Wall conduction effects in laminar counterflow parallel-plate heat exchangers

Wall conduction effects in multilayered, counterflow, parallel-plate heat exchangers are analyzed theoretically and numerically. The analysis, carried out for constant property fluids, considers a hydrodynamically developed laminar flow and neglects axial conduction both in the fluids and in the plates. The temperature field is expanded as an infinite series in terms of a complete set of eigenfunctions associated with sets of both positive and negative eigenvalues. In addition to the exact solution, an approximate solution that retains only the first two terms in the eigenfunction expansion is considered. The approximate two-term solution, which still incorporates the effect of higher order modes through apparent temperature offsets introduced at the inlet/outlet sections, provides an accurate representation for the temperature field away from the thermal entrance regions, thereby enabling simplified expressions for the wall and bulk temperatures, local Nusselt numbers, and overall heat-transfer coefficient. As main outcome of the analysis, it is seen that increasing the wall thermal resistance lowers the absolute value of both positive and negative eigenvalues—thus reducing heat-exchanger effectiveness—and increases the Nusselt number of the fluid with lower heat-capacity flow rate bringing it closer to its theoretical value 140/17=8.2353140/17=8.2353 corresponding to a constant heat flux boundary condition. Moreover, the proposed two-term solution is seen to reproduce with great accuracy the dependence of the outlet bulk temperatures with the wall thermal resistance. The asymptotic solution for nearly-balanced heat exchangers is also obtained, providing closed-form analytical expressions for this limiting case of practical interest.