What is Boundary: Definition and 999 Discussions

In physics and fluid mechanics, a boundary layer is the layer of fluid in the immediate vicinity of a bounding surface where the effects of viscosity are significant. The liquid or gas in the boundary layer tends to cling to the surface.
The boundary layer around a human is heated by the human, so it is warmer than the surrounding air. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boundary layer is the air layer (~ 1 km) near the ground. It is affected by the surface; day-night heat flows caused by the sun heating the ground, moisture, or momentum transfer to or from the surface.

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  1. U

    I Boundary conditions and discontinuity of EM fields

    Premise: everything that follows is done in the frequency domain. Boundary conditions If there are superficial currents (electric and magnetic) impressed on the boundary between two media, we have these discontinuities for the tangential components of the fields...
  2. B

    I Finding CDF given boundary conditions (simple stats and calc)

    I'm not quite sure if my problem is considered a calculus problem or a statistics problem, but I believe it to be a statistics related problem. Below is a screenshot of what I'm dealing with. For a) I expressed f(t) in terms of parameters p and u, and I got: $$f(t)=\frac{-u \cdot a + u \cdot...
  3. B

    A Point source with Dirichlet Boundary

    hi, all great brains, I have a question about BVP, which confused me a while, maybe someone can help to clarify it. For a point source with Dirichlet boundary in a 2D domain, the response at any coordinate except the source point is dependent on the surface of the source, for example, heat...
  4. maistral

    A General natural boundary condition?

    Hi, I'd like to be clarified regarding the general natural/Neumann boundary condition for a PDE. 1. The natural boundary condition is generally defined as: (1) and can be expressed as, according to this resource: (2) But apparently, according to...
  5. Othman0111

    How to deal with a circular light boundary conditions

    Hi everyone, in the attached file I tried to find the transmitted and the reflected coefficients. I ran into trouble applying the boundary conditions to the linear components of the electric field. Check the outlined boxes and see if they make sense. Thanks
  6. C

    What is the difference between flow energy and boundary work?

    What is the difference between the two? Also, as another question, for enthalpy, is it correct to define it to be the sum of internal energy and flow energy or is there another understanding for it? Thanks in advance
  7. K

    Solving a PDE with boundary problem

    Homework Statement I want to find the solution to the following problem: $$\begin{cases} \nabla^2 B=c^2 B &\text{ on the half plane } x>0 \\ B=B_0 \hat{z} & \text{ for } x<0 \end{cases}$$ in the ##xz## plane. ##c, B_0 \in \mathbb{R}## Homework Equations I am not really sure what would be...
  8. L

    What are the boundary conditions for this plate/ring system?

    Homework Statement [/B] I have a metal disc adhesively bonded at its edges to a piezoelectric ring. The piezoelectric ring vibrates radially which leads to the plate vibrating transversely. I am looking to work out the resonant frequency of the metal disc which I believe will depend on the...
  9. Othman0111

    Bessel Function Boundary Condition on the top of a Cylinder

    Hi everyone, I'm working through the boundary conditions and I could not figure out what to do with the last boundary condition (when z=L) I know that the values for K are: How so? 1. Homework Statement A hollow right angle cylinder of radius a and length l. The sides and bottom are...
  10. T

    A Determine PDE Boundary Condition via Analytical solution

    I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...
  11. B

    Green's Function Boundary Conditions

    Homework Statement I am trying to fill in the gaps of a calculation (computing the deflection potential ##\psi##) in this paper: http://adsabs.harvard.edu/abs/1994A%26A...284..285K We have the Poisson equation: ##\frac{1}{x}\frac{\partial}{\partial x} \left( x \frac{\partial \psi}{\partial...
  12. G

    Poisson's equation boundary conditions (electrostatics)

    Hi everyone! I have to solve a problem using Poisson's equation. There are two parallel infinite conductor planes in vacuum. The distance between them is d and they are both kept at a potential V=0. Between them there is a uniform volume density charge \rho_0>0 infinite along the directions...
  13. Nipon

    Green's function for a boundary value problem

    Homework Statement I try to integral as picture 1. The result that is found by me, it doesn't satisfy Green's function for boundary value problem. Homework EquationsThe Attempt at a Solution show in picture 2 & picture 3.
  14. I

    I Particle in a box, boundary co-ordinate change

    If you have a particle in a 1-d box with a finite potential when ##0 < x < L ## and an infinite potential outside this region, then the normalised wavefunction used to describe said particle is ## \psi (x) = \sqrt{\frac{2}{L}}\sin(\frac{n\pi x}{L})##. However, if you had say instead a finite...
  15. Sizhe

    Pipe flow with precipitation at boundary

    Homework Statement Consider a plug flow (slippery walls) with a uniform velocity ##U## in a circular pipe of diameter,##d## and length ##L##. The fluid is a supersaturated solution with a concentration ##c##. At the pipe wall, precipitation of solute happens at a net reaction rate per unit area...
  16. P

    I Boundary condition 1D beam

    Hi! I have a question related to boundary condition in a one dimensional beam subject to compression and traction efforts. In my class notes I have the following: If we consider a 1D beam of length L which is fixed at x=0 and subject to an effort F at x=0 we have the following boundary...
  17. S

    A Could information in a boundary be modified once encoded?

    Could information in a boundary be modified once encoded in holographic principle?There are models of universes where holographic principle has a different correspondence (there is absolutely no reason to assume that this would hold true for all possible universes. You could have a universe...
  18. B

    I Confused about the boundary conditions on a conductor

    In the textbook (attached image) it says that the boundary condition is V=0 at r=R. This creates a correlation that ##B_l=-A_l R^{2l+1}## but the potential at any boundary is continuous so when we take this account, we get. ##B_l=A_l R^{2l+1}## These two clearly contradict each other. I'd...
  19. Phys pilot

    Transform Dirichlet condition into mixed boundary condition

    Hello, If I have a homgeneous linear differential equation like this one (or any other eq): $$y''(x)-y'(x)=0$$ And they give me these Dirichlet boundary conditions: $$y(0)=y(1)=0$$ Can I transform them into a mixed boundary conditions?: $$y(0)=y'(1)=0$$ I tried solving the equation, derivating...
  20. A

    Exploring the Intersection of Ellipsoids and Spherical Shells

    Homework Statement I would like to know how the boundary of the inequality change when the origin of the coordinate system changes. Homework Equations The original inequality is[/B] $$ r_0 \le x^2+y^2+z^2 \le R^2$$ I would like to know the boundary of the following term, considering the...
  21. N

    Need help understanding "Electrostatic Boundary Conditions"

    We are using griffith's 4 edition in my electromagnetic course atm. and there's something I just don't understand about boundary conditions. It says that if we have a surface charge, and we put a pillbox on it, in such a way that half of it extends under the surface charge, and the other half...
  22. B

    Simple Harmonic Oscillator with Boundary Conditions

    How would you solve for the Amplitude(A) and Phase Constant(ø) of a spring undergoing simple harmonic motion given the following boundary conditions: (x1,t1)=(0.01, 0) (x2,t2)=(0.04, 5) f=13Hz x values are given in relation to the equilibrium point. Equation of Motion for a spring undergoing...
  23. C

    Would there be turbulence around objects w/o boundary layers

    According to wikipedia "The onset of turbulence can be predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a...
  24. T

    Electromagnetism Help-- Magnetostatics Boundary Problem

    Homework Statement Two magnetic materials are separated by a planar boundary. The first magnetic material has a relative permeability μr2=2; the second material has a relative permeability μr2=3. A magnetic field of magnitude B1= 4 T exists within the first material. The boundary is...
  25. evinda

    MHB Initial and boundary value problem

    Hello! (Wave) I want to find the solution of the following initial and boundary value problem: $$u_t(x,t)-u_{xx}(x,t)=0, x>0, t>0 \\ u_x(0,t)=0, t>0, \\ u(x,0)=x^2, x>0.$$I have done the following so far: $$u(x,t)=X(x) T(t)$$ $$u_t(x,t)=u_{xx}(x,t) \Rightarrow...
  26. Andy Resnick

    I Immersed Boundary method and No-Slip condition

    Just got back from a conference where one of the invited speakers presented his work on using the Immersed Boundary method with Adaptive Mesh (to model cardiovascular flow): https://cims.nyu.edu/~griffith/ This summer, I have an undergrad modeling pulsatile flow in an elastic tube using the...
  27. JTC

    A What is the difference between Flow and Boundary Separation?

    Could someone please go here... https://en.wikipedia.org/wiki/Flow_separation And explain to me the difference between Flow and Boundary Separation discussed in the opening. Because this explanation makes no sense to me. I have the problem. I just don't understand the difference.
  28. evinda

    MHB Boundary value problem for Laplace equation

    Hello! (Wave) Let $a,b>0$ and $D$ the rectangle $(0,a) \times (0,b)$. We consider the boundary value problem in $D$ for the Laplace equation, with Dirichlet boundary conditions, $\left\{\begin{matrix} u_{xx}+u_{yy}=0 & \text{ in } D,\\ u=h & \text{ in } \partial{D}, \end{matrix}\right.$...
  29. A

    Metal boundary and PML in Comsol

    Hello What is Metal and PML boundry condition in Comsol? How can i specify metals and insulators ?
  30. Zubair Ahmad

    I Boundary conditions for displacement vector D

    Griffith's writes in chapter 7 electrodynamics that D1.a - D2.a = sigma. a. But minus sine comes when we evaluate the dot product first. How does the minus sign occur without evaluating the dot product?
  31. T

    Boundary conditions errantly applied to pressure across flui

    I am trying to decipher if an error occurred in a calculation given in this paper. It is understandable that if two compressible fluids of different uniform densities have a common interface (e.g. Figure 1), then to be in equilibrium and supported against gravity, there must be a pressure...
  32. EastWindBreaks

    Heat transfer boundary condition

    Homework Statement I am confused on how it's using the surrounding temperature minus the surface temperature as its the other way around in the Newton's law of cooling, Doing that would change the sign of convection right? I don't see the reason to do that, since if left side is hotter, then...
  33. Z

    A Solve GHY Boundary Term Problem for Calculations

    Hi everybody ! In one of my papers I need to add Gibbons-Hawking-York boundary term in order to calculate everything properly. I found a paper (https://www.sciencedirect.com/science/article/pii/S0370269316306530 ) in which authors included this term into the action. My problem is: I tried to...
  34. yecko

    Boundary condition of pinned/fixed/roller support

    Homework Statement [/B]Homework Equations shear bending diagram The Attempt at a Solution May I ask for supports like these, if shear force V= 0 or not when x=L? From the shear diagram, it is a shape increase from -0.5P to 0 there. As the shear go back to zero is owing to the reaction force...
  35. BookWei

    I Solving Boundary Conditions in 4D Spacetime Volume

    Hi, my classmate asks me an interesting question: For a finite 4D volume in spacetime, its boundary is a 3D close surface. If the 4D volume is a 4D rectangular, the boundary consists of eight 3D surfaces. The boundary condition is specified on these eight 3D surface. Please explain the physical...
  36. stephen8686

    Introductory QM boundary conditions

    Homework Statement A particle is represented by the following wave function: ψ(x)=0 x<-L/2 =C(2x/L+1) -L/2<x<0 =C(-2x/L+1) 0<x<+L/2 =0 x>+L/2 use the normalization condition to find C Homework Equations ψ(x) must be...
  37. Skrphys

    Speed of a wave when crossing a boundary vs. not

    I am having a problem with understanding concepts related to the speed of a wave. Here are my thoughts laid out: 1) The speed of a wave is dependent only on the medium 2) When a wave crosses from a less dense medium into a more dense medium (or visa versa) the speed of the wave is always...
  38. J

    I Is the Boundary Chart for a Closed Unit Ball Injective?

    I want to show that a closed unit ball is manifold with boundary and I attempted as uploaded. But I am not happy with the way I showed the boundary chart is injective. Am I right?
  39. cromata

    I Boundary conditions of a forced oscillator (string)

    -If we have string of length L that has fixed ends, then we can easily find frequencies with which this string can oscillate: We just need to solve wave equation: ∂2y/∂x2=1/c2*∂2∂t2 (c is determined by strings properties (linear density and tension), with Dirichlet boundary conditions...
  40. ajbroadbent

    Curved Mesh on Symmetry Boundary in ANSYS Maxwell 3D

    I figured this would be the best place to ask as there doesn't seem to be a FEM/Simulation specific sub-forum here, but I am looking for some help regarding mesh generation in ANSYS Maxwell. I have an array of "micro-needles" that I am applying a voltage to in order to determine the electric...
  41. D

    What Does the 10% Resistance Boundary Mean in Circuit Measurements?

    Homework Statement if someone could help me with this it would be much appreciated. In physics, I used a 98Ω resistor in a series circuit and measured the current and voltage output from battery, using the current and voltage I calculated the resistance. I=0.0094A V=1 Rt=1/0.0094=106.38Ω even...
  42. dRic2

    I Fluid separation in boundary layer

    Hi PF, I'm trying to derive the Prandlt condition (not sure if it is Prandlt's work tough) for a fluid to separate from a surface in the boundary layer. The equation should be: ##\frac {\partial^2 v_x} {\partial y^2} = 0## which is quite "intuitive" to me. To derive it let's start from the...
  43. C

    (Numerical) Boundary Value Problem for Schrodinger's Equation

    Homework Statement Suppose we have the standard rectangular potential barrier in 1D, with $$ V = \left\{ \! \begin{aligned} 0 & \,\text{ if } x<0, x>d\\ V_0 & \,\text{ if } x>0,x<d\\ \end{aligned} \right. $$ The standard approach to solve for tunneling through the barrier is to match the...
  44. H

    A Applying boundary conditions on an almost spherical body

    I am solving the Laplace equation in 3D: \nabla^{2}V=0 I am considering azumuthal symmetry, so using the usual co-ordinates V=V(r,\theta). Now suppose I have two boundary conditions for [V, which are: V(R(t)+\varepsilon f(t,\theta),\theta)=1,\quad V\rightarrow 0\quad\textrm{as}\quad...
  45. B

    Schrodinger equation and boundary conditions

    Hi at all, I'm tring to solve Schrodinger equation in spherically symmetry with these bondary conditions: ##\lim_{r \rightarrow 0} u(r)\ltimes r^{l+1}## ##\lim_{r \rightarrow 0} u'(r)\ltimes (l+1)r^{l}## For eigenvalues, the text I'm following says that I have to consider that the...
  46. P

    Ansys Maxwell: Boundary definition

    Hello, I am trying to find a Magnetostatic(3D) solution for my design. My design consist of a coil embedded in Ceramic material developed by LTCC technology. I am below queries: 1. Is it important to define a material"Insulating"? How it will affect the Inductance of the system and the...
  47. Hypercube

    Electrostatic Boundary Conditions

    Hello PF community, I am currently self-studying electrodynamics from Griffiths textbook, and I'm at a point where the book discusses electrostatic boundary conditions. If someone can please check if my reasoning is right. So, as I am approaching an infinite, uniformly charged plane (let the...
  48. Mzzed

    I Boundary Conditions for System of PDEs

    I am unsure how to choose the boundary conditions for a system of PDEs or for a single PDE for that matter. The situation I am stuck with involves a system of 4 PDEs describing plasma in a cylinder. The dependent variables being used are Vr, Vt, Vz, ni, and the independent variables are Rr...
  49. M

    Green's Function with Neumann Boundary Conditions

    Homework Statement [/B] Determine the Green's functions for the two-point boundary value problem u''(x) = f(x) on 0 < x < 1 with a Neumann boundary condition at x = 0 and a Dirichlet condition at x = 1, i.e, find the function G(x; x) solving u''(x) = delta(x - xbar) (the Dirac delta...
  50. Dor

    Steady state boundary conditions between metal/dielectric?

    There are few thing I'm not sure of and be happy for clarifications. In general: at steady state, what are the electric-field,potential, and current boundary conditions between a conductor and a dielectric medium? more specific: a) When dealing with a perfect conductor there exist a surface...
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