Why does heat move? Heat-Entropy-Reynolds number triangle
A?heat?exchanger,?I?believe,?is?a?heat?transfer?device?housed?inside?a?triangle?with?the?three?arms?[1]?Heat,?[2]?Entropy,?and?[3]?Reynolds?number?connected?to?each?other.?A?heat?exchanger?cannot?function?if?one?of?the?three?arms?is?missing.
This?post?is?all?about?the?Heat-Entropy-Reynolds?triangle.
Let us question the role of the Reynolds number [Re = Duρ /μ] in heat transfer. Is it just a dimensionless number or more than that? ?When we boil milk, we see the Heat-Entropy-Reynolds number triangle every day. In a heat exchanger, the same thing happens. Your milk will not boil if any of them is missing. You see the 2nd law of thermodynamics working in your kitchen every day.
Reynolds number is a consequence of entropy.
Reynolds number is a ratio of = Inertial forces / Viscous forces
The more kinetic energy there is, the greater the entropy and the lower the viscous force. Viscous forces are nothing more than a measurement of how molecules diffuse energy. As a result of having more kinetic energy, there is more entropy, which means less viscous forces and thus a higher Reynolds number.
Let us imagine a shell and tube heat exchanger. It has two closed systems one is a shell and the other is a tube compartment separated by a heat-permeable metal wall that does not allow substance transfer.
Let us look at the 2nd law of thermodynamics
There are two fundamental laws that 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.
Heat exchanger and 2nd law of thermodynamics
Let us see how heat transfer meets these fundamental laws for energy transport in heat exchangers.
Imagine, the hot fluid in the red container flows to cold fluid in the 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 a wall.
By definition, heat is an energy that is randomly moving in the direction of a higher disorder or higher entropy. Heat has no fixed destination. Heat is always in transit. Heat does not belong to any particular substance or system
With this background, let us see what is happening in a heat exchanger.
We can write, Q as, Q = ?U+ T?S, Q carries useful internal energy and useless entropy.
Hot fluid loses heat and becomes cold as it flows to lower temperatures. Heat Q goes from a high-temperature T2 to a lower-temperature T1 only because the overall entropy always increases. S1 = Q/T1 > S2 = Q/T2.
Therefore, we can see that heat transfer meets this requirement of the second law of thermodynamics also.
Reynolds number is a consequence of entropy
Explanation
Reynolds number, which is an indicator of turbulence [ eddy] in the system infuses entropy and maintains overall ?t, and ensures energy flows from high energy to low energy [ second law of thermodynamics].
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: It is nothing but an entropy balance equation
Re = Inertia Force / Viscous fore
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 that are all directed towards an increase in entropy and it is not just a dimensionless number.
Reynolds number – Entropy interaction
Consider two layers of hot fluids, each with its own average velocity. Because these molecules have thermal energy, a random velocity is superimposed on this mean; this is simply due to these molecules bouncing around randomly, as they do. A molecule from the fast side will eventually move into the slow side and collide with a molecule there. This will transfer kinetic energy from the fast molecule to the slow molecule. Similarly, some molecules on the low-speed side will eventually collide with molecules on the high-speed side. This will transfer energy once more.
As more of these molecules "change sides" and bring their average momentum with them, the velocity difference between the two streams will narrow. When all of the molecules are moving at the same speed, there is no longer any viscosity because a molecule moving to one side is the same as the molecule it displaced. It is statistically the same state.
Looking at it from that angle, viscosity is caused by kinetic energy gradients. As a result, it is caused by the "tendency of energy to diffuse."
To summarise, the more kinetic energy there is, the greater the entropy and the lower the viscous force. Viscous forces are nothing more than a measurement of how molecules diffuse energy. As a result of having more kinetic energy, there is more entropy, which means less viscous forces and thus a higher Reynolds number.