Characteristic length (CL) is different than Length Scale (LS). Choosing CL is somehow arbitrary. For example in rectangular cavity, most people select the width of the cavity for scaling. However, nothing wrong if you use the height of the cavity, as far as using same length scale. In proper scaling, usually we select most influential length, such as the direction of boundary layer development. For example. cross flow over a cylinder, Diameter is the choose and not the length of the cylinder. But flow parallel to the cylinder axis, then the length of the cylinder is more important...

The geometry is important; the inclination can be adjusted/modified (e.g. by changing the axis/plane).

You have to assume your characteristic length first depending on your model design

Characteristic length (CL) is different than Length Scale (LS). Choosing CL is somehow arbitrary. For example in rectangular cavity, most people select the width of the cavity for scaling. However, nothing wrong if you use the height of the cavity, as far as using same length scale. In proper scaling, usually we select most influential length, such as the direction of boundary layer development. For example. cross flow over a cylinder, Diameter is the choose and not the length of the cylinder. But flow parallel to the cylinder axis, then the length of the cylinder is more important...

Dear Sir,

Characteristic Length is completely depens upon the geometry of your model and theconditions you considering to carry out your experiment.

As Abdulmajeed said, choosing characteristic length is arbitrary, mostly it is chosen based on the length of the wetted area along the direction of the flow. If you have inclination, you can choose the chord length as the CL. But you have to be careful when you are comparing the results of two cases where non-dimensional numbers are based on different CL. For example, let us assume, you are comparing the two results of flow over circular cylinder, in one case Reynolds number is based on Diameter of the cylinder and in another case Re is based on length of the cylinder. Then you have to convert the Re of one case based on the CL of another case. You cannot directly compare the results of same Re for both the cases.

Here is an idea: Characteristic Length is the length of the transport! ... then when you think of momentum transport in radial direction through a cylinder, CL can be diameter of the cylinder ... and then when you have a complex geometry with complex flow, think about the important transport phenomena happening within that geometry and find out which length scale is more important!

I believe the previous answers do not tackle the inclination part of the question, which seems to me to be the issue that may have motivated Bushan to post the question.

Let us first consider an horizontal flat plate, of width b and infinite length L, hotter than the environment. The flow established by natural convection on the top surface is different from that on the bottom surface. Heated up fluid from the bottom surface comes to the edges of the plate and rises. Colder surrounding fluid is then continuously pulled next to the bottom surface of the plate, to compensate for that fluid escaping at the edges. Due to the symmetry of the horizontal plate problem, the surrounding fluid approaches the bottom of the plate near its centreline and then progresses along half-width of the plate, i.e. along a distance b/2, until it reaches the edge of the plate and is allowed to rise. Therefore, the characteristic length (CL) could be taken as b/2. However, if the plate has an inclination, even a small one, then the symmetry of the problem is disrupted, and one can reason that the surrounding fluid shall approach the plate from its lower edge and then progress along its entire width before it is allowed to rise at the higher edge. Because the fluid is trying to rise, the flow remains attached to the bottom surface of the plate and does not detaches. Hence, CL could be taken as b this time. This example shows that for the same geometry one can have distinct CL, due to inclination. This should answer your question.

A similar discussion could be made to the top surface of this hotter-than-environment plate and again b and b/2 would appear as possible values for CL. However, in this case I should add that the particular value of b (not to mention L) and inclination can become important in what concerns the exact pattern of the flow that is established on the top surface. This is due to the possibility of formation of structures related to Bénard convection cells. In such case, the typical width of these cells would be a more suitable CL than the whole width b of the plate. Empirical correlations for plates exhibit this effect.

At the end of my previous answer, where it reads «the whole width b of the plate» it should have been better to have written «b/2 or b».

Thank you daniel

here i'll explain the problem

if the plate heated uniformly (two sides -top and bottom- with uniform heat flux), existing correlations are available and states that to replace "g" by "g cos(theta)" and it is valid up to 60 degree only,

most often it is said that if the plate is horizontal consider width or perimeter as characteristic length and in vertical case it is the height,

does it mean that up to 60 degree do there is no significance of height of the plate or cylinder in finding non dimensional numbers.,

My question is "is there any possibility to correlate non dimensionless numbers with reference to theta such that they are valid to any angle since the above correction is not valid for theta = 90 degree.,

Is there any possibility to propose a new characteristic length which satisfies both the cases like "horizontal perimeter and vertical height" and at any angle non dimensional numbers are not zero.

Thanks in advance

V_body/A_surface