Chapter 14

What is the physical significance of the Lewis number? How is it defined? What does a Lewis number of 1 indicate?

Under what conditions will the normalized velocity, thermal, and concentration boundary layers coincide during flow over a flat plate?

Heat convection is expressed by Newton's law of cooling as \(\dot{Q}=h A_{s}\left(T_{s}-T_{\infty}\right)\). Express mass convection in an analogous manner on a mass basis, and identify all the quantities in the expression and state their units.

What is the physical significance of the Sherwood number? How is it defined? To what dimensionless number does it correspond in heat transfer? What does a Sherwood number of 1 indicate for a plane fluid layer?

In natural convection mass transfer, the Grashof number is evaluated using density difference instead of temperature difference. Can the Grashof number evaluated this way be used in heat transfer calculations also?

What is the relation \((f / 2) \mathrm{Re}=\mathrm{Nu}=\mathrm{Sh}\) known as? Under what conditions is it valid? What is the practical importance of it? \(\mathrm{St}_{\text {mass }} \mathrm{Sc}^{2 / 3}\) and what are the names of the variables in it? Under what conditions is it valid? What is the importance of it in engineering?

Using the analogy between heat and mass transfer, explain how the mass transfer coefficient can be determined from the relations for the heat transfer coefficient.

What is the relation \(h_{\text {heat }}=\rho c_{p} h_{\text {mass }}\) known as? For what kind of mixtures is it valid? What is the practical importance of it?

The average heat transfer coefficient for air flow over an odd-shaped body is to be determined by mass transfer measurements and using the Chilton-Colburn analogy between heat and mass transfer. The experiment is conducted by blowing dry air at \(1 \mathrm{~atm}\) at a free stream velocity of \(2 \mathrm{~m} / \mathrm{s}\) over a body covered with a layer of naphthalene. The surface area of the body is \(0.75 \mathrm{~m}^{2}\), and it is observed that \(100 \mathrm{~g}\) of naphthalene has sublimated in \(45 \mathrm{~min}\). During the experiment, both the body and the air were kept at \(25^{\circ} \mathrm{C}\), at which the vapor pressure and mass diffusivity of naphthalene are \(11 \mathrm{~Pa}\) and \(D_{A B}=0.61 \times\) \(10^{-5} \mathrm{~m}^{2} / \mathrm{s}\), respectively. Determine the heat transfer coefficient under the same flow conditions over the same geometry.

In a manufacturing facility, \(40 \mathrm{~cm} \times 40 \mathrm{~cm}\) wet brass plates coming out of a water bath are to be dried by passing them through a section where dry air at 1 atm and \(25^{\circ} \mathrm{C}\) is blown parallel to their surfaces at \(4 \mathrm{~m} / \mathrm{s}\). If the plates are at \(15^{\circ} \mathrm{C}\) and there are no dry spots, determine the rate of evaporation from both sides of a plate.