Heat conduction Definition and 107 Threads

Homework Statement For the rod in Problem 10 (already solved this, see below): (a) plot u vs. x for t= 5, 10, 20, 40, 100, and 200 (b) plot u vs. t for x= 10, 20, and 30 (c) how long does it take for the entire rod to cool off to a temp. of no more than 1 degree C? Homework...

Homework Statement Folks, I am self studying through a heat conduction problem involving a 2nd order linear homogenous differential equation which has the solution of the form ##\theta (x)=C_1\cosh mx+ C_2\sinh mx## (1) where ##m \equiv \sqrt \frac{c}{a}= \sqrt{\frac{\beta P}{k A}} ##...

Is anyone here familiar with the speed of a temperature wave through Si02 or other electrical insulators? Thanks, S.L.

My hypothesis is to use two different stable heat sources with different tempreature T1 and T2 (T1>T2) transmits the heat . Then I let the distance between this two heat sourse filled with idea gas or ideal metal in a tube. So if the distance is L, the heat capacity is Cv (Constant). So the...

Say we have a laterally insulated beam and some boundary conditions at either end, be it convective or fixed-temperature, but the cross-sectional area is variable. If the cross-section were constant I'd just say it were a 1-D problem, but I'd imagine that having the cross-sectional area be a...

I have two questions. I believe I have solved the first question and would like confirmation of this answer; the second question I'm a little bit lost on so any help there would be greatly appreciated! I am working on a problem set in which I must derive the equation for heat conduction in...

Homework Statement Consider unsteady state heat conduction through an infinitely wide slab of solid material of thickness 2L. There is no internal heat generation and the thermal properties of the material are independent of temperature and position. Starting from an energy balance, show...

I used to think that the heat does rise even in solid metals with no gas/liquid around (No density argument is possible then.) But couldn't find anything describing or even verifying it. I'am pretty sure the gravitationally induced anharonicity in the atomic core potentials should have at...

Homework Statement Given is a hollow cilinder with inner radius R1 and outer radius R2. The heat conductivity of the material is k. The cilinder has length l and an inner temperature of T1 and outer temperature T2. Determine the temperature gradient in the cilinder and the heat flow that leaks...

Hi, I have written a numerical code to solve the 1D heat equation in cyclindrical coordinates: \frac{\partial T}{\partial t}=\kappa\left(\frac{\partial^{2}T}{\partial r^{2}}+\frac{1}{r}\frac{\partial T}{\partial r}\right) The problem I'm considering is a hollow cylinder in an infinite...

Homework Statement Find the solution of the heat conduction problem: 100Uxx=Ut, 0<x<1, t>0; U(0,t)=0, U(1,t)=0, t>0; U(x,0)=sin(2\pix)-sin(5\pix), 0\leqx\leq1 Homework Equations U(x,t)=\sumcne(-n2\pi2\alpha2t)/L2sin((n\pix)/L)...

In Bird, Stewart, Lightfoot "Transport Phenomena", they post the following equation for heat conduction with a nuclear heat source: Sn=Sn0 [1+b(r/R)^2] where Sn is volumetric thermal energy, r is radius and R is radius of the fuel pellet. The text state that b is a dimensionless...

1. The problem statement I'd like to use Matlab to help me model and solve a simple 2D steady state heat conduction problem: A square section duct is buried in the Earth some distance below the surface. This duct is at a steady temperature of 60 degrees C. I need to use the central divided...

Homework Statement There's a slab of a material with temperature T1 on the left and the T2 on the right. The thickness of the material is l with area A. In the centre, there is heat generation Qvol in the centre, which is a thin rod. Find the heat transfer Q through the material. Homework...

Hi everyone, I recently started studying heat conduction using differential equations and this has been stumping me for a while. I am having trouble understanding what type of heat conduction problem this is. We are given a 100cm long copper rod with ends maintained at 0 C. The center of the...

Homework Statement Let the ends of a copper rod 100 cm long be maintained at 0 degrees C. Suppose that the center of the bar is heated to 100 degrees C by an external heat source and that this situation is maintained until a steady state results. Find this steady-state temperature...

Hi, I am trying to work this problem out but I don't know how to solve the boundary value. here is the problem statement thanks in advance

Homework Statement Hello! I am supposed to explain the behaviour of the thermal conductivity of tungsten. I have plotted the relation http://img340.imageshack.us/img340/9776/heatcond.jpg is also experimental data Temp[0 10 50 100 300 500 1000 2000 3400] and thermal conductivity...

Homework Statement a) A slab of thickness L and constant thermal conductivity \lambda generates heat at a constant rate throughout of g W m–3. The heat is dissipated from both sides of the slab by convection into the ambient air at a temperature Tf with a heat transfer coefficient h. The...

Hello friends Fourier law of heat conduction states that: Q ~ A.(Dt/Dx) where A= area normal to direction of heat flow. Dt/Dx= temp gradient in same direction. Now, obviously rate of heat flow will depend upon temp gradient but my doubt is how/why...

Hey guys, I was wondering about problem 12C.1 in Transport phenomena by Bird, Stewart and lightfoot. The problem states that a block of material initially at uniform T0 is suddenely exposed to T1 at all surfaces. Assume a solution of T=X(x,t)Y(y,t)Z(z,t) any help with...

Dear all, I have difficulty in solving this problem (see the figure in attached thumbnails) I have a rectangular shape with length/height of L and the thickness/width of \delta Within the rectangular area, a heat conduction occurred. I would like to determine the temperature profile within the...

Homework Statement I need to set up the mathematical formulation of the following heat conduction scenarios: a) A slab in 0\le x \le L is initially at a temperature f(x). For times t>0 the boundary at x=o is kept insulated and the boundary at x=L dissipates heat by convection into the...

Help! Heat Conduction into a gas! Hello All, I have a problem I've been trying to solve for some time and can't quite seem to figure it out. I need the help of some experts out there. I am no physics expert but I do have a basic understanding of math, algebra, and geometry. I am a beginner...

Hi all, I am working on the problem below, and I wrote the code, but it's not working. Can anyone help me out? And even any ideas on how to improve the code to make it more succinct? http://i25.tinypic.com/2v0zi8m.jpg Basically, it is a 2D conduction problem with convection heat...

Homework Statement I need to go into this test with great aplomb. In each of Problems 1 through 8 find the steady-state solution of the heat conduction equation a2uxx=ut that satisfies the given boundary conditions. 1. u(0,t)=10, u(50,t)=40 ... 3. ux(0,t)=0, u(L,t)=0...

Homework Statement In each of Problems 1 through 8 find the steady-state solution of the heat conduction equation ∂2uxx=ut that satisfieds that given set of boundary problems. ... 3. ux(0,t)=0, u(L,t)=0 Homework Equations Assume u(x,t)=X(x)T(t) The Attempt at a...

Hello, I am trying to understand one-dimensional unsteady state heat conduction for a program I am writing. The program will eventually be coded for two and three dimensional structures. Can anyone provide some basic background info./tutorial to understand the governing equation and...

Describe the physics behind an engineering system where heat conduction phenomena plays an important role. (a familiar system)

Homework Statement A cubical box 22cm on a side is constructed from 1.3cm -thick concrete panels. A 100 W lightbulb is sealed inside the box. What is the air temperature inside the box when the light is on if the surrounding air temperature is 20 C? Homework Equations rate of heat transfer...

I need a fem code either in MATLAB or fortran to refer to as I am stuck at some places. Please help.

Homework Statement There's a radioactive isotope placed inside an iron sphere (R=2cm), which acts as a source of constant heat (P=1W). The isotope is uniformly distributed over a very thin spherical layer (r=1cm). How much higher is temperature in the center of the sphere compared to...

[b]1. Suppose the insulating qualities of the wall of a house come mainly from a 4.0-in. layer of brick and an R-19 layer of insulation. What is the total rate of heat loss through such a wall, if its total area is 195 ft^2 and the temperature difference across it is 15 degrees F. [b]2...

Homework Statement Show that the equation governing the stead-state radial conduction of heat in a sphere or spherical shell with volumetric heat production is given by \frac{k}{r^2}\frac{d}{dr}(r^2\frac{dT}{dr})+\rho H = 0 where k is thermal conductivity, H is the heat production per unit...

My question pertains to mechanisms for heat transfer in an everyday situation. I've put that sentence first (rather than the next one) so that people looking at the post preview wouldn't think I was posting irrelevant threads. In Canada, today is Thanksgiving day. The packaging on my Turkey...

I am not sure how to approach this problem. If you have a carbon steel pipe that is being heated on one end at a constant temperature of 1500C. Can you figure out how much distance in pipe will it require before it cools to 790C? The thermal conductivity of Carbon steel is 54 W/mk. Another...

Homework Statement A copper bar of thermal conductivity 401 W/(m·K) has one end at 102°C and the other end at 23°C. The length of the bar is 0.10 m and the cross sectional area is 1.0 multiplied by 10-6 m2. (a) What is the rate of heat conduction along the bar? (b) What is the temperature...

What is the dissipation due to heat conduction? D = -k \frac{\vec q\cdot\nabla T}{T} where q is the heat flux, k is the coefficient of heat conduction and T is the absolut temperature. What is the physical meaning of this?

Homework Statement The one dimensional steady-state heat conduction equation in a medium with constant conductivity (k) with a constant volumetric heat generation in three different coordinate systems (fuel rods in a nuclear power plant) is given as: \frac{d^2 T}{dx^2}=-\frac{\dot{q}}{k}...

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...

Hey all, This is the equation of heat conduction in my PDE textbook: \int ^{t_{2}}_{t_{1}} \int\int\int_{A} [c \rho \frac{\partial u}{\partial t} - \nabla \dot \left( k \nabla u \right)]dxdydzdt = 0. where c is specific heat, rho is density, A is the subregion bounded by a smooth...

I have to solve a problem regarding "2D steady state heat conduction problem with an internal heat generation source". For boundary value, dirichlet is applied at 3 sides and neumann is at one side. I can solve this problem when no internal heat source exists and only dirichlet is applied...

If a wooden cylinder at 298K with perfectly insulated sides (other than the one in contact with the hot plate) where placed with one end on a hot plate until any point on the cylinder reached a temperature of 523K and the power of the hot plate is known and it all goes into the wood. How long...

If heat is applied to one side of a cube, how can the temperature at different distances into the cube be calculated after different amounts of time have elapsed?

Homework Statement My problem is not necessarily the 2D problem, it's getting the answer in one dimension (I have the y-direction). The problem is the boundary conditions...anyways. Solve for the temperature of a 1D transient metal bar, with the following boundary conditions. Imposed...

Hey everyone! I am currently on a project building a small CanSat. This is a small satellite of the size of a coke can which will be launched together with a balloon and then descend from an altitude of 35 000 m. My problem now is to work out the heat conduction to see if our insulation is...

In the steady state heat conduction through a solid rod the theoretical derivation tells that heat in-heat out-heat accumulated =0. What is a practical steady state heat conduction problem? what is transient heat conduction

I know how to solve a 1-D heat conduction equation when both ends are kept at 0 temperature(using separation of variables and Fourier series.). In the notes, the prof asked us to solve for one end kept at zero and the other insulated (at x=L) and referred to a non-existent chapter in our...

Homework Statement The elements of a boiling water nuclear reactor consist of long cylindrical rods of uranium dioxide (U02) of diameter 8mm surrounded by a thin layer of aluminium cladding. In the reactor core the elements are cooled by boiling water at 285°C with a heat transfer...

A solid sphere of radius a is immersed in a vat of fluid at a temperature T_0. Heat is conducted into the sphere according to dT/dt = D(d^2T/dr^2) (d-> partial derivative btw) If the temperature at the boundary is fixed at T_0 and the initial temperature of the sphere is T_1, find the...