- #1
kmarinas86
- 979
- 1
http://en.wikipedia.org/wiki/Stagnation_temperature
It appears to me that if we have two fluids which are in "heat conduction" contact with each other, then the body with the highest stagnation temperature will transfer heat to the body with the lowest stagnation temperature.
However, it is possible for the fluid having the higher stagnation temperature to also have a lower static temperature, provided that it has a higher velocity (with respect to the chosen frame of reference). Now, if one were to remove the ability for heat to transfer by means of conduction and also that of convection, then any heat between them must be radiation. The radiative emissions would flow from one fluid to the other according to which medium has highest temperature from the point of view of Stefan–Boltzmann law. Is the temperature relevant to heat transfer by radiation, in this case, the static temperature and not the stagnation temperature? If that is so, doesn't it suggest that one can reverse heat flow between the two fluids (as evaluated by the arbitrary inertial observer) by simply adding or removing means of conducting heat between them so as long as the two fluids have relative motion?
Stagnation temperature said:In thermodynamics and fluid mechanics, stagnation temperature is the temperature at a stagnation point in a fluid flow. At a stagnation point the speed of the fluid is zero and all of the kinetic energy has been converted to internal energy (adiabatically) and is added to the local static enthalpy. In incompressible fluid flow, and in isentropic compressible flow, the stagnation temperature is equal to the total temperature at all points on the streamline leading to the stagnation point.
===Adiabatic===
Stagnation temperature can be derived from the [[First Law of Thermodynamics]]. Applying the Steady Flow Energy Equation
<ref>Van Wylen and Sonntag, ''Fundamentals of Classical Thermodynamics'', equation 5.50</ref> and ignoring the work, heat and gravitational potential energy terms, we have:
:[itex]h_0 = h + \frac{V^2}{2}\,[/itex]
where:
:[itex]h_0 =\,[/itex] stagnation (or total) enthalpy at a stagnation point
:[itex]h =\,[/itex] static enthalpy at any other point on the stagnation streamline
:[itex]V =\,[/itex] velocity at that other point on the streamline
Substituting for enthalpy by assuming a constant specific heat capacity at constant pressure ([itex]h = C_p T[/itex]) we have:
:[itex]T_0 = T + \frac{V^2}{2C_p}\,[/itex]
or
:[itex]\frac{T_0}{T} = 1+\frac{\gamma-1}{2}M^2\,[/itex]
where:
:[itex]C_p =\,[/itex] [[Heat capacity ratio|specific heat]] at constant pressure
:[itex]T_0 =\,[/itex] stagnation (or total) temperature at a stagnation point
:[itex]T =\,[/itex] temperature (also known as static temperature) at any other point on the stagnation streamline
:[itex]V = \,[/itex] velocity at that other point on the streamline
:[itex]M =\,[/itex] Mach number at that other point on the streamline
:[itex]\gamma =\,[/itex] [[Heat capacity ratio|Ratio of Specific Heats]] ([itex]C_p/C_v[/itex]), 1.4 for air
It appears to me that if we have two fluids which are in "heat conduction" contact with each other, then the body with the highest stagnation temperature will transfer heat to the body with the lowest stagnation temperature.
However, it is possible for the fluid having the higher stagnation temperature to also have a lower static temperature, provided that it has a higher velocity (with respect to the chosen frame of reference). Now, if one were to remove the ability for heat to transfer by means of conduction and also that of convection, then any heat between them must be radiation. The radiative emissions would flow from one fluid to the other according to which medium has highest temperature from the point of view of Stefan–Boltzmann law. Is the temperature relevant to heat transfer by radiation, in this case, the static temperature and not the stagnation temperature? If that is so, doesn't it suggest that one can reverse heat flow between the two fluids (as evaluated by the arbitrary inertial observer) by simply adding or removing means of conducting heat between them so as long as the two fluids have relative motion?