Axial conduction in cross-flow heat exchangers: An analytical approach to the coupled heat transfer problem. (January 2023) - Mitra, Indrasis; Ghosh, Indranil
Highlights: Analytic modelling of two-fluid crossflow exchanger incorporating axial conduction. 3D approach simultaneously incorporates thermal resistance in the separating wall. Capable of handling both balanced and unbalanced flow. Axial conduction induced ineffectiveness most prominent in high NTU exchangers. Highly conductive separating wall suitable if design NTU is low. Abstract: Cross-flow heat exchangers are widely used in the process intensification and air separation industry. Its miniaturized versions are touted to be especially useful for aircraft heat exchange, portable cooling systems, and micro-combustion chambers for fuel cells. The desired thermal effect is often obtained in a cross-flow heat exchanger of a shorter length leading to a lower pressure drop penalty. Although miniaturization leads to high heat transfer to volume ratio, the low flow rates and large solid cross-section area to fluid free-flow area ratio might lead to intense axial conduction. Standard mathematical models for macro-scale exchangers neglect this effect and must be modified for micro-scale applications. While the analytical models are available for the counter-current exchanger, a similar analytical tool is missing for the cross-flow device. The present work attempts to develop such a tool, wherein, unlike previous attempts, a three-dimensional modelling approach is undertaken. The unique flow configuration in the cross-flow system necessitates this modification if both axial conduction and thermal resistance of the separating wall (missing in earlier two-dimensional attempts) are to be simultaneously tackled. The developed model can handle both balanced and unbalanced flows. Validations have been performed using conjugate computational studies (with exact geometry and solved in COMSOL), a simplified numerical model, and by comparison with some of the standard cross-flow expressions in the limit of no axial conduction. Results are presented in the form of three-dimensional temperature profiles, effectiveness- N T U (number of transfer units), and conduction effect factor curves for different flow and geometric configurations. It is found that the balanced cross-flow exchanger can experience performance deterioration of ∼ 45 % at low flow rates. The fast convergence of the proposed theory allows it to be nested in heat exchanger optimization routines, where a detailed computational step would have led to prohibitive computational costs.