Heat conduction Definition and 107 Threads

I'm trying to calculate the thermal conductance of the disc segment shown in the figure below. We consider a thickness ##d##, only a non-zero heat flux only in the angular direction (no thermal loss through the sides or above and below), no heat generation and steady state condition. Also, the...

Consider a sphere of thermal diffusivity ##\kappa_2## is submerged in an incompressible and stationary fluid of thermal diffusivity ##\kappa_1##. The fluid is held between 2 large plates ( at T_0 for the top plate and T_1 for the bottom plate). What is the stationary temperature distribution...

I've been studying a few books on PDE's, specifically the heat equation. I have one book that covers this topic in cylindrical coordinates. All the examples are applied to a solid cylinder and result in a general Fourier Bessel series for 3 common cases that can be found easily with an online...

Dear all, I am having some difficulties in generating some heat conduction curves. My problem is: I have an object at a temperature (Th) of 900 K placed on top of a surface with a temperature (Ta) of 300 K (see Figure). The thermal conductivity (K; W M-1 K-1) is 1.5 whilst the thermal...

Hello everyone, since several weeks, no response from the other forums, I tried to compute a simple model for a greenhouse in a garden. First idea was to compute mass transfer, Navier-Stokes and heat equation all together but in my knowledge no analytical solution exists.I need to build a simple...

I've found this question online and don't agree with the explanation given. Explanation I disagree. If you heat the jar, the diameter of the top opening increases more than the diameter of the wooden lid, making it looser. The opposite happen if you cool the jar and the lid. Can you please...

On the surface of a semi-infinite solid, a point heat source releases a power ##q##; apart from this, the surface of the solid is adiabatic. The heat melts the solid so that a molten pool forms and grows. Let's hypothesize that the pool temperature is homogeneously equal to the melting...

I've tried to explicitly solve the Fourier's equation in cylindrical coordinates but I'm getting some messy integrals which cannot be solved analytically. Additionally my instructor said that there's a neat trick for this problem and it's possible to obtain the answer in a rather elementary...

Are there any known instances of heat transfer via conduction or convection happening at relativistic speeds? Is this even possible or is there a non-relativistic limit to how fast heat can transfer in these ways, like how sound can only move so fast?

In this case with a presence of the airgap, what should I do with the equation that is provided to be? Must the temperature gradient be caculated spearately (glass+air+glass) ? My tutor provided the hint that the heat flux should be constant for the windows, so in this case should I just omit...

It is easy to understand heat conduction in a gas as the nucleus of atoms may collide with transfer of kinetic energy. But the space within a solid is vastly empty space and the nucleus of the atoms cannot collide. So if the surface of a solid is in contact with a hot gas, how is kinetic energy...

Homework Statement I don't understand the derivation of the right side of the last equation. Homework EquationsThe Attempt at a Solution I got to this point, I also don't understand why it did not include C_2 for the variation of temp. along the fin. I am guessing the right side is the...

Homework Statement A 1.75m long PVC pipe with a thermal conductivity of 0.19 W/mK has an internal diameter of 3mm and an external diameter of 5.5mm. Inner temperature is 298K and outer temperature is 273K. Calculate the heat transfer rate through the pipe and thus the decrease in the inner...

Homework Statement Question C(ii) Homework Equations dQ/dt =-kA(dθ/dx) dQ/dt = (θ1-θ2)/ ((lx/kxAx)+ (ly/kyAy)) The Attempt at a Solution So the first time I tried at this question, I was using the second equation provided above,but when I check the answer, they put the area on the numerator...

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...

Can someone tell me if my logic is correct here. I am trying to figure out how the cross sectional area to make the heat transfer from one object be the maximum amount of heat transfer with the minimal amount of area... I know the thermal transfer coefficient is watts per (meter*kelvin). I find...

How do I relate Fourier's Law of Heat Conduction for 1-D Heat Conduction with the Heat Conduction Equation in a large plane wall and energy balance equation? Fourier Energy Balance energy in - energy out = system energy change rate of energy in - rate of energy out = rate of system energy...

Homework Statement I have one dimensional heating system. In the center is heating source which is heating two PVC elements located on both sides of the heating source. Heat distribution in other dimensions is negligible because of insulation. Thickness of one PVC element is 0,051 m and surface...

Homework Statement In a container of negligible mass, equal amounts (in weight) of ice at 0°C and steam at 100°C are mixed at atmospheric pressure. Assuming no heat exchange with the surroundings, what is the temperature when the system reaches equilibrium? What are the fractions of weights of...

Homework Statement In order to stay warm, divers often wear some sort of thermal protection, like a "wetsuit". Often this is a neoprene "foamed" material, which traps gas bubbles as the insulating material. For this problem, assume: the thermal conductivity is that of air (κ = 0.03 W/m-K) the...

Homework Statement so, i had this question where i had a sphere and a cylinder with given dimensions and propreties ( roh, C and k) he also gave me initial temperatures, then both of them dipped in a bath of water of given temperature but unknown h ( convective coefficient) then he gave me the...

Homework Statement Problem data:[/B] http://imgur.com/a/hEz16 Homework Equations Rconduction=ln(rout/rin)/2*pi*Length*thermal conduct Rconvection=1/2*pi*Length*routside*convective heat transfer outside =>Qconduct=2*pi*Length*thermal conduct*(Tin-Tout)/ln(rout/rin)...

Homework Statement This is the question as it was given...no other data was given. Obtain Fourier's heat conduction equation in three dimensions in an infinite medium in steady state.What modifications will be required in case of a finite body? 2. The attempt at a solution Well I can derive 3D...

Homework Statement We previously solved the heat conduction problem in a ring of radius a, and the solution is c into the sum, perform the sum first (which is just a geometric series), and obtain the general solution, which should only involve one integral in ϑHomework Equations...

I'm designing an oven and want to ensure that the insulation I specify has a low enough Thermal Conductivity (k) to resist excessive heat loss. I determine heat loss (Hout)with the following equation: Hout=A*U*(T1-T0). U is dependent on k (U=k/L). I omitted the heat transfer coefficient in...

Homework Statement Suppose we have a lake and a layer of ice on top such that the bottom of the lake is maintained at a constant temperature T_{bot} which is above the freezing point of water, and top of the ice is maintained at the air temperature T_{air} which is below the freezing point of...

Hello, forum! I'm just starting a new course on heat transfer and we're using Incropera's book. Last time I studied heat transfer was in my transport phenomena course, using BSL, so it was kind of a culture shock using the new book, because the methods used are kind of different in some cases...

Homework Statement A very long cylinder has temperature T1 impressed on half of its peripheral surface and temperature T2 impressed on the other half. Find T(r, θ).Homework Equations governing eq 1/r ∂/∂r(r∂/∂r)+∂2T/∂z2 The Attempt at a Solution I am right at r=0 ;T=T1 at r=r' T=T2 to make BC...

Just wondering if there are substances (even just theoretical ones) able to conduct heat without heating up itself. How does that operate? What properties are different from that of ordinary substances?

[FONT=Georgia]Considering one dimensional heat conduction we may write the Fourier's law of heat conduction in the x-direction as, ##\dot{Q}_{x}=-kA\Big(\frac{∂T} {∂x}\Big)## [FONT=Georgia]where, ##\frac{∂T} {∂x}## is the temperature gradient which is basically the slope of the temperature...

Homework Statement This is a problem regarding transient heat conduction in an undefined semi-infinite solid, initially at a temperature T0 whose surface temperature is suddenly raised to a new constant level at Ts. I also supplied the problem as an attachment for ease in explaining the...

Hi Guys, I'm new on this forum, currently studying Aerospace Engineering and am trying to produce the model of a radioisotope thermoelectric generator using numerical methods to solve the heat conduction equation as part of my research. The way it works is that I have a radioisotope source in...

Homework Statement http://postimg.org/image/4ctgrkoop/ I don't understand the final bit, for the 'steady rate of heat transfer for the entire fin', how they went from Fourier's Law to that final expression. Homework EquationsThe Attempt at a Solution I think it involves the previous expression...

Say you have a flat resistor that is producing heat. You place the resistor against a sheet of steel and wait for equilibrium. One side of the steel is now at the same temperature as the resistor (assuming negligible contact resistance), the other free-air side of the steel is at a lower...

Hello, I just began learning mass transfer, and I am trying to use analogies from heat transfer to help me solve problems. For example, if you have one dimensional heat transfer through a plane wall, I would start with a general energy balance. $$\frac {dE}{dt} = \dot Q_{x} - \dot Q_{x + \Delta...

When you have energy going through a plane wall, I know that the heat flow rate should be constant, meaning what comes in should go out. But is this true even if it is transient, and a non-steady state process? I think the energy content of the plane will not change for steady state, but for...

Hi everyone I am trying to solve non linear heat conduction where thermal conductivity is function of temperature, I am solving it by finite difference method. this is my equation ∂2t/∂x2+∂2t/∂y2 *k(t)= -q (x,y) i have solved the equation taking k(t)= a-b*t,and when i further solved the...

Hi guys,I am new for programming. I made my first attempt to solve an heat equation by finite difference method and wrote a code for it in Matlab.I got a solution but i need help from you guys to (vectorize) increase the speed of my program. ((∂^2 T)/(∂x^2 )+(∂^2 T)/(∂y^2 )+(∂^2 T)/(∂z^2...

Homework Statement In general, a sphere with conductivity ##\kappa##, heat capacity per unit volume ##C## and radius ##R## obeys the differential equation at time t: C\frac{\partial T}{\partial t} = \kappa \frac{\partial^2 T}{\partial r^2} + \frac{2\kappa}{r}\frac{\partial T}{\partial r}...

Hi, I am trying to formulate a 2D model to calculate the temperature change over time in a composite material. The material consists of several layers, and is heated from all edges by a known temperature vs time profile. I was thinking of creating a finite element model. Can someone...

Homework Statement A cylindrical wire with radius ##r_i## carries a current ##I \frac{A}{cm^2}## with a resistance of ##\Omega \: ohms\times cm##. It is insulated with a material with radius ##r_o## whose thermal conductivity is ##k \frac{W}{cm \times K}##. The insulator is exposed to air that...

I have derived the weak form of the transient heat conduction equation (for FEM) and I am having trouble trying to assemble the mass matrix This is the PDE: \frac{\partial U}{\partial t} = \alpha \nabla^2U This is the equation for the mass matrix for an element: M^e = \int \Psi...

Homework Statement Find an expression for thermal conductivity using kinetic theory. Given a vacuum flask of these dimensions, find the heat loss per unit time. Estimate the time taken for the water to cool down to 40 deg. Homework Equations The Attempt at a Solution...

Do you know of any material/compound/alloy which have low coefficient of heat conduction at room temperature and higher one at greater temperatures?

Homework Statement Problem 1.60. A frying pan is quickly heated on the stovetop to 200 C. It has an iron handle that is 20 cm long. Estimate how much time should pass before the end of the handle is too hot to grab with your bare hand. (Hint: The cross-sectional area of the handle doesn't...

1D solid, 0<x<L, with the following boundary conditions: The whole solid is at T = T1 at t=0. x = 0 is held constant at initial temperature T1 for all t. There is a constant flow of heat, dQ/dt out of the solid at x = L. T(0,t) = T1, T(L,0) = T1, How do we go about solving the heat equation...

Homework Statement A semi-infinite bar (0 < x < 1) with unit thermal conductivity is fully insulated at x = 0, and is constantly heated at x = 1 over such a narrow interval that the heating may be represented by a delta function: \frac{\partial U}{\partial t}=\frac{\partial^2 U}{\partial...

One can show that mass diffusion without chemical reactions obeys the same basic equation as heat conduction. The one dimensional equation in dimensionless variables is given by $$ D_{AB}\frac{\partial^2 C_A}{\partial x^2} = \frac{\partial C_A}{\partial t} $$ where C_A is the concentration...

If I have the equation -k*dT/dr=0 do I get rid of the constant k and integrate, or do i integrate first and keep the constant?