Recent content by phioder

Hello How are the sinh() zeros defined? Unfortunately I don't understand the definitions found, google and wikipedia was searched, any help would be appreciated Thank you and best Regards phioder

Hello, The following equation: \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial r}+ \frac{\partial^2 u}{\partial z^2} = 0 is solved by separation of variables assuming a solution of the form: u=R(r)Z(z) In other cases the assumed solution is of the...

Hello coomast Absolutely not a waste of time, your answers give me a great feedback to understand better the equation and also included a lot of motivation. IMPO there are many small things that are not explained in books that save paper and ink and on the other side engineers are lost...

Hello coomast Thank you very much for your answer. You make special comments that make me further understand small details I haven't understand yet. After doing some research, as much as I understand now, the problem is indeed complicated and not trivial. During all this thread I have tried...

Hello coomast Thank you for all your assistance and help Does the solution to the problem changes a lot if the heat source is not uniform? Best Regards phioder

Hi, The following book https://www.amazon.com/dp/0534373887/?tag=pfamazon01-20 has a very good explanations on basic cylindrical problems, it shows some of the algebraical steps on how to go from Cartesian to cylindrical coordinates in 3D. The book also may give you some tips and could...

Hello coomast This will be a quick post, thank you again for your answers and the clear solution with separation of variables. Trying to associate physical quantities to the steady state problem the Poisson Eq. crossed the way...

Hi Could you cite 17, 18, original paper? Best Regards

Hello coomast If possible I would thank you if we come back to the steady state problem, unfortunately I still don't understand many things and I'm not ripe for transients The equation would be following 0 = \frac{\partial^2 u}{\partial r^2}+\frac{1}{r} \cdot \frac{\partial u}{\partial...

Hello coomast The first disappointment on the trip was that separation of variables does not work anymore, the equation has three variables and I suppose this method does not function anymore. The equation is following \frac{\partial u}{\partial t} = \frac{k}{c_p \rho} \cdot...

Dear coomast, Thank you for the great and clear explanation and the book recommendation. I will try to solve the equation \frac{\partial u}{\partial t} living out \varphi, steady state is left behind and transient is in the horizon. I will give a try to the book of Spiegel. Next step is to have...

Hello The temperature in the cylinder is given by the above equation, but is dimensionless, what about if one would like to calculate the temperature of cylinders of different materials? Is there a way to add to that equation, the density, thermal conductivity or other variables that would...

Dear Coomast Thank you very much for the answer and motivation. It helped much more than a bit forward. I'm currently trying to understand the idea of orthogonal bases and on the way want to try see the differences of expanding a function with different orders. Have seen some sights of...

Thank you for your reply and information, it seems that the book is what I'm looking for, but I have some questions before ordering (~$100 USD). As for now I have being using Dennis G. Zill, Differential Equations with Boundary-Value Problems with a very good but quick introduction to Partial...

Hello Looking for basic boundary-value problems with von Neumann conditions, more specific the applied ones to heat transfer or the wave equation. Could anyone recommend some good book that explains in an easy way the von Neumann conditions or has some solved problems related to the von...