Please answer the 3 questions and type your answer or post c

Please answer the 3 questions and type your answer or post clear pics!!! Thanks

How does you explain the phenomena of cold bathroom floor vs. a warmer bathroom rug when both are at the same temperature T? What are the two conditions that make mass transfer coefficients and heat transfer coefficients analogous in boundary flow? What dimensionless thermophysical property is analogous to the Schmidt number in mass transfer? And what insight does this parameter give with regards to temperature boundary layers in laminar flow?

Solution

1) The bathroom floor conduct heat much better than the fluffy rug. It Is because of high thermal conductivity of the tiles on the floor. For instance granite tiles have a thermal conductivity that is nearly 100 times higher than that of cotton bathroom rugs. This means your warm feet lose heat 100 times faster to the room-temperature tiles than to the room-temperature rug.

2) The first condition is that both heat and mass are transported by turbulent eddies, thus we can assume that the eddie diffusivities are the same for both modes of transport.

The second condition is that since both mass and heat transfer normally occur through a thin boundary layer close to the wall. The equations governing the transport of these quantities are analogous and are exact for laminar flow if the pressure gradient is equal to zero and the Prandtl Number (Pr) and Schmidt Number (Sc) are equal to unity.

3) Prandtl number in heat transfer is analogous to Schmidt number in mass transfer.

This parameter controls the relative thickness of the thermal boundary layers. When it is small, it means that the heat diffuses quickly compared to the velocity (momentum).