A New Modeling Method to Evaluate Effective Forced-Convective Heat Transfer Rate of Pipe Flow with Endothermic Chemical Reactions

Heat transfer correlation describes the relationship between heat transfer and factors such as fluid properties and flow conditions. The establishment of heat transfer correlations is of paramount importance in the design and calculation of heat exchangers and reactors in various chemical engineering fields as well as in certain aerospace applications. In this study, we present a theoretical derivation of a heat transfer correlation model for fully developed flow with gas-phase homogeneous chemical reactions. By means of theoretical derivations, the modeling of complex multi-physics coupling problems can be significantly simplified, and the impact of chemical reactions can be effectively demonstrated. The concept of effective specific heat and effective thermal conductivity are generalized to finite-rate chemically reacting flow. Modifications are proposed for Nusselt number correlation. It is shown by preliminary verification that evaluating error of new correlation has been significantly decreased by the modification. The enhancement factor can be evaluated by specific ratio cpr,x/cp*. To demonstrate the reliability of the derived correlation, we carry out numerical simulations and compare the results with derived formulations. The simulations show good agreement with the theoretical values, demonstrating that the derived correlation is both theoretically grounded and practically usable.