Think out of box: What is the role of Reynolds number [Re = Duρ /μ] in heat transfer. Is it just a dimensionless number or more than that?
I have given my opinion. The relevance of entropy in heat transfer is beyond any controversy. All depends how we bring it to relevance. That is what I have done in this post .
I request you to share your views.
Let us imagine a shell and tube heat exchanger. It has two closed systems one is shell and the other is tube compartment separated by a heat permeable metal wall which does not allow substance transfer.
There are two fundamental laws which any energy transport system has to satisfy [1] Energy flow from high energy level to low energy level and [2] entropy of universe [system+ surrounding] always increases.
Let us see how heat transfer meets these fundamental laws for energy transport in heat exchanger.
Imagine, hot fluid in red container flows to cold fluid in blue container through a heat permeable connection which does not allow any matter to flow between containers. Both containers are closed systems. A shell and tube heat exchanger consists of similar two closed systems separated by heat permeable metal wall.
By definition, heat is an energy in transit. It does not belong to any particular substance or system. Its job is to carry energy from high temperature to low temperature. Heat always carries useless entropy because it is part of heat wherever it goes. Heat does not carry work energy.
With this background , let us see what is happening in the heat exchanger.
We can write, Q = ?U+ T?S +W [Q is heat [total energy] , U is internal energy, T is temperature in kelvin and S is entropy, W is work [W can have +ve or -ve sign].
Q does not carry W, so equation can be re-written as, Q = ?U+ T?S, Q carries useful internal energy and useless entropy. But important to remember that total Q when heat is in transit, is sum of internal energy and entropy.
Hot fluid loses heat and becomes cold as it flows to lower temperature. While fluid is hot, sum of total energy , [entropy + plus heat] > than cold system. It is at higher energy level and it goes to a lower energy level. This is perfectly in accordance with the law.
Hot fluid has higher entropy than cold fluid, but when it transfers heat to a cold body, it generates more disorder in cold body because body is cold, more ordered system goes to more disordered system, a cold body has therefore much bigger scope to disorganise itself than a hot body can do. So, overall, when a hot body transfers heat to a cold body there is gain in entropy. Entropy increases. Therefore, we can see the heat transfer meets this requirement also.
Now let us come to the role of Reynold number. How it helps?
As explained above, hot body has less useful energy and more entropy compared to cold body on a per unit mass basis. On enthalpy / weight basis, energy at high temperature means low useful heat + more useless entropy, in contrast, at low temperature, energy has more useful heat + less entropy . But in terms of total Q, hot body has more energy and that drives heat transfer.
Reynolds number, which is an indicator of turbulence [ eddy] in the system infuses entropy and maintains overall ?t and ensures energy flows from high entropy to low entropy [ second law of thermodynamics]. I believe, the relevance of entropy in heat transfer is beyond any controversy.
Reynolds number [Re = Duρ /μ] [ ρ is the density of the fluid (SI units: kg/m3),u is the flow speed (m/s), D is the diameter of the tube (m), μ is the dynamic viscosity] .
Analysis of Reynolds number
D = diameter increase reduces pressure drop , more flow, more entropy
u = velocity increase means more entropy
ρ = density increase means less volume, more entropy
μ = viscosity decrease means more velocity, more entropy
Therefore, Reynolds number is a collection of properties of fluid which are all directed towards increase in entropy and it is not just a dimensionless number.
In the image below, blue dots line is HTC of water vs Reynolds number. The image suggests that with increase of Reynolds number and if my thinking is right , with increase of useless entropy , heat transfer declines beyond a point when there is less useful heat and more useless entropy.
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Finally, I am not suggesting even for a minute that Reynolds number has no other role
Naval Architecture Course Director @ Lloyd's Training Academy Informa KNECT 365
4 年Nikhilesh Mukherjee, Thanks for sharing. The Reynolds number derived from the criterion of the similitude?Reynolds which defines the proportionality between the viscosities forces and convective inertia forces within equation Navier-Stokes(NE) As you know the NE equations have not yet straightforward solutions. That's why in fluid mechanics a number of 6 criteria ( Reynolds amongst them ) were defined to try to develop partial solutions for NE equations. On the other hand the NE equations were derived by studying the dynamics of material point. They do not incorporate the aspects like phases transitions therefore they are used to describe movements of particles rather than operating statistically with large number of molecules like in case of thermodynamics. Therefore I am not sure that Reynolds number is applicable. Unfortunately has neither physical support nor maths support. On the other hand if consider variables which are increasing based on same parameter i.e. Reynolds number link in math multiplied and divide in same time quote D = diameter increase reduces pressure drop , more flow,?more entropy u = velocity increase means more entropy ρ = density increase means less volume, more entropy μ = viscosity decrease means more velocity, more entropy unquote Re = Duρ /μ As can be seen in Re definition all the variables relative to entropy increase the entropy. But in maths if have only for example variables x and y function of same parameter entropy(e) any result might be valid if x=e and y= e^2 than x/y=e/e^2=1/e the e increase means that overall value decrease. If is x=e^2 and y=e than x/y =e^2/e=e the overall value increase with e increasing Therefore processes need to be further analysed to validate such correlation. Otherwise maybe only experimental fact can give an indication but whilst psychics and maths model are not developed to demonstrate this correlation is quite difficult to accept it.