Dominant fluid-solid heat transfer

Dominant fluid-solid mass and heat transfer... 

Different types of heat transfer processes are called modes. The main modes of heat transfer are convection, radiation, and conduction. For a temperature gradient that exists between a surface and a moving fluid, one should use the term convection. The radiation mode of heat transfer is driven by electromagnetic waves emitted from all surfaces of finite temperature, so there is a net heat transfer by radiation between two surfaces at different temperatures. When a temperature gradient exists in a stationary medium, heat fiows under the law of conduction heat transfer. In the case of solid materials, such as polymers, conduction is the dominant mechanism for heat transfer, involving mainly lattice vibrations and, in few cases, the transfer of kinetic thermal energy from one electron to another. 

Convective heat transfer, or convection, is the transfer of heat from one place to another by the movement of fluids, a process that is essentially the transfer of heat via mass transfer. Bulk motion of fluid enhances heat transfer in many physical situations, such as between a solid surface and the fluid. Convection is usually the dominant form of heat transfer in liquids and gases. Although sometimes discussed as a third method of heat transfer, convection is usually used to describe the combined effects of heat conduction within the fluid (diffusion) and heat transference by bulk fluid flow streaming. 

Due to the low permeability of shales, the coefficient of thermal diffusivity is at least a few orders of magnitude greater than the coefficient of fluid diffusivity. Hence, heat transfer in the formation will be dominated by diffusion, and convective transfer by fluid flow may be ignored. Since the coefficient of thermal expansion of pore fluid is much larger (in the order of 100 times) than the coefficient of rock solid, temperature change will result in a change in pore pressure. 

Qe is the energy transferred per imit total area of the particle normal to the direction of heat transfer. The effective thermal conductivities of catalyst pellets are remarkably low because of the pore structure. The contribution of the thermal conductivity of the solid skeleton is little, since the extremely small heat transfer areas existing at solid-solid contact points offer substantial resistance to heat transfer. The gas phase filling the void spaces in the pores also participates in hindering heat conduction experimental results indicate that decreases as Gp increases. At low pressures, when the mean free path of molecules is greater than or equal to pore size, increases with total pressure since free-molecule conduction starts to dominate. There are no general correlations for predicting Ae from the physical properties of the solid and fluid phases involved. An approximate correlation based on the thermal conductivities of the individual phases and the porosity of the particle has been proposed ... 

At high velocities where turbulence dominates, the main body of flowing fluid is well mixed in the direction normal to the flow, minor differences in temperature and concentration can be neglected, and the film concept can be applied. This describes the flow as if all gradients for temperature and concentration are in a narrow film along the interface with the solid (Nernst 1904), and inside the film conduction and diffusion are the transfer mechanisms. This film concept greatly simplifies the engineering calculation of heat and mass transfer. 

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