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.

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.