ANS:C - Peclet

The Peclet number (Pe) is a dimensionless quantity used in fluid dynamics and heat/mass transfer to characterize the relative importance of advection (convection) to diffusion within a fluid flow. The Peclet number is defined differently depending on the context of its application:

1. In heat transfer: 𝑃𝑒=convective heat transfer rateconductive heat transfer rate=fluid flow rate×characteristic lengththermal diffusivityPe=conductive heat transfer rateconvective heat transfer rate​=thermal diffusivityfluid flow rate×characteristic length​

Here, the Peclet number represents the ratio of the rate of heat transfer by convection to the rate of heat transfer by conduction. It indicates the dominance of advection (fluid motion) relative to thermal diffusion. A high Peclet number signifies that convection is the dominant mode of heat transfer, whereas a low Peclet number indicates that thermal conduction plays a significant role.

2. In mass transfer: 𝑃𝑒=convective mass transfer ratemolecular mass transfer rate=fluid flow rate×characteristic lengthmass diffusivityPe=molecular mass transfer rateconvective mass transfer rate​=mass diffusivityfluid flow rate×characteristic length​

In this context, the Peclet number represents the ratio of the rate of mass transfer by convection to the rate of mass transfer by molecular diffusion. It indicates the dominance of advection (fluid motion) relative to molecular diffusion. A high Peclet number signifies that convection is the dominant mode of mass transfer, whereas a low Peclet number indicates that molecular diffusion plays a significant role. Overall, the Peclet number is a useful dimensionless parameter for analyzing the relative importance of advection and diffusion in fluid flow, heat transfer, and mass transfer processes.