Dissipation of mechanical energy

Thomson, W. (1882-1911). On a Universal Tendenq" m Nature to the Dissipation of Mechanical Energy. In Mathematical and Physical Papers Collected from Different Scientific Periodicals from May 1841 to the Present Time, in 6 Vols., vol. 1, pp. 511—514. Cambridge, Eng. Cambridge University Press. 

A fermentation broth contained in a batch-operated stirred-tank fermentor, 2.4m in inside diameter D, is equipped with a paddle-type stirrer of diameter (L) of 0.8 m that rotates at a speed Af = 4s -. The broth temperature is maintained at 30 °C with cooling water at 15°C, which flows through a stainless steel helical coil that has a 50 mm outside diameter and is 5 mm thick. The maximum rate of heat evolution by biochemical reactions, plus dissipation of mechanical energy input by the stirrer, is 51000 kcal h , although the rate varies with time. The physical properties of the broth at 30 °C were density p = 1000 kg m " , viscosity p = 0.013 Pa s, specific heat Cp = 0.90 kcal kg °C , and thermal conductivity K = 0.49 kcal h m °C = 0.000136 kcals m °C . ... 

The losses in the reactor are chemical exergy losses, whereas the cooler losses can be attributed to physical exergy losses. Mixing constitutes physical losses as do the losses in the extruder due to the dissipation of mechanical energy to heat. The losses in the purge vessel (V3) are due to the fact that the gas is incinerated. The sum of all losses equals 4.73MJ/kg PE, or US 0.0465 per kg PE. 

Frictional dissipation of mechanical energy can result in significant heating of fluids, particularly for very viscous liquids in small channels. Under adiabatic conditions, the bulk liquid temperature rise is given by AT=AP/CV p for incompressible flow through a channel of constant cross-sectional area. For flow of polymers, this amounts to about 4°C per 10 MPa pressure drop, while for hydrocarbon liquids it is about... 

Hruby, M., Int. Chem. Engng. 7 (1967) 1, 86-90 Relationship between the dissipation of mechanical energy and heat transfer in agitated vessels... 

Without the assumption of a frictionless piston, we cannot imagine a reversible process. If the piston sticks because of friction, a finite mass must be removed before the piston breaks free. Thus the equilibrium condition necessary to reversibility is not maintained. Moreover, friction between two sliding parts is a mechanism for the dissipation of mechanical energy into internal energy. 

This equation is based on the assumption that the change of state resulting from the process is accomplished reversibly. However, the viscous nature of real fluids induces fluid friction that makes changes of state in flow processes inherently irreversible because of the dissipation of mechanical energy into internal energy. In order to correct for this, we add to the equation a friction term F. The mechanical-energy balance is then written ... 

Industrial catalyst bed pressures are typically 1.1 to 1.4 bar. They are highest in 1st catalyst beds and lowest in last beds - due to dissipation of mechanical energy as gas passes through the beds. 

The numerator is the rate of production of turbulence energy, and the denomenator is the rate of dissipation of mechanical energy by the mean field. The turbulent viscosity can therefore be described in terms of the rate of turbulence production. 

The term Ey is the rate of viscous dissipation of mechanical energy its estimation is described in Bird, Stewart, and Lightfoot (2002). is a reference pressure, in units of M/Lt the resulting SI unit is the Pascal. 

The behavior of a flowing fluid depends strongly on whether or not the fluid is under the influence of solid boundaries. In the region where the influence of the wall is small, the shear stress may be negligible and the fluid behavior may approach that of an ideal fluid, one that is incompressible and has zero viscosity. The flow of such an ideal fluid is called potential flow and is completely described by the principles of newtonian mechanics and conservation of mass. The mathematical theory of potential flow is highly developed but is outside the scope of this book. Potential flow has two important characteristics (1) neither circulations nor eddies can form within the stream, so that potential flow is also called irrotational flow, and (2) friction cannot develop, so that there is no dissipation of mechanical energy into heat. 

From the results of part (a) we find that for the gas all e.xpansion proces.ses are reversible (i.e.. there are no dissipative mechanisms within the gas). However, from part fb), we. see that when the piston, cylinder, and gas are taken to be the system, the expansion process is irreversible unless the expansion occurs in differential steps. The conclusion, then, is that the irreversibility, or the dissipation of mechanical energy to thermal energy, occurs between the piston and the cylinder. This is, of course, obvious from the fact that the only source of dissipation in this problem is the friction between the piston and the cylinder wall. ... 

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