The relation, Sc = Pr = 1, is valid, when the mechanism of __________ ansfer is same.

ANS:A - heat and mass

The relation 𝑆𝑐=𝑃𝑟=1Sc=Pr=1 is valid when the mechanism of heat and mass transfer is the same. Explanation:

• 𝑆𝑐Sc (Schmidt number) represents the ratio of momentum diffusivity to mass diffusivity. It quantifies the relative importance of momentum transport to mass transport in a fluid.
• 𝑃𝑟Pr (Prandtl number) represents the ratio of momentum diffusivity to thermal diffusivity. It quantifies the relative importance of momentum transport to heat transport in a fluid.

When 𝑆𝑐=𝑃𝑟=1Sc=Pr=1, it means that the rates of diffusion of momentum, heat, and mass are similar, indicating that the transport mechanisms for momentum, heat, and mass are all dominated by diffusion to the same extent. This scenario commonly occurs in certain types of fluid flows and processes where the transport of momentum, heat, and mass are closely coupled and exhibit similar behavior. Heat and mass transfer are two fundamental processes that involve the movement of energy and matter, respectively, from one location to another. Here's a brief explanation of each:

1. Heat Transfer:
   • Heat transfer is the process of energy transfer between two bodies or systems due to a temperature difference.
   • It occurs in three main modes: conduction, convection, and radiation.
   • Conduction is the transfer of heat through a material medium by molecular motion.
   • Convection is the transfer of heat through the movement of fluid (liquid or gas) particles.
   • Radiation is the transfer of heat through electromagnetic waves, such as infrared radiation.
   • Heat transfer plays a crucial role in various engineering applications, including heating and cooling systems, thermal insulation, and cooking processes.
2. Mass Transfer:
   • Mass transfer is the process of movement of one or more substances from one phase to another phase, usually involving a solid, liquid, or gas.
   • It occurs due to concentration gradients and can happen by diffusion, convection, or a combination of both.
   • Diffusion is the movement of molecules from an area of high concentration to an area of low concentration, resulting in the equalization of concentration.
   • Convection mass transfer involves the bulk movement of fluid carrying mass, often driven by pressure differences or mechanical agitation.
   • Mass transfer is essential in various industrial processes such as distillation, absorption, evaporation, and chemical reactions where the separation, purification, or mixing of substances is required.

In many practical situations, heat and mass transfer processes occur simultaneously and are interrelated. For example:

• In evaporative cooling, heat transfer occurs as energy is absorbed by a liquid during vaporization, while mass transfer occurs as the vapor is carried away from the liquid surface.
• In drying processes, heat is used to vaporize moisture from a material, and mass transfer occurs as the water vapor moves away from the material surface.
• In absorption processes, heat transfer may accompany the transfer of a solute from one phase to another, such as the absorption of gases into a liquid solvent.

Understanding the principles of heat and mass transfer is crucial in fields such as chemical engineering, mechanical engineering, and environmental science, as it allows engineers and scientists to optimize processes, design efficient systems, and solve practical problems related to energy and material transport.