat by radiation may be ascribed to a photon gas, and a close analogy exists between such radiative transfer processes and molecular transport of heat, particularly in optically dense media. However, our primary concern is with liquid flows, so we do not consider radiative transfer because of its limited role in such systems. 

Thermal conduction is the molecular transport of heat energy caused by a temperature gradient. The heat is transported from regions of high temperature towards those at lower temperatures, i.e. in the opposite direction to the temperature gradient. The corresponding law is FOURIER S law. The same phenomenon of transport of energy... 

The Seebeck effect corresponds to the electricity production from a difference of temperature. This effect can be reversible and is the inverse of the Peltier effect, which is the phenomenon of conversion of electric energy into thermal energy (heat). These effects can be superimposed onto the dissipative processes of transport by conduction of electric charges (Joule effect) and to the transport of heat (Fourier equation) which are both irreversible processes. 

The latent heat for vaporisation determines the amount of vapour to be transported from the feed to the permeate side increasing heat for vaporisation increases permeate product. Nevertheless, the amount of latent heat depends on the extent of temperature polarisation and heat conduction (which is heat loss, thus should be minimised).This heat loss is influenced by membrane porosity and membrane thickness, and can be reduced by increasing the membrane thickness. However, such an increase results in a decrease of the resulting mass transfer. As such, this trade-off phenomenon could be solved by identifying and using an optimised thickness. 

Heat conduction is the exchange of heat by the transport of vibrational states (phonons) without any concomitant transport of mass by flow or diffusion. Consequently, pure heat conduction occurs only in solid bodies. The differential equation that defines this phenomenon has the form of a transport equation its solution characterizes the temperature field that causes the heat exchange. The differentia] equation is... 

Microscale thermal transport phenomenon involves complex transfer mechanism of free electrons and phonons. The molecular dynamics and processes are not significant in most of the microscopic engineering applications. However, scale effects become extremely important in system with sudden high heat flux irradiation by laser pulses and some other dimensionally space- and time-governed problems. Anisimov etal. (1974) proposed the first two-step model for microscale conduction as... 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

The thermal diffusion potential, td> arises if an electrochemical system is nonisothermal. This phenomenon is due to the heat transport of ionic species and can be taken into account if the individual ion entropy of transport, conductivity, and activity coefficients of the species of interest are known. Therefore, the thermal diffusion potential depends on the temperature, pressure, and composition of the electrolyte liquid junction. Also, td is a function of the temperature gradient and can be a substantial value from tens to hundreds of millivolts [19]. 

Thermal conduction is the phenomenon by which heat is transported from high- to low-temperature regions of media that are in intimate contact. The ability of a material to transfer heat is described by thermal conductivity, which is a... 

The radiative heat-flux q is generally treated separately from the other heat flux contributions because these physical phenomena are quite different in nature and involve unacquainted mathematics. Besides, the radiative contributions in the bulk of the fluid are limited because this flux is merely a smface phenomenon. Nevertheless, the radiative losses from solid surfaces are often significant in combustion and in particular chemical reactor processes. A brief introduction to the theory of thermal radiation is presented in Sect. 5.2.6. In summary, the heat transport by conduction is generally important in reaction engineering applications. The thermal radiation flux is important in particular cases. The multi-component mixture specific contributions to the total energy flux are usually negligible. 

In order to incorporate the shape of the p>articles (e.g. cylinders) and the interaction between the particles, extensions of this Maxwell model were later developed by (Hamilton and Grosser, 1962) and (Hui et al., 1999). However, these classical models were found to be unable to accurately predict the anomalously high thermal conductivity of nanofluids (Murshed et al., 2008a). Thus, researchers have proposed several mechanisms to explain this phenomenon. For example, (Kebflnski et al., 2002) systematized the four different mechanisms for heat transfer to explain these enhancements, namely (i) Brownian motion of the nanoparticles (ii) liquid layering at the liquid/ particle interphase, (iii) the nature of the heat transport in the nanoparticles and (iv) the effect of nanoparticle clustering. From the analysis made in an exhaustive review paper on nanofluids (Murshed et al., 2008a) and other publications cited, therein, it is our belief that the effect of the particle surface chemistry and the structure of the interphase partide/fluid are the major mechanisms responsible for the unexpected enhancement in nanofluids. 

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