Temperature Field in N=4 Geometry

To calculate the development of the temperature profile in the bed, a series of simulations has to be performed. In the series of simulations the generic sections are virtually stacked by imposing the outlet temperature conditions of one section as the inlet conditions of the downstream section. In this approach, axial conduction cannot be included, as there is no mechanism for energy to transport from a downstream section back to an upstream section. Thus, this method is limited to reasonably high flow rates for which axial conduction is negligible compared to the convective flow of enthalpy. This figure shows the result of placing the temperature maps of four consecutive simulations together. The figure for x = 0 corresponds to a section through the length of the tube The main axial flow is from left to right, and Re_p = 1000. An initial temperature of 300 K was taken for the inlet of the first stage, and the wall temperature was constant at 400 K. The fluid properties were those of air, giving a Prandtl number of approximately Pr = 0.7, and the particle properties were those of alumina. The simulation therefore corresponds to a typical laboratory heat transfer experiment set-up, in which the tube wall is heated by a steam jacket, for example, and energy is transferred from the wall into the colder flowing fluid.

The overall picture of the temperature field confirms our intuitive expectation of a classical “boundary-layer” type of development, with a colder inner core and a warmer near-wall region. Closer inspection shows that the boundary layers are, in fact, interrupted by the presence of the particles. These are not isothermal, despite their higher thermal conductivity, yet the temperature field within a particle differs from that in the surrounding fluid. Fingers of warmer fluid infiltrate between the particles as flow is deflected radially. The behavior of local heat transfer rates, and of catalyst particles situated in these temperature fields, will depend on the local temperature and flow conditions, which are difficult to isolate in the larger view. There is a slight discontinuity in the temperature contours between the sections, most noticeably between the first and second sections. This is related to the neglect of axial conduction between stages mentioned above. This is not evident in the fluid phase, as axial conduction through the fluid is small compared to the convective transport. In the solid phase, however, back-conduction from the warmer second stage results in a higher temperature at the stage entrance, as there is no heat flux between the stages in the solid phase.