Q1: The equation, , corrosponds to __________ analogy.

ANS:D - Prandtl

The Prandtl analogy is a concept in fluid mechanics and heat transfer that relates the momentum and heat transfer characteristics of a fluid flow. It is based on the idea that there exists a similarity between the transport of momentum (momentum diffusivity) and the transport of heat (thermal diffusivity) in a fluid flow. The Prandtl analogy is particularly useful for analyzing turbulent boundary layers where both momentum and heat are transferred through the fluid. The analogy allows engineers and researchers to predict heat transfer rates based on known velocity profiles and vice versa. Mathematically, the Prandtl analogy is expressed as: ∂22∂y2∂2u​=σ1​∂y2∂2T​ Where:

• u is the velocity component in the direction of flow,
• y is the distance normal to the surface,
• T is the temperature,
• σ is the Prandtl number of the fluid.

This equation essentially states that the second derivative of the velocity profile with respect to distance (y) is proportional to the second derivative of the temperature profile with respect to distance, with the proportionality constant being 1/1/σ, where σ is the Prandtl number of the fluid. The Prandtl analogy allows engineers to relate the thermal boundary layer thickness to the velocity boundary layer thickness, enabling them to predict heat transfer rates based on known velocity profiles and vice versa. It simplifies the analysis of heat transfer problems by providing a convenient means of estimating heat transfer coefficients and temperature distributions in fluid flow situations. Overall, the Prandtl analogy provides a valuable tool for analyzing convective heat transfer problems and is widely used in engineering practice.