Asymptotic conditions is reached, when for a fluid flowing in laminar flow through a long tube

ANS:C - exit fluid temperature = wall temperature.

Asymptotic conditions are reached when the exit fluid temperature approaches the wall temperature in a fluid flowing in laminar flow through a long tube. Explanation:

1. Laminar Flow in a Long Tube: In laminar flow through a long tube, the temperature profile of the fluid gradually approaches a steady-state condition as the fluid moves along the length of the tube. As the fluid moves closer to the outlet, its temperature approaches that of the tube wall due to heat transfer between the fluid and the wall.
2. Exit Fluid Temperature and Wall Temperature: Asymptotic conditions are reached when the exit fluid temperature becomes very close to the wall temperature. At this point, the temperature difference between the fluid and the wall becomes negligible, indicating that the heat transfer process has reached a quasi-steady-state condition.
3. Graetz Number: The Graetz number (��Gr) is a dimensionless parameter used to characterize the ratio of convection heat transfer to axial conduction heat transfer in a fluid flowing through a tube. While a Graetz number greater than 100 generally indicates that axial conduction effects are significant, it is not directly related to the asymptotic conditions in laminar flow.
4. Significance of Exit Fluid Temperature = Wall Temperature: When the exit fluid temperature equals the wall temperature, it signifies that the temperature profile of the fluid has fully equilibrated with the temperature of the tube wall. This indicates that the heat transfer process has approached a steady-state condition, and further changes in the fluid temperature become negligible as it exits the tube.

In summary, asymptotic conditions are reached in laminar flow through a long tube when the exit fluid temperature approaches the wall temperature, signifying that the temperature profile of the fluid has equilibrated with the temperature of the tube wall. This condition indicates quasi-steady-state heat transfer behavior in the system.