Incremental Heat Transfer Number for Laminar Flow in Circular Tubes with the Boundary Condition of the Third Kind and Simple Design Formula for Shell-and-Tube Laminar Flow Heat Exchangers with Constant External Resistance
Dimitrios M. Zarkadas and Kamalesh K. Sirkar
Plastic heat exchangers are increasingly gaining attention for lower temperature applications. Their analysis is more complicated than conventional metal heat exchangers since their low thermal conductivity necessitates the incorporation of the significant wall thermal resistance in the model. Based on existing analytical solutions for laminar flow inside circular tubes with the boundary condition of the third kind, we have calculated for the first time the incremental heat transfer number as a function of the external resistance for Nuw numbers ranging between 0.01-10000, a range covering almost all practical applications. The values obtained were used to construct a simple relationship for the calculation of the mean Nusselt number of the tube, which is only a function of the external resistance and the hydrodynamic conditions prevailing in the tube. This equation is accurate to within 3% of the analytical solution for Gz &Mac178; 26. It can be used for design purposes for shell-and-tube plastic heat exchangers with laminar flow in the tube side and cross flow polymeric hollow fiber heat exchangers (PHFHEs).