Entropy production in a packed duct flow

The energy equation for a fully established laminar flow is 

The heat flux at the upper and lower surfaces specifies the temperature gradient at the wall, and the necessary boundary conditions 

The linearity of the energy equation suggests that the superposition method may be applied to build solutions by adding two fundamental solutions for the top and bottom walls. For a constant heat flux, a simple energy balance is 

Using Eqs. (4.59)-(4.64), we can determine the velocity and temperature profiles and derive the rate of entropy production in the packed bed 

the first term on the right shows entropy production due to heat transfer, and the second term shows entropy production due to fluid friction. Equation (4.65) relates the rate of entropy production to H/dv, heat duty q, the Reynolds number, and the Stanton number St = /z/pvavCp. 

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Example 4.6 Entropy production in a packed duct flow Fluid flow and the wall-to-fluid heat transfer in a packed duct are of interest in fixed bed chemical reactors, packed separation columns, heat exchangers, and some heat storage systems. In this analysis, we take into account the wall effect on the velocity profile in the calculation of entropy production in a packed duct with the top wall heated and the bottom wall cooled (Figure 4.7). We assume... 

Example 4.5 Entropy production in a packed duct flow with asymmetric heat effects... 

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