# How to compute velocity distribution in the developing boundary layer on the cylinder

Air flows perpendicular to the axis of a cylinder $$a=1$$ cm in diameter. Air speed upstream of the cylinder is $$U=6.72$$ mm/s and its kinematic viscosity is $$2.1×10^{-5}$$ at 350 K. I want to obtain the velocity distribution in the developing boundary layer on the cylinder by using a numerical method. Which numerical method do you suggest to approach this question?

Moreover, I am curious to know the thermal boundary layer equations in this case.

I would be grateful if you hint me how should I solve this kind of problems or refer me to a relevant reference for these kinds of questions.

• So how are you calculating friction factor? 64/Re or Colebrook White? Feb 8 at 5:10

Which numerical method do you suggest to approach this question?

I have used finite volume method (FVM) before, It's used in big CFD codes like OpenFOAM and Fluent and you can find lots of resources on FVM to get started.

Moreover, I am curious to know the thermal boundary layer equations in this case.

In this case you need to solve the energy equation $$\frac{\partial}{\partial t} (\rho c_p T) + \nabla . [\rho c_p \boldsymbol v T] = \nabla . [k \nabla T] + Q^T$$

Where $$Q^T$$ is the temperature source term (assuming you're familiar with remaining basic variables $$\rho, T, v, k, c_p$$). However, the energy equation is hardly ever solved in such form, and based on your problem you're going to make lots of assumptions and (justified) simplifications.

I would be grateful if you hint me how should I solve this kind of problems or refer me to a relevant reference for these kinds of questions.

CFD is a big topic, and involves many steps, like physical domain discretization, governing equations discretization into algebraic equations and finally solving the system of equations. If you are willing to deeply understand FVM in CFD and write your own solvers, I highly recommend The Finite Volume Method in Computational Fluid Dynamics.

There is also a simple OpenFOAM tutorial for flow around cylinders that may get you started.