Temperature jump heat exchange

The bed and the fluid are considered as a pseudo-homogeneous medium, and the heat transfer in the bed up to the internal side of the wall is represented by two parameters, the radial effective conductivity snd the internal wall heat transfer coefiident aw,int- The introduction of aw.mt allows us to take into account a weaker heat transfer (smaller effective radial heat transfer coefficient X ad) close to the wall due to less mixing and a higher void fraction of the bed (Figure 4.10.64). Thus, combines the interplay of convective flow at the wall and of conduction by contact between the bed and the heat exchange surface (internal wall), and assumes a jump in temperature direcily at the wall. For relative simple modeling, the consequence of the introduction of mt is also that we use a constant value of within the bed. 

Another example of gas temperature growth behind the shock wave relates to pressure wave penetration into an obstructed space. The obstruction may result from particles spattered into the space (Fig. 8.1 lb) or obstacles located on the duct walls (Fig. 8.1 Ic). Following the temperature jump from Tq to T, behind the wave front, the temperature grows like T x) due to friction and heat exchange with other objects in the continuum. 

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