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Chapter 14: Problem 113

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

Short Answer

Expert verified
Answer: The Lewis number (Le) is a dimensionless number that represents the relative rate of diffusive transport of heat and mass in a fluid system, helping to understand the balance between heat and mass transfer. A Lewis number of 1 implies that the rates of heat and mass diffusion are equal in the system, meaning that the temperature and concentration fields in the system are similar and the analysis of the problem becomes simpler.

Step by step solution

01

Define the Lewis number

The Lewis number (Le) is a dimensionless number used in analyzing heat and mass transfer problems. It represents the relative rate of diffusive transport of heat and mass in a fluid system. The Lewis number is defined as the ratio of the thermal diffusivity, α, to the mass diffusivity, D: \[Le = \frac{α}{D}\]
02

Explain the physical significance of the Lewis number

The Lewis number helps to understand the balance between the heat and mass transfer in a system. In other words, it quantifies the relative importance of heat conduction to mass diffusion in a medium. When studying transport phenomena such as simultaneous heat and mass transfer in problems like evaporation, condensation, or combustion, the Lewis number becomes a crucial parameter for deciding appropriate models and approximations.
03

Interpret what a Lewis number of 1 indicates

A Lewis number of 1 implies that the rates of heat and mass diffusion are equal in the system. This means that the rate at which heat is conducted through the medium is the same as the rate at which mass diffuses through the medium. In such cases, the temperature and concentration fields in the system are similar, making the analysis of the problem simpler. Lewis number of 1 is typically assumed in many engineering applications where the difference between heat and mass transfer rates does not significantly affect the overall performance of the system.

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Most popular questions from this chapter

Air flows through a wet pipe at \(298 \mathrm{~K}\) and 1 atm, and the diffusion coefficient of water vapor in air is \(2.5 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\). If the heat transfer coefficient is determined to be \(35 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), the mass transfer coefficient is (a) \(0.0326 \mathrm{~m} / \mathrm{s}\) (b) \(0.0387 \mathrm{~m} / \mathrm{s}\) (c) \(0.0517 \mathrm{~m} / \mathrm{s}\) (d) \(0.0583 \mathrm{~m} / \mathrm{s}\) (e) \(0.0707 \mathrm{~m} / \mathrm{s}\)

In natural convection mass transfer, the Grashof number is evaluated using density difference instead of temperature difference. Can the Grashof number evaluated this way be used in heat transfer calculations also?

The diffusion coefficient of carbon in steel is given as $$ D_{A B}=2.67 \times 10^{-5} \exp (-17,400 / T) \quad\left(\mathrm{m}^{2} / \mathrm{s}\right) $$ where \(T\) is in \(\mathrm{K}\). Determine the diffusion coefficient from \(300 \mathrm{~K}\) to \(1500 \mathrm{~K}\) in \(100 \mathrm{~K}\) increments and plot the results.

Determine the mole fraction of dry air at the surface of a lake whose temperature is \(15^{\circ} \mathrm{C}\). Take the atmospheric pressure at lake level to be \(100 \mathrm{kPa}\).

Air at \(40^{\circ} \mathrm{C}\) and 1 atm flows over a \(5-\mathrm{m}\)-long wet plate with an average velocity of \(2.5 \mathrm{~m} / \mathrm{s}\) in order to dry the surface. Using the analogy between heat and mass transfer, determine the mass transfer coefficient on the plate.
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