In the laminar flow in the constant heat wall pipe the fully developed Nu magnitude is 4.36, then is the average Nu still same or different in magnitude?
The local Nu is used to show the development of heat flow along a wall ( we chose same points to do the study) ; In the case of average Nu wall is considered as a whole body, and the heat flow is global.
So we can say that there are some cases where the average Nu equals the local Nu , and others not.
The local Nu is used to show the development of heat flow along a wall ( we chose same points to do the study) ; In the case of average Nu wall is considered as a whole body, and the heat flow is global.
So we can say that there are some cases where the average Nu equals the local Nu , and others not.
In developing flow inside pipes the Nu number changes along the axial position. After the flow is fully developed the Nu number remains constant along the axial position (Nu=4.36 for laminar flow, constant heat flux at wall, circular pipe). Depending on the tube lenght you are averaging the Nu can be 4.36 (total tube lenght considered is in fully developed region) or diferent (part of tube lenght in developing region). If the entrance lenght is short compared to total tube lenght you can neglect the tube entrance effect and assume Nu=4.36 for all tube (aproximation. Be carefull).
the Nu is a dimensionless number that shows how much heat transfer from a surface to a moving fluid. to be able to understand the difference between both, check the difference between average (which consider the body as whole) and the fully developed flow which differ according to the case studied internal or external constant surface temperature or constant heat flux. Again imagine the curve for the convection heat transfer coefficient with distance which start high then decreases in laminar region jump up in the transition and slow down in turbulent flow. so they are two different values you may search for a relation but it will be dependent on the case studied.
Nusselt number is a dimensionless parameter indicative of the ratio of heat transfer by convection to conduction across a fluid layer. It is a coefficient indicating the rate at which a geometry transfer heat.
Average Nusselt number is the mean of Local Nusselt numbers over the entire heat transfer surface. Therefore, its value depends on the geometry or surface of heat transfer. The type of the flow regime or region is not a constraint for the use of average Nusselt number as heat transfer coefficient. It can be used to estimate the heat transfer at the entrance region as well as in a fully developed region.
Fully developed Nusselt number is only for the fully developed region. It is an average Nusselt number estimated when the flow is fully developed. The Nusselt number is a constant throughout the region, but its value depends on the surface thermal condition
Thanks for all of you for your interest, i think all of your answers are correct depends on the point of view. thanks for Dr. Bahiraei, Dr. Das , Dr. Benarab, Dr. Alves , Dr. Beithou, Dr. Kayode . Really i appreciate you sharing for knowledge.
The local Nu number is constant throughout the fully developed region, however its value depends on the flow structure , the geometry and surface thermal condition. for laminar flow in circular tube under a uniform surface temperature (Nu=3.66) or uniform surface heat flux (Nu=4.36)..
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