You can calculate the average Nusselt number. Then, you can plot the Nu as a function of turbulent intensity. Amirreza Rezayan

really thanks dear Shayan Davani

 I calculated Nusselt number and turbulent intensity over my wall, they were similar in trend. Is it true by having Nusselt and heat flux calculate my bulk temperature? [nu=hl/k and then h=q/(tw-tb)] i want relate change of temperature to turbulent intensity and make a conclusion that how Turbulent intensity affect temperature gradient, do you think the procedure is correct?

best wishes

Amirreza

Dear Amirreza Rezayan

The Reynolds number for hot air passes over a cold plate, is given by:

Re=ρVL/μ

Typically Re > Re-critical is classified as turbulent flows. The relation between Heat Transfer and Reynolds number for this particular system can be written as:

Nu=A*Re^B * Pr^C ( Pr = Prandtl number, A, B and C are constant numbers up to your case like Nu=0.023*Re^0.8Pr^n)

Here Nu is the Nusselt Number and is given by

Nu=hL/k

>>> A*Re^B * Pr^C ~ hL/k (higher Re means more (intensive) turbulence)

This particular relation of the Nusselt number, Reynolds number and Prandtl number is called the Dittus-Bolter equation. From this equation we can make a very qualitative inference that the heat transfer rate increases with turbulence for this particular system in consideration.

thanks for your consideration Amir Reza Ansari Dezfoli but i have another question, increasing in Nusselet number means higher heat transfer coefficient(HTC). when HTC increases and assuming constant heat flux, so temperature difference should decrease, as I guess. am I right?

Dear Amirreza Rezayan

Yes, but need some considerations:

Bulk air Temp = Tb, Wall Temp. = Tw.

1- If both Tw and Tb be constant (hear/mass source on wall and air ....) then when laminar flow change to turbulence or turbulence intensity increases, then boundary layer { Where T change from Tw to Tb} increases which means higher rate of heat transfer.

2- If Tw or Tb can change, then higher HTC means air become hotter faster or wall become colder faster.

Can you get the point? boundary layer thickness and heat transfer rate should be considered.

yes , I get the point.

I didn't considered boundary layer thickness and I guess it leads me to error in calculation of Tb. T wall is constant in my problem and I just need to calculate Tb. Amir Reza Ansari Dezfoli

While Nu increases as Reynolds, how it affects temperature? the hot fluid (air) which is passing over the cold plate, how react to Nu increasing? Amir Reza Ansari Dezfoli Shayan Davani

Factors that affect rate of heat flow include the conductivity of the material,temperature difference across the material, thickness of the material, and area of the material. Different materials have greater or lesser resistance to heat transfer, making them better insulators or better conductors.

The heat transfer coefficient increases when the fluid velocity increases (better mixing in the turbulent boundary layer, thinner laminar su-blayer). That's why 'Heat Transfer Coefficient' (which is the combined property of fluid+flow+geometry of body) increases with increase in the velocity of fluid. In Newton's law of cooling, the heat transfer coefficient acts as a constant of proportionality. However, the heat transfer coefficient will still decrease along the length of the surface, but to a lesser degree than for laminar flow. On the other hand, a turbulent flow can be either an advantage or disadvantage. A turbulent flow increases the amount of air resistance and noise; however, a turbulent flow also accelerates heat conduction and thermal mixing. Therefore, understanding, handling, and controlling turbulent flows can be crucial for successful product design.

Dear Rezayan,

To quantify the heat transfer improvement, you can calculate the average Nusselt number in a local position, or to localisate a turbulence zones by calculating the local Re Number and then you can calculate the average Nusselt Number in theses regions by the following formulas:

Nu= -(dT/dx) at x=xi or Nu= -(Knf/Kf)(dT/dx) at x=xi for nanofluids cases.

You can do the following:

1. Simulate and calculate heat transfer ( by calculating h) in laminar and turbulent flows using two equations ( Sieder Tate and Gnielinski ) or any other correlations. All such correlations are provided in any standard heat-transfer book.

Better to read any of the 'forced heat transfer chapter for it".

Then you can plot "h" with Nre, and you will come to know that the value of heat transfer coefficient suddenly increases because of transition from Laminar to Turbulent region.

You will get a plot such as mentioned on this page:

https://www.hrs-heatexchangers.com/resource/comparison-laminar-turbulent-flow/

Thanks

Parag Patil thanks , I found it useful. really thanks