Boundary condition Definition and 136 Threads

Hello all: I would very much appreciate advice on setting up a problem. Apologies in advance... This is probably a silly question--I'm more of a chemist than an engineer/math person! I have written a code for calculating changes in concentration/mass within a domain over time, as new...

I'm asked to determine if for the solution y=c_{1}e^{x}cos(x)+c_{2}e^{x}sin(x) for: y"-2y'+2y=0 whether a member of the family can be found that satisfies the boundary conditions: y(0)=1, y'(\pi)=0 Not quite sure what to do here. The examples in my book give boundary conditions for the same...

Is there a term to describe something like a boundary condition but which can be applied within the domain, not just on the boundaries? For example in a heat transfer problem you might specify a constant rate of heat generation in some region. Is that still called a boundary condition...

Lets us say I have a cube and I apply to a face of the cube a heat flux of 100 watt/m^2. Lets us say i divide the face of the cube into say 10 elements (area of each face of the element is 1 m^2). What will be the flux on each element , will it also be 100 watt/m^2? Sorry for a...

Hi, I was reading Lemon's Perfect Form and it talked about "natural boundary conditions". But I don't understand exactly how one determines them. It seems to me that one imposes some random condition then deduce stuff from it...?! Advanced thanks for any enlightenment!

Hi I am studying magnetic vector potential from Griffiths book. The eq 5.76 in his book gives the boundary condition for the magnetic vector potential. \frac{\partial \vec{A_2} }{\partial n}- \frac{\partial \vec{A_1} }{\partial n}=-\mu_o \vec{K} where n is the vector perpendicular to the...

This is an example shown in "Introduction to Electrodynamics" by Griffiths. Page 226 example 5.8. Given a sheet of current K on the xy-plane where current traveling in +ve x direction. Find the magnetic field. I am confused on the way the book justify the z direction of B is zero. The...

Given a bounded domain with the homogeneous Neumann boundary condition, show that the Laplacian has an eigenvalue equal to zero (show that there is a nonzero function u such that ∆u = 0, with the homogeneous Neumann B.C.). I said: ∇•(u∇u)=u∆u+∇u2, since ∆u = 0, we have ∇•(u∇u)=∇u2 ∫...

Standard electrostatics problem (in spherical polar coords): spherical cavity of radius R in an infinite dielectric of permittivity ε centred at origin of the coord system. Surface charge stuck on to the cavity: \sigma(\theta) = \sigma_0 \cos (\theta) Problem is to find the potential in...

Homework Statement "Solve for t > 0 the one-dimensional wave equation \frac{\partial^2 u}{\partial t^2} = c^2 \frac{\partial^2 u}{\partial x^2} with x > 0, with the use of Fourier transformation. The boundary condition in x = 0 is u(0,t) = 0. Assume that the initial values u(x,0) and...

I'm playing with the PDE toolbox in Matlab and solving Laplace's equation, ∇2V = 0, for various electrostatic geometries. I say 'playing' because I started in the wrong end (or right end, depending on how you look at it) by simple trial and error until the solutions looked like something...

My understanding of: \int_S \nabla X \vec{H} \cdot d\vec{S} = \int_C \vec{H} \cdot d \vec{l} = I Means the current I creates the magnetic field in the form of \nabla X \vec{H} instead of magnetic field creates the current I. But in the boundary condition, it claims the tangential...

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

It's obvious that if Maxwell equations are fulfilled by some E(x,y,z,t) and B(x,y,z,t), they are also fullfiled by E(x,y,z,t)+ E_0 and B(x,y,z,t)+B_0, where E_0 and B_0 are constants. This freedom has physical significance as it changes the Lorentz force which act on a charge. It...

I'm solving a 2D forced convection problem by using finite difference method. It involves solving the vorticity-stream function equations. I met some problem when I'm trying to solve the vorticity equation, which can be stated as follows: How to deal with the vorticity boundary condition? after...

Let's consider two media with magnetic permeability \mu_1, \mu_2 . What's the condition for magnetostatic vector potential \vec{A} on the boundary. Is it true that its tangent component should be continuous. Thanks for replay.

Apparently Fluent has this thing called an "overflow" boundary condition. I tried searching the help files and found absolutely nothing about it. Does anyone know what this is and why someone would want to use it?

Homework Statement A string is attached to a ring of mass m which is free to move up and down a frictionless pole. The string is subject to tension T and its mass per unit length is \rho. The displacement of the string from its equilibrium position along the x -axis is y(x,t). The boundary...

Hey all, I am try to model a problem in which one fluid (of known properties) sits on top of another fluid (with different properties) and there is an imposed slip boundary condition at the interface. I'm wondering if COMSOL has a Slip boundary condition that can be readily used or if...

Hi all, I am facing difficulties about boundary condition in Hollow Cylinder. its like wave diffusion equation in hollow cylinder. can anyone help me out to solve this problem. I need some good reverences. Thank you

Using perturbation theory, I'm trying to solve the following problem \frac{\partial P}{\partial \tau} = \frac{1}{2}\varepsilon^2 \alpha^2 \frac{\partial^2 P}{\partial f^2} + \rho \varepsilon^2 \nu \alpha^2 \frac{\partial^2 P}{\partial f \partial \alpha} + \frac{1}{2}\varepsilon^2 \nu^2...

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...

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...

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...

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...

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...

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...

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...

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...

The question : Consider a thin spherical shell of radius R with a uniform charge density sigma. If a very small piece of this surface were removed, leaving a small hole, what would the electric field be at a point just above/below the hole? Relevent info : the field due to the patch of...

If not, then what are the conditions for us to construct a periodic boundary condition(PBC)? If so, then please help me construct a PBC for the lattice shape in the attachments. I want to ask that what lattice site m's left neighbor is and what lattice site i's down neighbor is.From the...

I am confused on the definition of the "no-slip" boundary condition because of two seemingly contradicting definitions. Definition 1: The no-slip condition for viscous fluid states that at a solid boundary, the fluid will have zero velocity relative to the boundary. Definition 2: The fluid...

Hi, I have to solve diffusion-advection PDE using finite difference method. The problem has two regions with different diffusion coefficients and velocities. At the interface between the two regions types of boundary condition : 1. No contact resistance C1 = C2 - D1*dC1/dx + v1*C1 = -...

Does anybody know how to put BC at the center of a circle.

Hi, this question has been bugging me for weeks and any help would be greatly appreciated. In lectures we derived a general expression for the potential distribution across the xy half plane (y>0) in terms of a known potential distribution along the boundary defined by the x-axis where the...

I got some problem about using boundary conditions,especially in the fifth pics,those sentences marked by red.I really don't know how to use Js=An x H,since I don't know the fields well enough.Some questions of mine are illustrated in the sixth pic by different colors. I'm sorry the pics are...