Consider heat transfer between two identical hot solid bodies and the air surrounding them. The first solid is being cooled by a fan while the second one is allowed to cool naturally. For which solid is the lumped system analysis more likely to be applicable? Why?

The solution to the question above is explained below:

Explanation:

For which solid is the lumped system analysis more likely to be applicable?

Answer

The lumped system analysis is more likely to be applicable for the body cooled naturally.

Question :Why?

Answer

Biot number is proportional to the convection heat transfer coefficient, and it is proportional to the air velocity. When Biot no is less than 0.1 in  the case of natural convection, then lumped analysis can be applied.

Further explanations:

Heat is a form of energy.

Heat transfer describes the flow of heat across the boundary of a system due to temperature differences and the subsequent temperature distribution and changes. There are three different ways the heat can transfer: conduction, convection, or radiation.

Heat transfer  analysis which utilizes this idealization is known as the lumped system analysis.

The Biot number is a criterion dimensionless quantity used in heat transfer calculations which gives a direct indication of the relative importance of conduction and convection in determining the temperature history of a body being heated or cooled by convection at its surface. In heat transfer analysis, some bodies are observed to behave like a "lump" whose entire  body temperature remains essentially uniform at all times during a heat transfer process.

Conduction is the transfer of energy in the form of heat or electricity from one atom to another within an object and conduction of heat occurs when molecules increase in temperature.

Convection is a transfer of heat by the movement of a fluid. Convection occurs within liquids and gases between areas of different temperature.

here we know that ball will drop down by total distance 3.2 m

so here we know that

now using kinematics

now in the same time it will cover horizontal distance of 0.75 m

so speed of the ball will be

nah.   i'm just sleepy.