Question

What is the physical significance of the Lewis number? How is it defined? What does a Lewis number of 1 indicate?

Short answer

Answer: A Lewis number of 1 signifies that the thermal diffusivity and mass diffusivity are equal, meaning the rates of thermal and mass diffusion are the same. In this case, the temperature and concentration gradients have similar influences on the transport processes, indicating that the reaction front is neither limited by heat diffusion nor by mass diffusion; instead, both factors play a role in the overall process.

Step-by-step solution

Definition

The Lewis number (Le) is a dimensionless number used in fluid mechanics and heat and mass transfer problems. It is defined as the ratio of the thermal diffusivity (α) to the mass diffusivity (D). Mathematically, the Lewis number is given by: Le = \frac{α}{D} Where, α is the thermal diffusivity and D is the mass diffusivity. #Step 2: Describe the physical significance of the Lewis number#

Physical Significance

The Lewis number characterizes the relative rates of thermal and mass diffusion in a system. It is used to study coupled heat and mass transfer processes, such as evaporative cooling or combustion. A high Lewis number indicates that thermal diffusion is much faster than mass diffusion, while a low Lewis number suggests the opposite. The Lewis number is important when analyzing systems in which temperature and concentration gradients coexist, as it shows how these gradients interact with each other and which one has a greater influence on the transport process. #Step 3: Discuss what a Lewis number of 1 means#

Lewis number equal to 1

A Lewis number of 1 means that the thermal diffusivity and mass diffusivity are equal, or in other words, the rates of thermal and mass diffusion are the same. In this case, the temperature and concentration gradients will have similar influences on the transport processes. This situation is sometimes encountered in combustion or gas-phase reaction problems, where the reaction rates depend on both temperature and concentration gradients. In these cases, a Lewis number of 1 indicates that the reaction front is neither limited by heat diffusion nor by mass diffusion; instead, both factors play a role in the overall process.