Question

can someone explain what is going on in the first 3 steps?

Answer 1

http://www.thermalfluidscentral.org/encyclopedia/index.php/Integral_solution_for_laminar_and_turbulent_natural_convection

Answer 2

@Directrix @zepdrix
any ideas, or know who might know?

Answer 3

@518nad

Answer 4

no idea what the equation is about but mathetatically, the first 2 steps are pretty strand forward. I have no idea how they get to (1) by integration though

Answer 5

the first 2 lines are definition of the continuity equation and momentum equation

its how they got to the 3rd equation which is bugging me

Answer 6

because they told you to multiply u on both sides of the fist equation and add it to the second, they created an equation where the left side can be simplified suing reverse chain rule and multiplication rule

Answer 7

ah ok, ill double check that part, but couldnt grasp what method they were using

Answer 8

at the time

Answer 9

I seem to be about to simplify the equation down to a result pretty similiar to their (1) where the only difference is that mine has +v*partial of u wrt y

Answer 10

I believe that the assumption is made that we're dealing with the region outside the boundary layer or on the boundary layer and thus there would be no changes in the y direction
which is why anything wrt y is neglected or =0
@caozeyuan

Answer 11

I am a biochemist not a fluid mechanic, so I can only comment on the math, not the physics.