Prandtl-Taylor analogy

This is known as the Taylor-Prandtl analogy. In order to apply it, the value of uju has to be known and the way in which this can be found will now be discussed. 

Using the Taylor-Prandtl analogy, determine the relation between the velocity and temperature profiles in the boundary layer. 

Modify the integral equation computer program to use the Taylor-Prandtl analogy. Use this modified program to determine the local Nusselt number variation for the situation described in Problem 6.6. 

The so-called Taylor-Prandtl analogy was applied to boundary layer flow in Chapter 6. Use this analogy solution to derive an expression for the Nusselt number in fully developed turbulent pipe flow. 

Taylor-Prandtl modification of Reynolds analogy for heat transfer and mass transfer... 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy for momentum and heat transfer, and give the corresponding relation for mass transfer (no bulk flow). 

Obtain the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer and write down the corresponding analogy for mass transfer. For a particular system, a mass transfer coefficient of 8,71 x 10 8 m/s and a heat transfer coefficient of 2730 W/m2 K were measured for similar flow conditions. Calculate the ratio of the velocity in the fluid where the laminar sub layer terminates, to the stream velocity. 

Derive the Taylor-Prandtl modification of the Reynolds analogy between heat and momentum transfer and express it in a form in which it is applicable to pipe flow. 

Obtain the Taylor-Prandtl modification of the Reynolds Analogy between momentum transfer and mass transfer (equimolecular counterdiffusion) for the turbulent flow of a fluid over a surface. Write down the corresponding analogy for heat transfer. State clearly the assumptions which are made. For turbulent flow over a surface, the film heat transfer coefficient for the fluid is found to be 4 kW/m2 K. What would the corresponding value of the mass transfer coefficient be. given the following physical properties ... 

The Taylor-Prandtl modification of the Reynolds analogy for heat transfer and mass transfer is discussed in Section 12.8.3 and the relevant equations are ... 

Derive the Taylor-Prandtl modification of the Reynolds analogy between momentum and heat transfer. 

Taylor(4) and Prandtl(8 9) allowed for the existence of the laminar sub-layer but ignored the existence of the buffer layer in their treatment and assumed that the simple Reynolds analogy was applicable to the transfer of heal and momentum from the main stream to the edge of the laminar sub-layer of thickness <5. Transfer through the laminar sub-layer was then presumed to be attributable solely to molecular motion. 

---