Heat conduction is the transfer of energy between neighboring molecules in a substance due to a temperature gradient. In metals also the free electrons transfer energy. In solids which do not transmit radiation, heat conduction is the only process for energy transfer. 'According to this formula, when a metal rod is getting heated through conduction, the temperature gradient decides what the temperature will be at different points down the length.' (emphasis mine) Basically, the gradient can only exist when there is heat being transferred through the rod. If one end of a metal rod is at a higher temperature, then energy will be transferred down the rod toward the colder end because the higher speed particles will collide with the slower ones with a net transfer of energy to the slower ones.

1. Heat Transfer Through A Metal Rod Experiment
2. Heat Transfer In Metal Rod Design
3. Heat Transfer In Metal Rod Making

This example shows how to simplify a 3-D axisymmetric thermal problem to a 2-D problem using the symmetry around the axis of rotation of the body.

This example analyzes heat transfer in a rod with a circular cross section. There is a heat source at the bottom of the rod and a fixed temperature at the top. The outer surface of the rod exchanges heat with the environment because of convection. In addition, the rod itself generates heat because of radioactive decay. The goal is to find the temperature in the rod as a function of time.

The model geometry, material properties, and boundary conditions must all be symmetric about the axis of rotation. The toolbox assumes that the axis of rotation is the vertical axis passing through r = 0.

Steady-State Solution

First, compute the steady-state solution. If the final time in the transient analysis is sufficiently large, the transient solution at the final time must be close to the steady state solution. By comparing these two results, you can check the accuracy of the transient analysis.

Create a steady-state thermal model for solving an axisymmetric problem.

The 2-D model is a rectangular strip whose x-dimension extends from the axis of symmetry to the outer surface and y-dimension extends over the actual length of the rod (from -1.5 m to 1.5 m). Create the geometry by specifying the coordinates of its four corners.

Include the geometry in the model.

Plot the geometry with the edge labels.

Heat Transfer Through A Metal Rod Experiment

The rod is composed of a material with these thermal properties.

For a steady-state analysis, specify the thermal conductivity of the material.

Specify the internal heat source.

Define the boundary conditions. There is no heat transferred in the direction normal to the axis of symmetry (edge 1). You do not need to change the default boundary condition for this edge. Edge 2 is kept at a constant temperature T = 100 °C.

Specify the convection boundary condition on the outer boundary (edge 3). The surrounding temperature at the outer boundary is 100 °C, and the heat transfer coefficient is $50\mathrm{W}/\left(\mathrm{m}{\cdot }^{\circ }\mathrm{C}\right)$.

The heat flux at the bottom of the rod (edge 4) is $5000\mathrm{W}/{\mathrm{m}}^2$.

Generate the mesh.

Solve the model and plot the result.

Transient Solution

Create a transient thermal model for solving an axisymmetric problem.

Use the same geometry and mesh as for the steady-state analysis.

Specify the thermal conductivity, mass density, and specific heat of the material.

Specify the internal heat source and boundary conditions.

Specify that the Initial temperature in the rod is 0 °C.

Compute the transient solution for solution times from t = 0 to t = 50000 seconds.

Plot the temperature distribution at t = 50000 seconds.

Find the temperature at the bottom surface of the rod: first, at the center axis and then on the outer surface.

Plot the temperature at the left end of the rod as a function of time. The outer surface of the rod is exposed to the environment with a constant temperature of 100 °C. When the surface temperature of the rod is less than 100 °C, the environment heats the rod. The outer surface is slightly warmer than the inner axis. When the surface temperature is greater than 100 °C, the environment cools the rod. The outer surface becomes cooler than the interior of the rod.

Heat escapes (or transfers) from inside to outside (high temperature to low temperature) by three mechanisms (either individually or in combination) from a home:

• Conduction
• Convection
• Radiation

Click here to open a text description of the examples of heat transfer by conduction, convection, and radiation

• Conduction: heat moving through walls of a home from high temperature inside to low temperature outside.
• Convection: heat circulating within the rooms of a house.
• Radiation: Heat from the sun entering a home.

Conduction

Conduction is a process by which heat is transferred from the hot area of a solid object to the cool area of a solid object by the collisions of particles.

In other words, in solids the atoms or molecules do not have the freedom to move, as liquids or gases do, so the energy is stored in the vibration of atoms. An atom or molecule with more energy transfers energy to an adjacent atom or molecule by physical contact or collision.

In the image below, heat (energy) is conducted from the end of the rod in the candle flame further down to the cooler end of the rod as the vibrations of one molecule are passed to the next; however, there is no movement of energetic atoms or molecules.

Click play to start animation.

Click here to open a text description of the Conduction Candle animation

Example of Conduction

A hand holds a metal rod above a lit candle. The molecules quickly heat up at the point where the flame touches the rod. The heat then spreads across the entire metal rod and the heat is then able to be felt by the hand.

With regard to residential heating, the heat is transferred by conduction through solids like walls, floors, and the roof.

Click here to open a text description of Conduction in Regard to Residential Heating example

Example of Conduction in Regard to Residential Heating

Picture the cross section of a wall in a house. Inside the house it is 65°F and outside it is 30°F. Two arrows point from inside the house to the outside to show how heat is transferred from the inside of the house to the outside through the wall via conduction.

Heat loss across a solid wall by conduction

Heat Transfer In Metal Rod Design

Convection

Convection is a process by which heat is transferred from one part of a fluid (liquid or gas) to another by the bulk movement of the fluid itself. Hot regions of a fluid or gas are less dense than cooler regions, so they tend to rise. As the warmer fluids rise, they are replaced by cooler fluid or gases from above.

In the example below, heat (energy) coming from candle flame rises and is replaced by the cool air surrounding it.

Click here to open a text description of the Convection Candle animation

Example of Convection

A hand is held above a lit candle. As the candle heats the air, the heat rises to the hand. Eventually, it gets too hot and the hand pulls away from the candle.

In residential heating, convection is the mechanism by which heat is lost by warm air leaking to the outside when the doors are opened, or cold air leaking into the house through the cracks or openings in walls, windows, or doors. When cold air comes in contact with the heater in a room, it absorbs the heat and rises. Cold air, being heavy, sinks to the floor and gets heated, and thus slowly heats the whole room air.

Instructions: Press the play button below and observe what happens to the cold air (blue arrows) as it enters the house and encounters the warm air (red arrows) coming from the heating vent:

Click here to open a text description of the Convection in a Room animation

Example of Convection in Regard to Residential Heating

Picture a room with an open door letting in cool air on the left and a radiator creating heat on the right. As the radiator heats the air around it, the air rises and is replaced by cool air. Once the warm air hits the ceiling, it travels left towards the open door, cooling as it moves. The cool air from the open door travels to the right across the floor towards the radiator to be heated. The overall effect is a circular convection current of air within the room.

Radiation

Radiation is transfer of heat through electromagnetic waves through space. Unlike convection or conduction, where energy from gases, liquids, and solids is transferred by the molecules with or without their physical movement, radiation does not need any medium (molecules or atoms). Energy can be transferred by radiation even in a vacuum.

In the image below, sunlight travels to the earth through space, where there are no gases, solids, or liquids.

Click here to open a text description of the Radiation Example animation

Example of Radiation

Picture the Sun and the Earth with arrows traveling from the Sun to the Earth through space. The arrows represent the energy that travels to the Earth via radiation, which does not require any medium (atoms or molecules) to do so.

Test Yourself

First, identify the type of home heat loss pictured in images A-J as either: conduction, convection or radiation. Then click and drag each image down to the correct category at the bottom of the screen.

Click here to open a text description of the Test Yourself activity

Test Yourself: Types of Heat Loss

Identify the type of heat loss (conduction, convection, or radiation) for each of the following examples:

1. Heat escaping through the roof of a house
2. A hot stove burner
3. Boiling water
4. A torch halogen lamp producing light and heat
5. A door hanging wide open, letting in cold air
6. A fire creating heat
7. Heat escaping through a wall
8. A mirror reflecting sunlight
9. Heat escaping through a window
10. Heat escaping through a chimney

Answers:

A. Conduction

B. Radiation

C. Convection

D. Radiation

E. Convection

F. Radiation

G. Conduction

H. Radiation

I. Conduction

J. Radiation

Reducing Energy Consumption

There are two ways in which we can reduce energy consumption.

Heat Transfer In Metal Rod Making

1. The most cost-effective way is to improve the home’s “envelope”—the walls, windows, doors, roof, and floors that enclose the home—by improving the insulation (conduction losses) and sealing the air leaks with caulking (convection losses).
2. The second way to reduce the energy consumption is by improving the efficiency of the furnace that provides the heat.

Click here to open a text description of the Conduction and Convection diagram

Line drawing of a house with arrows pointing out from the walls and roof showing conduction & arrows flowing in a circular motion inside the house showing convection.