Solving Unsteady Problems in Mechanical Engineering

[JohnJohn8]

Hello all,

I am recently graduated in mechanial engineering and started working and so I don't have much experience yet. I have to deal with an unsteady problem.

Now in the textbooks a lot steady assumptions are made and so these relations are not really valid for my problem.

This is maybe a stupid question, but how should a tackle this problem?

Thank you in advance for your help.

 

[BvU]

Hello JJ,

You forgot to tell us about the problem !

 

[Nidum]

What is the problem ?

 

[JohnJohn8]

Oh yes sorry, it is about cooling a block which moves which a certain velocity. There is a flow going over the block. The textbook in question is 'heat and mass transfer' from Cengel.

 

[Nidum]

Diagram and complete description of problem please .

 

[BvU]

Maybe this helps (it's the template from the homework forum -- where a moderator will probably move this thread anyway)
This kind of approach is very sensible in almost all exercises!
Steady state problems put all time derivatives to zero; unsteady state problems leave them in place. So your relevant equations should show that.

Homework Statement

Homework Equations

The Attempt at a Solution

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[JohnJohn8]

So a block moves with a certain velocity (dependant on time). There is a free stream going around the block which cools it. I am interested in the temperature distribution of the block. This is a 3D unsteady heat conduction problem with convection boundary conditions. For convection boundary conditions a heat transfer coëfficiënt is needed. For determining a heat transfer coeffcient, the Nusselt number is needed and that is related to the Reynolds and the Prandtl number. The relations given in the textbook by solving the boundary layer equations, but is assumed that there is steady, incompressible and laminar flow. However these assumptions are not correct for my case. How should I proceed? Thanks in advance. (See also the picture).

 

[Chestermiller]

The first step is to convert this from a 3D problem to a 1D problem. Is the block you have shown in the sketch roughly to scale? If so, suppose you assume that the slab is of infinite width (rather than finite width). And suppose you can assign an approximate constant average value to the convective heat transfer coefficient on top and bottom surfaces, rather than one that varies along the length of the block. Now you have a 1D problem for a slab of finite thickness, with a convective heat transfer coefficient at the larger surfaces. Incidentally, what is the boundary condition at the bottom surface?

I will continue after you have had a chance to digest what I have said above, and have had a chance to ask questions.

Chet