What is Boundary: Definition and 1000 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. E

    Understanding the Non-Manifold Property of Euclidean Half-Space

    Because of boundary points, I can sort of see intuitively why Euclidean half-space, i.e. {(x_1, ... , x_n) : x_n >= 0} is not a manifold, but is there a simple rigorous argument for why Euclidean half-space is not homeomorphic to an open set of R^n. I do not know too much topology and the...
  2. J

    Finding the solution of the wave equation that satisfies the boundary conditions

    Homework Statement Homework Equations N/A The Attempt at a Solution Really stuck with this, i can't work out how to apply the boundary conditions to generate the simultaneous equations to find the specific solution. Can't find any similar examples either. Help appreciated.
  3. J

    Finding the particular solution to an ODE with set boundary conditions.

    Homework Statement Homework Equations N/A The Attempt at a Solution The problem and attempt are as above, I'm not sure where to go from here though. I'm not sure what to do with the boundary condition of dx/dt=-2 and t=0. Any help appreciated.
  4. I

    Problem with a boundary condition in Comsol

    hi, I'm a chemical engineering student with a little problem with Comsol multiphysics; in practice, i have to solve a problem of diffusion in a solid sphere. after drawing the domain, i have to set a boundary condition on sphere's surfaces. this condition, for my problem, is FLUX=Kc(Cb-C) and...
  5. S

    Transmission Lines: Boundary Conditions Meaning

    what do boundary conditions mean wid respect to transmission lines??
  6. S

    Is the universe truly isotropic at its boundary?

    the universe is supposedly isotropic. it is also supposedly finite. if i were on a galaxy farthest from the earth, i would experience nonIsotropy (forgive the made up word). because if i look in the direction of the Earth i would see a appropriately populated neighborhood with galaxies moving...
  7. J

    Boundary Value Problem , triangular plate

    This exercise deal with the temperature u(x,y,t) in a homogeneous and thin plate. We assume that the top and bottom of the plate are insulated and the material has diffusivity k. Write the BVP . Problem: The plate is triangular , picture this as a right triangle with this coordinates, (0,0) ...
  8. A

    How can you find a recursive sequence that converges to a desired limit point?

    Hi guys. I'm apprently stuck on the basics of the analysis. On the proof that Q lacks least upper boundary property to be precise. The example I have uses a set A (p in Q | p > 0, p^2 < 2) then q is defined as p - \frac{p^{2} - 2}{p + 2} . Then they show that if p is in A then q is in A too...
  9. J

    Boundary of open set always zero measure?

    Is this true? V\subset\mathbb{R}^n\;\textrm{open}\quad\implies\quad m_n(\partial V)=0
  10. N

    Waves in a coaxial cable: Boundary conditions

    Homework Statement Hi all. I have the following expression, which relates the incoming amplitude with the reflected amplitude at a point x = L in a coaxial cable: A_{\text{reflected}} = \frac{R-Z_0}{R+Z_0}A_{\text{incoming}}. Here R is the resistance at the point x = L and Z0 is the...
  11. L

    Extending a function from the boundary of an open set

    See the link, please http://camoo.freeshell.org/quest1.pdf" Laura
  12. J

    COMSOL doing periodic boundary conditions in navier stokes

    Please can anyone tell me how to set this up? I know how to do the required settings in the Physics/Period Conditions. However, to fully implement it, I'm also required to choose boundary conditions in the 2D incompressible navier stokes solver (e.g. wall, inlet, outflow, open boundary...
  13. MTd2

    How to impose a boundary on higgs mass given the top mass?

    Please, I would like sugestions on how to calculate that. It seems a very common topic on higgs experimental search, and I would like to understand that. Thanks!
  14. K

    Electric field and boundary conditions

    Homework Statement One half of the region between the plates of a spherical capacitor of inner and outer radii a and b is filled with a linear isotropic dielectric of permittivity \epsilon_1 and the other half has permittivity \epsilon_2, as shown in the figure. If the inner plate has total...
  15. K

    Boundary condition of EM field

    On the boundary (surface) of two regions, the tangential components of electric fields on above and below surface are continuous. I wonder if it is also true for displacement \vec{D} and polarization \vec{P}? That is, can I say: the tangential component of \vec{D} or \vec{P} on above and below...
  16. S

    How is entropy defined by boundary area in Holographic Principle?

    Reference: http://en.wikipedia.org/wiki/Holographic_Principle The principle states that the description of a volume of space should be thought of as encoded on a boundary to the region, preferably a light-like boundary like a gravitational horizon. For a black hole, the principle states that...
  17. L

    Comsol help write a boundary condition

    Hi there, I'm using comsol for the first time, and I think I've got everything working, except that I need to write a boundary condition that is dependent upon the gradient of a variable. How do I tell Comsol to take the gradient? I suppose I can define my own function, but I don't even know...
  18. B

    Boundary Value Problem for y'' -2y' + 2y = 0: Help and Solution Guide

    Homework Statement solve the BVP: y'' -2y' + 2y = 0 ... (1) reduction y(0) = 1 y(pi) = 1 Homework Equations y= emx The Attempt at a Solution substitution y=emx & its derivatives in (1) we get: m2 -2m +2 = 0 = (1+i)(1-i) then y = e(c1 sinx + c2 cosx) using the...
  19. P

    Electric Boundary Value Problem

    Homework Statement A pair of infinite, parallel planes are equipotential surfaces. The plane at z = 0 has an electric potential of 0 and the plane at z = b also has a potential of zero. The electric field at b is 0 at time t at which there is a constant, positive charge density between the...
  20. C

    Hydrogen Atom Wavefunction Boundary conditions

    Hi, I have been given a differential equation to use in order to solve for the Hydrogen wavefunction in the ground state using Euler's method. d^2u_nl/dr^2 -(l(l+1)/r^2)*u_nl + 2k*(E_nl-V(r))*u_nl = 0 V(r) = -a/r where a = 1/137.04 I have been given initial conditions u_nl(0) = 0 an...
  21. M

    Boundary condition at junction of heated rods

    1. 1D heat conduction problem: Two rods, the first of length a , the second of length L-a with respective cross sectional areas A_1 , A_2 and heat conductivities k_1 , k_2 , are joined at one end. There are some boundary conditions on the other ends of the rods, but my question is only...
  22. S

    Applying Boundary Conditions for the Heat Conduction Equation

    Homework Statement Solve \left(\frac{\partial^{2}}{\partial z^{2}}- \frac{1}{\kappa} \frac{\partial}{\partial t}\right) T=0 with boundary conditions (i) T(0,t)=T_{0}+T_{1} Sin[\omega t] (ii) T is finite as z\rightarrow\inftyHomework Equations Separation of Variables gives: T =...
  23. U

    Trying to solve a boundary value problem

    Trying to solve the following boundary value problems. y'' + 4y = cos x; y(0) = 0, y(pi) = 0 y'' + 4y = sin x; y(0) = 0, y(pi) = 0 The answer key says that there's no solution to the first part, but there is a solution to the 2nd part. I'm really lost and am not sure how to go...
  24. JasonJo

    Help me visualize this, boundary of the future

    Let S be any subset of M, where (M, g_ab) is a spacetime. Can you guys help me kind of visualize why the boundary of the chronological future of S is an achronal, 3 dimensional embedded manifold? I am just having a hard time seeing why this is so. I'm picturing a sphere, and then having...
  25. N

    How do i deal with integral boundary conditions?

    I am trying to solve an ode of the form u"(x)=a(x) where a(x) is some known function and the domain is from -inf to +inf. I am required to use Green's function. The boundary condition is u(0) = Integral[u(x),{x,0,1}] = 0 My Green's function has the form G(x,y) = A(y)*x+B(y) x<y G(x,y)...
  26. S

    Comsol moving boundary+ Heat Transfer

    Hi guys, I have a question in using comsol software, particularly on heat transfer. Its a 2D geometry. A rectangle whereby heat is applied on the top surface at the particular point and the 3 sides are thermally insulated. As more heat is applied over time, a hole will be created. A...
  27. C

    Boundary condition at the Sphere in ambient fields

    Homework Statement The Problem is mentioned in the attachment. Homework Equations substitute C2 in terms of C1. Can we use the identity that trace of rate of strain tensor equals 0 in an incompressible flow? The Attempt at a Solution I arrived at the following equation V...
  28. L

    How Can You Prove the Boundary of a Set in Topology?

    Homework Statement Let X be a space. A\subseteqX and U, V, W \in topolgy(X). If W\subseteq U\cup V and U\cap V\neq emptyset, Prove bd(W) = bd(W\capU) \cup bd (W\cap V) Homework Equations bd(W) is the boundary of W... I think I have the "\supseteq" part, but I am having trouble with...
  29. T

    Solve Laplace equation with boundary conditions

    Homework Statement Calculate potential function and the electric field for the region between two concentric cylinders, where V ( inner cylinder) = 0 at r = 0.015 m and V(outer cylinder) = 100 for r = 0.025 Homework Equations \Delta (square ) V = 0 The Attempt at a Solution so...
  30. G

    [Q]One question about Magnetic boundary conditions.

    Hi. You know that B_{1n} = B_{2n} as one of the boundary condition when magnetic field is go across from material 1 to material 2, n means direction perpendicular to the boundary surface. I wander this theorem is right in non-uniform field which is function of space variable r...
  31. B

    Heat conduction in bars: varying the boundary condition. Harmonics problem

    Homework Statement A problem with odd harmonics only. Show that the solution of the heat equation du/dt=c2*(d2u)/(dx2), subject to boundary conditions u(0,t)=0 and ux(L,t)=0, and the initial condition u(x,0)=f(x) , is u(x,t)= \sum Bnsin[(\pi/2L)(2n+1)x]e-((c*\pi/2L)*(2n+1))^2 where n...
  32. F

    Understanding Boundary Conditions for Electric Fields

    Hello everyone, if an electric field in a medium with permittivity eps_1 moves at an angle into a material with eps_2, there is refraction. The field in the second medium changes angle. we can see that the tangential component is not changed but the one normal to the surface of separation...
  33. K

    Finding D2 for a Dielectric Interface with Given Conditions

    Urgent: Boundary Condition querries. Homework Statement Question given: A dielectric interface is described by 4y+3z=12. The side including the origin is free space and its electric flux density, D=ax+3ay+2az (micro) C/m2. On the other side, (Epsilon)r2 = 2. Find D2. Homework Equations...
  34. O

    Question related to fill in boundary conditions in comsol

    Firstly I really feel so lucky to find this forum. Since I don't have a strong physics background but now dealing with many problems directly related to physics. I'm now doing some simulation in comsol and need to solve some PDEs. I'm using this PDE coefficient form in comsol. The equations...
  35. N

    Diff. eq. and boundary conditions

    Homework Statement Hi all. I am given the following differential equation: X'' - k*X=0. I am told that k = -m^2, so the general solution is given by: X = a*cos(m*x)+b*sin(m*x), where a and b are constants. I am also given boundary conditions: 1) X(-Pi) = X(Pi) 2) X'(-Pi) =...
  36. A

    Tripping the boundary layer why?

    Tripping the boundary layer...why?? I don't understand why we have these "vortex generators" to trip the boundary layer into becoming turbulent...i've seen this a lot on F1 cars. On a regular car you can trip the boundary layer in front of your windshield...does the boundary layer somehow...
  37. N

    Laplace's equation on a rectangle with mixed boundary conditions

    Homework Statement Solve Laplace's equation inside the rectangle 0 \le x \le L, 0 \le y \le H with the following boundary conditions u(0,y) = g(y)\text{, } u(L,y) = 0\text{, } u_y(x,0) = 0\text{, and } u(x,H) = 0 Homework Equations The Attempt at a Solution I know that with...
  38. D

    Free Electron Model: Why periodic boundary conditions and what is L ?

    Free Electron Model: Why periodic boundary conditions and what is "L"? Right, hello! The quantum free electron model for electrons in solids (in One dimension) says we need to use periodic boundary conditions such that if Y(x) is the wavefunction, then Y(x) = Y(x+L). Where L seems to be...
  39. M

    Boundary Conditions and Trig Identities in Solving Differential Equations

    Homework Statement I have the solution to the differential equation : Phi = A*sin(x) + B*cos(x) and need to apply the boundary conditions Phi(-a/2) = Phi(a/2) = 0. Homework Equations The Attempt at a Solution I am confused. If I plug these in, then I get A*sin(-ka/2) = -...
  40. A

    Electric Potential across a Boundary

    Hi everyone, I have a uniform electric field in which I place an object. I have read that the electric potential inside my object, \Phi_{in}, and the one on the outside, \Phi_{out} must be equal at the boundary. (ie. \Phi_{in}=\Phi_{out} on the boundary) I don't understand why this is...
  41. N

    Evaluating integrals with infinity as boundary

    Homework Statement Hi all. Please take a look at this: \int_{ - \infty }^\infty {x \cdot \exp } \left( { - \left| x \right|} \right){\rm{d}}x = \left. {\left( { - \exp \left( { - \left| x \right|} \right) \cdot x} \right)} \right|_{ - \infty }^\infty + \int_{ - \infty }^\infty {\exp...
  42. N

    Relation between codifferential and boundary operator

    As we know,the codifferential \delta is the adjoint of the exterior derivative,and the boundary operator \partial is also the adjoint of exterior derivative according to stokes' theorem, then what is the relation between codifferential and boundary operator?
  43. N

    Boundary Conditions, Continuum Mechanics

    Mods: I wasn't sure if I should put this here or in DE's, if you think it would be better there, feel free to move it. Everyone: If I have a bunch of particles, which I'm modelling as a continuum, and I want to put periodic boundary conditions which reflect (completely specular reflection)...
  44. R

    Green Function and Boundary Conditions

    Hey folks, I'm trying to find the Green function for the equation -\partial_\mu \partial^\mu \phi = K where K is some source term. Its a 2D problem with the wave confined to a rectangular cavity where the cavity is located at z = 0 and z=a. This tells me that G|_0= G|_a=0 I've pretty...
  45. T

    Boundary Conditions Laplace

    Hi there, I am solving laplace equation in a code i made in C. I am using Finite Difference Method in order to simulate the current pattern. I used the stream function to do that...
  46. B

    Shooting method and a shock wave (discontinuity at the inner boundary condition)

    I've done searching on the topic, and I really don't know where else to turn, so here it goes. I hope somebody can point me in the right direction. I've been working on using a shooting method to solve the steady-state spherically symmetric fluid equations for an accreting plasma. Basically, it...
  47. H

    Circular Plate w/ Hole: Boundary Conditions

    Hey people can u please tell me what will be the boundary conditions for a circular plate with a central hole clamped at the circumference... Plate is axis symmetric and is under uniform load..
  48. E

    Boundary conditions for fluid flow

    What are the general boundary conditions for nonviscous, incompressible fluid flow? I am trying to find the velocity of fluid at the surface of a sphere with the incident fluid having uniform velocity. I am surprised to find in the solution that the radial velocity at the surface does not...
  49. U

    Problem with a boundary value problem non linear

    i've some problem to solve this kind of differential equation, i 've put the link where is the file of my equation, i search a methods that solve it iterativly. the file is there diablo221 .altervista.org / risultato. nb
  50. N

    Born-Von Karman boundary conditions

    I can't understand this conditions, and in general every boundary conditions for problems like this. they states "the choice of boundary conditions can be determined by mathematical convenience (!?) ... for if the metal is sufficiently large, we should expect its bulk properties not to be...
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