Convection is the process by which warm air rises and cooler air falls. The Prandtl number (Pr) is used when mechanical engineers analyze certain heat transfer and convection processes. It is defined by the equation

where c_p is a property of the fluid called the specific heat having the SI units kJ/(kg · °C); µ is the viscosity as discussed in Problem P3.16; and k is the thermal conductivity as discussed in Problem P3.22. Show that Pr is a dimensionless number. The lowercase Greek characters mu (µ) and kappa (k) are conventional mathematical symbols used for viscosity and thermal conductivity. Appendix A summarizes the names and symbols of Greek letters.

Problem P3.22

Heat Q, which has the SI unit of joule (J), is the quantity in mechanical engineering that describes the transit of energy from one location to another. The equation for the flow of heat during the time interval Δt through an insulated wall is

where κ is the thermal conductivity of the material from which the wall is made, A and L are the wall’s area and thickness, and T_h − T_l is the difference (in degrees Celsius) between the high- and low-temperature sides of the wall. By using the principle of dimensional consistency, what is the correct dimension for thermal conductivity in the SI? The lowercase Greek character kappa (κ) is a conventional mathematical symbol used for thermal conductivity. Appendix A summarizes the names and symbols of Greek letters.

Problem P2.16

The property of a fluid called viscosity is related to its internal friction and resistance to being deformed. The viscosity of water, for instance, is less than that of molasses and honey, just as the viscosity of light motor oil is less than that of grease. A unit used in mechanical engineering to describe viscosity is called the poise, named after the physiologist Jean Louis Poiseuille, who performed early experiments in fluid mechanics. The unit is defined by 1 poise = 0.1 (N · s)/m² . Show that 1 poise is also equivalent to 1 g/(cm · s).

Transcribed Image Text:

uc d. Pr =