Heat diffusion Definition and 25 Threads

Knowing that we are in equilibrium ##\frac{\partial}{\partial t} = 0##. We now have a Laplace's equation ##\kappa \frac{\partial^2 T}{\partial x^2} = 0## I separated the rod in 2 halves. The solution of this equation is ##\kappa_1 \frac{\partial2 T}{\partial x2} = C_1## Integrating both side...

TL;DR Summary: Solve heat equation in a disc using fourier transforms Carbon dioxide dissolves in the blood plasma but is not absorbed by red blood cells. As the blood returns to an alveolus, assume that it is well-mixed so that the concentration of dissolved CO2 is uniform across a...

I was reading posts this morning on another forum and came across a question that made me start thinking about physics. Since I've always tried to satisfy my curiosity through reading and trying to learn new things, or trying to remember the things that I've forgotten years ago, I went to...

I've tried to show b) by using the sine Fourier series on ##[0,2a]##, to get ##g_k = \Sigma_{n=0}^{2a} \sqrt\frac{2}{a} Sin(q_k x)## Therefore ##\sqrt\frac{2}{a} = \frac{1}{a} \int_0^{2a} Sin(q_kx)g_k dx## These are equal therefore it is an orthonomal basis. I'm not sure if this is correct so...

I'm trying to compute a 2D Heat diffusion parabolic PDE: $$ \frac{\partial u}{\partial t} = \alpha \{ \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} \} $$ by the ADI method. I am actually trying to go over the example in this youtube video. The video is in another...

I have recently been curious about heat diffusion. If there is space in one dimension with any kind of temperature dispersed throughout, then the heat equation states that the derivative of the temperature with respect to time at any point equals some constant (k) multiplied by the second...

Preserving food at home involves putting produce in glass jars and heating them to kill pathogens like bacteria, fungus, yeast, etc... The USDA recommends AGAINST using an oven to preserve food. They only support the boiling water method, which involves submerging the jars in a pot of boiling...

I am trying to write code for analytical solution of 1D heat conduction equation in semi-infinite rod. The analytical solution is given by Carslaw and Jaeger 1959 (p305) as $$ h(x,t) = \Delta H .erfc( \frac{x}{2 \sqrt[]{vt} } ) $$ where x is distance, v is diffusivity (material property) and t...

Consider the conceptual model presented in the attached image, of heat conduction in a bar. There is a heat source at left side and heat is observed at point Ho after a distance L from the source. If we consider only heat transfer through conduction then this problem can be modeled by...

We solved a simple looking heat diffusion problem because it describes an apparatus used in an NIH sponsored research project. It resembles problems discussed in textbooks and in many papers on the web. A textbook method solves all those problems but a straight forward application of that...

Hey guys, I have a problem that is giving me trouble. Homework Statement I have to solve time dependent diffusion equation ##D\nabla^2 T(r,t)=\frac{\partial T}{\partial t}## (##D## is diffusion constant and ##T(r,t)## is temperature function) for a spherical shell of radii ##r_1## and ##r_2##...

Hi all, I'm working on a heat transfer problem with a gas stream in a tiny tube. At my dimensions and flow rates, the flow still has a parabolic velocity profile. The mean radial velocity of the gas is zero, and I've treated the radial aspect of the heat transfer as strictly diffusion...

Hello everyone! I hope you may be able to shed light on a recent problem that i have to deal with. I keep working on a numerical solution on a heat diffusion problem. It is a numerical solution for the PDE θT/θt=a*(θ^2T/θx^2 + θ^2Τ/θy^2), that describes the heat diffusion on a two...

Homework Statement The one-dimensional heat diffusion equation is given by : ∂t(x,t)/∂t = α[∂^2T(x,t) / ∂x^2] where α is positive. Is the following a possible solution? Assume that the constants a and b can take any positive value. T(x,t) = exp(at)cos(bx) Homework Equations...

Homework Statement One face of a thick uniform layer is subject to a sinusoidal temperature variation of angular frequency ω. SHow that the damped sinusoidal temperature oscillation propagate into eh layer and give an expression for the decay length of the oscillation amplitude. A cellar...

Hello there! I am solving a heat diffusion problem which is described by the differential equation: θΤ/θt=a*(θ^2Τ/ΘΤ^2). I will apply two diffrent temperatures on the ends of a metal rod. Solving the equation i conclude, according to the boundary conditions of course, at the function...

Hi. I don't know if this is the correct place to ask this, but prefer you to suggest me where I should ask. I'm starting with numerical simulation and I've been playing with the finite differences method to solve the heat equation on 1D, 2D and 3D uniform grids. This was really simple. Now I...

Homework Statement http://img42.imageshack.us/img42/1082/clipboard01lx.jpg Homework Equations (see solution) The Attempt at a Solution I literary just spent 5 hours trying to apply those boundary conditions, trying exponentials, sines, cosines, hyperbolic function etc... I...

I have to write a FD expilicit method, for temp dist on 2D plane. I am trying to mod the 1D solver to 2D solver, the code below is a 1D solver. Any possible suggestions how it can be done? I initially, derived u(i,j+1) for 2D for in that derivation i,j corresponds to x,y... where as in 1D...

Homework Statement The Fourier method specifies that change of heat energy of = heat out from left boundary - heat in from right boundary segment in time Δt If vars such as c,p.. are constant in the equation, and T(-L,L) = T_a, does the the aforementioned Fourier method...

Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...

Homework Statement a material occupies -L < x < L and has uniform ambient temperature T_a. A chemical reaction begins within the body leading to the 1-d heat equation: pc \frac {\partial{T}}{\partial{t}} = k \frac {\partial^2{T}}{\partial{x^2}} + pQAe^\frac{-E}{RT} with BC and IC T(+/-...

I have trying solving this PDE for some random boundary values, and were wondering if someone could verify my calculations? \[ \begin{array}{l} T_t = DT_{xx} \\ T\left( {0,t} \right) = 0,T(\pi ,t) = 0,T(x,0) = \frac{1}{4}\left( {\left( {x - \frac{\pi }{2}} \right)^2 + \frac{{\pi ^2...

Hi, I'd like to figure out the amount of heat lost in the kinematic action of putting your foot on the ground while walking. I'm not interested in the diffussion of body heat through the shoe or anything, just the heat energy released by the impact itself. I know this is obscure, and probably...

Hey there I was wondering if someone maybe be able to help me with a couple of questions I have. I attach a set of equations the help define the heat diffusion throughout a sphere could you please tell me; in V=rT What is V when r is the radius of the sphere and T is the temperature ...