In case of cooling towers, the ratio of the rates of heat and mass transfer is indicated by the __________ number.

ANS:A - Lewis

The Lewis number (𝐿𝑒Le) is a dimensionless parameter used in the analysis of heat and mass transfer processes, particularly in situations where both heat and mass transfer occur simultaneously. It is defined as the ratio of thermal diffusivity (𝐷𝑇DT​) to mass diffusivity (𝐷𝑀DM​) of a fluid: 𝐿𝑒=𝐷𝑇𝐷𝑀Le=DM​DT​​ Here's a breakdown of its significance and application:

1. Heat and Mass Transfer: The Lewis number quantifies the relative importance of heat transfer to mass transfer in a fluid system. It indicates how quickly heat diffuses compared to how quickly mass diffuses.
2. Physical Interpretation:
   • When 𝐿𝑒>1Le>1: Heat diffuses more rapidly than mass. This typically occurs in systems where heat transfer dominates over mass transfer, such as in cases where thermal gradients drive the transfer of energy more effectively than concentration gradients drive the transfer of mass.
   • When 𝐿𝑒<1Le<1: Mass diffuses more rapidly than heat. This scenario is common in systems where mass transfer is dominant over heat transfer, such as in cases where concentration gradients drive the transfer of mass more effectively than thermal gradients drive the transfer of energy.
   • When 𝐿𝑒=1Le=1: Heat and mass transfer occur at similar rates, indicating that both mechanisms are equally significant in the system.
3. Applications:
   • Chemical Engineering: In chemical engineering applications, the Lewis number is crucial for understanding processes involving simultaneous heat and mass transfer, such as in absorption, distillation, evaporation, and drying processes.
   • Combustion: In combustion processes, the Lewis number plays a role in determining flame structure and stability, as it affects the relative rates of heat release and species diffusion.
   • Environmental Engineering: In environmental engineering, the Lewis number is relevant for studying pollutant dispersion and mass transfer in air-water systems, such as in the absorption of gases by water bodies.