Liquid thermal energy conducted

The physical mechanism of thermal-energy conduction in liquids is qualitatively the same as in gases however, the situation is considerably more complex because the molecules are more closely spaced and molecular force fields exert a strong influence on the energy exchange in the collision process. Thermal conductivities of some typical liquids are shown in Fig. 1-5. 

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 ... 

When an atom or molecule receives sufficient thermal energy to escape from a liquid surface, it carries with it the heat of vaporization at the temperature at which evaporation took place. Condensation (return to the liquid state accompanied by the release of the latent heat of vaporization) occurs upon contact with any surface that is at a temperature below the evaporation temperature. Condensation occurs preferentially at all points that are at temperatures below that of the evaporator, and the temperatures of the condenser areas increase until they approach the evaporator temperature. There is a tendency for isothermal operation and a high effective thermal conductance. The steam-heating system for a building is an example of this widely employed process. 

In Chapter 1 heal conduction was defined as the transfer of thermal energy from the more energetic particles of a medium to the adjacent less energetic ones. It was stated that conduction can take place in liquid.s and gases as well as solids provided that there is no bulk motion involved. 

Further, A5, Gb and Gi denote thermal conductivities and temperature gradients in the liquid and solid, and D the solute diffusivity in the liquid. m = dTjdCoo and k are volumetric latent heat of fusion, liquidus slope and interfacial distribution coefficient. G o is the concentration far from the interface and F = Tmlsi/Ly the Gibbs-Thompson parameter based on the solid liquid interfacial energy 7 / and melting temperature Tm is the solidification velocity and uj = 27t/A the wave number of a perturbation. 

D. Most heat is transferred because the cup of hot chocolate is in direct contact with the hands. This movement of thermal energy between two objects in direct contact is conduction. However, within the cup, the hot chocolate nearest the edges will be cooler (as heat is transferred through the cup to the hands) and this will cause warmer liquid in the center of the cup to move towards the edges. This is convection. 

Answer The mass transfer calculation is based on the normal component of the total molar flux of species A, evaluated at the solid-liquid interface. Convection and diffusion contribute to the total molar flux of species A. For thermal energy transfer in a pure fluid, one must consider contributions from convection, conduction, a reversible pressure work term, and an irreversible viscous work term. Complete expressions for the total flux of speeies mass and energy are provided in Table 19.2-2 of Bird et al. (2002, p. 588). When the normal component of these fluxes is evaluated at the solid-liquid interface, where the normal component of the mass-averaged velocity vector vanishes, the mass and heat transfer problems require evaluations of Pick s law and Fourier s law, respectively. The coefficients of proportionality between flux and gradient in these molecular transport laws represent molecular transport properties (i.e., a, mix and kxc). In terms of the mass transfer problem, one focuses on the solid-liquid interface for x > 0 ... 

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