Heat flow Definition and 96 Threads

I'm pretty sure I understand why q^i u^j + u^i q^i is the stress component (i \neq j) of the Heat Flux Stress/Energy Tensor but I can't think of, or find any explanation for why q^i u^i + u^i q^i = 0. I found one reference in Lightman, Press, Price and Teukolsky - Problem Book in Relativity...

Hello, I have the following problem and hope you can help me. I have the setup as shown in the drawing. A pipe that is flowed through, and in the middle of it another pipe, but at the end of this branch is a sensor. Initially the fluid would flow, with a temperature of 25°C. If my thought is...

Hi, starting for this thread Question about entropy change in a reservoir consider the spontaneous irreversible process of heat transfer from a source ##A## at temperature ##T_h## to another source ##B## at temperature ##T_c## (##T_h > T_c##). The thermodynamic 'system' is defined from sources...

Yes, heat can flow into a body without increasing the mean kinetic energy of its molecules. Transferring heat energy to an object will raise its internal energy, this will not necessarily cause an increase in temperture. Specific latent heat is the energy required to change the state of one...

I've come to a grinding halt with this and I can't see a way forward. Can someone please take a look at what I've done so far and let me know if what I have done is OK and then if it is, give me a hint on how to proceed. First up, Is ## u \cdot \nabla \cdot T = u_\alpha...

Hi, I am trying to calculate the heat flow across the boundary of a solid cylinder. The cylinder is described by x^2 + y^2 ≤ 1, 1 ≤ z ≤ 4. The temperature at point (x,y,z) in a region containing the cylinder is T(x,y,z) = (x^2 + y^2)z. The thermal conductivity of the cylinder is 55. The...

I tried to created it but i dknt know how to even start

Here is the Q below I want to see if my values for part b) is okay? This is what I have tried: Any help would be nice! Thanks

What is the origin of the fact that heat flows from hot to cold? Does it have something to do with fluctuations?

This problem seems best treated in cylindrical coordinates. There is azimuthal symmetry, and there is no heat loss or generation within the cone, so our thermal conductivity equation reads: $$\vec{q} = -k(\frac{\partial T}{\partial \rho} \hat{\rho} + \frac{\partial T}{\partial z} \hat{z})$$ We...

Homework Statement Keeping the cabaret door closed is important, so you install a sophisticated door control system that keeps the air exchange between inside and outside to a minimum. Why will such air exchanges always require the climate control system to work harder and consume extra...

Recently looked at why temperature flows from high Temperatures to Low temperatures.Essentially it was laid on two Fundamental Assumptions: 1.Energy is conserved in the isolated system 2.Entropy in isolated non quasi static systems will always tend to increase. Lets take a brief look at...

I recently read in a Khan Academy article that the rate of energy exchange through heat across a material of thickness ##d##, surface area ##A##, and thermal conductivity ##k## can be approximated by $$\dot{Q} = \frac{kA\Delta T}{d}$$ where ##\dot{Q}## is the heat rate and ##\Delta T## the...

Homework Statement One end of a solid cylindrical copper rod 0.200 m long and 0.0250 m in radius is inserted into a large block of solid hydrogen at its melting temperature, 13.84 K. The other end is blackened and exposed to thermal radiation from surrounding walls at 500.0 K. (Some telescopes...

Homework Statement A 529 g piece of copper tubing is heated to 89.5°C and placed in an insulated vessel containing 159 g of water at 22.8°C. Assuming no loss of water and a heat capacity for the vessel of 10.0 J/°C, what is the final temperature of the system [c of copper = 0.387 J/g · K]...

Homework Statement What is the net heat flow of an aluminum disk (emissivity = 0.05) with radius 10 cm and temperature 293K placed inside a room where the temperature is 300K? Asurface = π*r2 = 0.01π m2 Homework Equations Hnet = A*e*σ(Tradiate4-Tabsorb4) The Attempt at a Solution By simply...

Homework Statement q = -kdp/dx Homework Equations q = heat flow k = constant p = thermal energy density The Attempt at a Solution This equation says that when heat flows from hot to cold the thermal energy density increases but why? I thought heat meant a higher thermal energy density and hot...

Homework Statement An Aluminium rod has a diameter of 40mm. and is 750mm long. If the temperature difference between the ends of the rod is 100C . Take the thermal conductivity of Aluminium to be 235 Wm-1K-1 Homework Equations k * A * ΔT / L The Attempt at a Solution 235 * 0.097 m * 100 /...

Homework Statement This problem belongs to the Intermediate Physics for Medicine and Biology, Hobbie Chapter 4. The heat flow equation in one dimension $$ j_H=-\kappa \partial_x T $$ where ## \kappa ## is the termal conductivity in ## Wm^{-1}K^{-1}##. One often finds an equation for the...

Homework Statement n = 3.8-mol of diatomic gas is allowed to expand isothermally from Vini = 1.9-m3 to Vfin = 10.5-m3. The initial pressure is Pini = 1.38-atm. After this the gas is raised at a constant volume by a temperature ΔT = 35-K. Calculate the total heat flow into the gas. Homework...

Homework Statement I have this problem in an online assignment. Someone told me the answer, so I already got it right, but I don't know why my logic leads me to the wrong answer. The problem: The temperature u of a star of conductivity 1 is defined by u = \frac{1}{sqrt(x^2+y^2+z^2)}. If the...

Hello, I am working a designing a cooking pot with thermoelectrics integrated into the design. I am trying to find the heat flow through the pan to estimate how much electricity the design will produce. First off some constants - The design has a base area of .0491 m2, or a diameter of 25 cm...

An ideal Carnot engine is composed of two reservoirs and a working fluid. The hot Reservoir and the cold one have temperatures ##T_1## and ##T_2## respectively, with ##T_1>T_2##. The working fluid is in a phase transition and has temperature ##T_1## at the start of the Carnot cycle. It undergoes...

Two metal rods, one silver and the other gold, are attached to each other. The free end of the silver rod is connected to a steam chamber, with a temperature of 100oC, and the free end of gold rod to a ice water bath, with a temp of 00 C. The rods are 5.0 cm long and have a square cross-section...

Here is a review article identifying some causes for the high temperature in the central volume of the Earth. http://www.scientificamerican.com/article/why-is-the-Earth's-core-so/ Inside all massive astronomical bodies like the Earth, collisions of atoms occur in a gravitational field. Because...

Homework Statement Hot magma (1500 K) is flowing into the Earth at rates of 0.05 meters/year, 0.5 meters per years and 1 meter per year. Although more total volume of magma will retain a temperature at or above 1150 K at higher rates of flow for any given time (say, at 1000 years), a higher...

Im working on a project for fun using a peltier cooler. A tec1-12706. If i am operating the peltier at 9v, 6.4 amps of current and dt =45ºC (from datasheet) and bring its cold side in contact with a body at 33ºC for 10 seconds. Keeping hot side at 27ºC(cold side =-18) using sink, what will be...

Homework Statement Consider the following multi-layer wall consisting of an interior insulation layer and an external light-weight concrete layer. Calculate the heat flow thorugh the structure and the temperature at the interface between the two materials. Layer 1: Thermal insulation...

Homework Statement The cross section of a 20 cm thick, 3 m wide, and 1 m high composite wall is shown. The conductivities of materials A, B and C are 1.0, 0.1, and 0.05 W m-1 K-1, respectively. One side is exposed to air at 295 K with a heat transfer coefficient of 4 W m-2 K-1, and the other...

Homework Statement Consider a large plane wall with thickness L whose thermal conductivity varies in a specified temperature range as k(T) = k_{0}(1 + \beta T) where ##k_{0}## and ##\beta## are two specified constants. The wall surface at ##x=0## is maintained at a constant temperature of...

Homework Statement The same question was asked on this forum about two years ago, however I did not find any of the given answers clear. The question was the following: A small pond has a layer of ice 1cm thick floating on its surface. The air temperature is -10C. (a) What is the temperature...

Homework Statement The problem is here: Homework Equations q = heat flow k = thermal conductivity q = -k (dT/dY)The Attempt at a Solution While this is quite an easy question, I just want to verify that I'm doing it correctly. Would it be correct to begin at the bottom of the rock layer...

Hi! Been lurking around here for a while but joined today :) My question is about heat transfer in low pressures. I have an object in a vacuum chamber that is much smaller than the mean free path of the air in the chamber. However, the general dimensions of the chamber are much larger than the...

If heat flow is the momentum change from a faster moving atom or molecule to a slower moving one, and momentum is mass x velocity is it possible - for a very limited amount - for heat to flow from a slower (colder) heavy atom to a faster moving (hotter) atom ?

Homework Statement A copper bar with a cross sectional area of 4.40 cm2 and a length of 0.62 m has one end at 1 °C and the other end at 97 °C. Find the heat flow through the bar if the thermal conductivity of copper is 385 W/(m·K) Homework Equations R = (λ*L)/A I = ΔT / R k = 1/λ...

I have a rubber sample here, basically it is a slice with a diameter of 45mm and a depth of 3mm. If this sample was at 25 degrees Celsius and I applied 180 degrees temperature all around it (top, bottom faces and outside diameter) how long would it take for the centre point (last point to get...

How do you determine the u-factor of a window assembly? I understand that the u-factor is reciprocal of the sum of resistance (U=1/Σr) for wall assembles, but I’m unable to find any relevant arithmetic for windows. I understand that heat flow rates vary between the center of glass and frame, and...

Three identical rods are welded together to form a Y-shaped figure. The cross-sectional area of each rod is A, and they have length L and thermal conductivity k. The free end of rod 1 is maintained at T_1 and the free ends of rods 2 and 3 are maintained at a lower temperature T_0. You may...

The temperatures at ends \(x = 0\) and \(x = \ell\) of a rod length \(\ell\) with insulating sides held at temperatures \(T_1\) and \(T_2\) until steady-state conditions prevail. Then, at the instant \(t = 0\), the temperatures of the two ends are interchanged. Find the resultant temperature...

Suppose I have a closed end aluminum pipe of 3cm diameter with .5cm walls Cylinder is 10cm tall , 8mm of which is submerged in a cold bath of approximately constant temperature of -10°c I feel it with water at 3°c to 7cm height and stick a cork in it. How long till the water freezes...

"What is the heat flow rate [...]?" Homework Statement The problem is: "A copper tube (length, 3.0 m; inner diameter, 1.500 cm; outer diameter, 1.700 cm) extends across a 3.0-m long vat of rapidly circulating water maintained at 20 °C. Live steam at 100 °C passes through the tube. (a)...

Say I have a metal object and a wooden object at 0 degrees and I touch them. The metal object would feel colder because it is a better conductor of heat and so it removes heat away more quickly. Would it be because each collision between the atoms of the two materials increases the kinetic of...

Are these statements true? (Regarding heat flow) I'm revising for an exam, and this is what I think I know so far. It will really help if someone can confirm these statements for me. Consider an iron pipe with inner diameter 20mm and outer diameter 30mm. The inside surface of the pipe is...

Homework Statement The fluid inside the pipe shown has a temperature of 350 K, but the temperature of the air in the room is only 306 K. Therefore, heat flows at a constant rate from the fluid, through the pipe walls, and into the room. The inner pipe radius is 4 cm, and the outer radius is...

What happens in an heat flow apparatus when you reduce the length of the disk? The apparatus is this 1st level: A resistor to produce heat 2nd level: A metal disk with known thermal conductivity coefficient 3rd level: A metal disk with an unknown thermal conductivity coefficient 4th level...

Homework Statement Length of rod = 1 Initial Conditions: u(x,0)=sin(πx) Boundary conditions: u(0,t)=0 and u(1,t)=5. Alright I am supposed to find the temperature at all times, but I am curious about the setup of the problem itself. When x = 1, the boundary condition says...

Homework Statement A very simple problem, but part of an assignment regarding heat flow. The question is: A 15 cm rod is insulated at one end, the other is in contact with a reservoir of temperature 37C. By thinking of the physics, after a long time, what is the temperature at the point 5...

Two 0.525 m rods, one lead and the other copper, are connected between metal plates held at 2.00°C and 106°C. The rods have a square cross section of 1.50 cm on a side. How much heat flows through the two rods in 1.0 s? Assume no heat is exchanged between the rods and the surroundings...

I'm really not sure, have I gone through the right process here? I didn't actually finish the calculation, I'm just curious about the process.

EDIT: Typo, the Z' should be Z''