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cs Classroom Tutorial
Rates of Heat Transfer
On previous pages of this lesson, we have learned that heat is a form of energy transfer from a high temperature location to a low temperature location. The three main methods of heat transfer – conduction, convection and radiation – were discussed in detail on the previous page. Now we will investigate the topic of the rate of heat transfer. This topic is of great importance because of the frequent need to either increase or decrease the rate at which heat flows between two locations. For instance, those of us who live in colder winter climates are in constant pursuit of methods of keeping our homes warm without spending too much money. Heat escapes from higher temperature homes to the lower temperature outdoors through walls, ceilings, windows and doors. We make efforts to reduce this heat loss by adding better insulation to walls and attics, caulking windows and doors, and buying high efficiency windows and doors. As another example, consider electricity generation. Household electricity is most frequently manufactured by using fossil fuels or nuclear fuels. The method involves generating heat in a reactor. The heat is transferred to water and the water carries the heat to a steam turbine (or other type of electrical generator) where the electricity is produced. The challenge is to efficiently transfer the heat to the water and to the steam turbine with as little loss as possible. Attention must be given to increasing heat transfer rates in the reactor and in the turbine and decreasing heat transfer rates in the pipes between the reactor and the turbine.
So what variables would affect the heat transfer rates? How can the rate of heat transfer be controlled? These are the questions to be discussed on this page of Lesson 1. Our discussion will be restricted to the variables affecting the rate of heat transfer by
. Once the variables affecting the rate of heat transfer are discussed, we will look at a mathematical equation that expresses the dependence of rate upon these variables.
In conduction, heat is transferred from a hot temperature location to a cold temperature location. The transfer of heat will continue as long as there is a difference in temperature between the two locations. Once the two locations have reached the same temperature, thermal equilibrium is established and the heat transfer stops. Earlier in this lesson, we discussed the transfer of heat for a situation involving a metal can containing high temperature water that was placed within a Styrofoam cup containing low temperature water. If the two water samples are equipped with temperature probes that record changes in temperature with respect to time, then the following graphs are produced.
In the graphs above, the slope of the line represents the rate at which the temperature of each individual sample of water is changing. The temperature is changing because of the heat transfer from the hot to the cold water. The hot water is losing energy, so its slope is negative. The cold water is gaining energy, so its slope is positive. The rate at which temperature changes is proportional to the rate at which heat is transferred. The temperature of a sample changes more rapidly if heat is transferred at a high rate and less rapidly if heat is transferred at a low rate. When the two samples reach thermal equilibrium, there is no more heat transfer and the slope is zero. So we can think of the slopes as being a measure of the rate of heat transfer. Over the course of time, the rate of heat transfer is decreasing. Initially heat is being transferred at a high rate as reflected by the steeper slopes. And as time progresses, the slopes of the lines are becoming less steep and more gently sloped.
What variable contributes to this decrease in the heat transfer rate over the course of time? Answer: the difference in temperature between the two containers of water. Initially, when the rate of heat transfer is high, the hot water has a temperature of 70°C and the cold water has a temperature of 5°C. The two containers have a 65°C difference in temperature. As the hot water begins to cool and the cold water begins to warm, the difference in their temperatures decrease and the rate of heat transfer decreases. As thermal equilibrium is approached, their temperatures are approaching the same value. With the temperature difference approaching zero, the rate of heat transfer approaches zero. In conclusion, the rate of conductive heat transfer between two locations is affected by the temperature difference between the two locations.
The first variable that we have identified as affecting the rate of conductive heat transfer is the temperature difference between the two locations. The second variable of importance is the materials involved in the transfer. In the previous discussed scenario, a metal can containing high temperature water was placed within a Styrofoam cup containing low temperature water. The heat was transferred from water through the metal to water. The materials of importance were water, metal and water. What would happen if the heat were transferred from hot water through glass to cold water? What would happen if the heat were transferred from hot water through Styrofoam to cold water? Answer: the rate of heat transfer would be different. Replacing the inner metal can with a glass jar or a Styrofoam cup would change the rate of heat transfer. The rate of heat transfer depends on the material through which heat is transferred.
The effect of a material upon heat transfer rates is often expressed in terms of a number known as the thermal conductivity. Thermal conductivity values are numerical values that are determined by experiment. The higher that the value is for a particular material, the more rapidly that heat will be transferred through that material. Materials with relatively high thermal conductivities are referred to as thermal conductors. Materials with relatively low thermal conductivity values are referred to as thermal insulators. The table below lists thermal conductivity values (k) for a variety of materials, in units of W/m/°C.
Polyvinyl chloride (PVC)(s)
Concrete (Low Density)(s)
Concrete (High Density)(s)
As is apparent from the table, heat is generally transferred by conduction at considerably higher rates through solids (s) in comparison to liquids (l) and gases (g). Heat transfer occurs at the highest rates for metals (first eight items in left-hand column) because the mechanism of conduction includes mobile electrons (as discussed on a previous page). Several of the solids in the right-hand column have very low thermal conductivity values and are considered insulators. The structure of these solids is characterized by pockets of trapped air interspersed between fibers of the solid. Since air is a great insulator, the pockets of air interspersed between these solid fibers gives these solids low thermal conductivity values. One of these solid insulators is expanded polystyrene, the material used in Styrofoam products. Such Styrofoam products are made by blowing an inert gas at high pressure into the polystyrene before being injected into the mold. The gas causes the polystyrene to expand, leaving air filled pockets that contribute to the insulating ability of the finished product. Styrofoam is used in coolers, pop can insulators, thermos jugs, and even foam boards for household insulation. Another solid insulator is cellulose. Cellulose insulation is used to insulate attics and walls in homes. It insulates homes from heat loss as well as sound penetration. It is often blown into attics as loose fill cellulose insulation. It is also applied as fiberglass batts (long sheets of paper backed insulation) to fill the spacing between 2×4 studs of the exterior (and sometimes interior) walls of homes.
Another variable that affects the rate of conductive heat transfer is the area through which heat is being transferred. For instance, heat transfer through windows of homes is dependent upon the size of the window. More heat will be lost from a home through a larger window than through a smaller window of the same composition and thickness. More heat will be lost from a home through a larger roof than through a smaller roof with the same insulation characteristics. Each individual particle on the surface of an object is involved in the heat conduction process. An object with a wider area has more surface particles working to conduct heat. As such, the rate of heat transfer is directly proportional to the surface area through which the heat is being conducted.
Thickness or Distance
A final variable that affects the rate of conductive heat transfer is the distance that the heat must be conducted. Heat escaping through a Styrofoam cup will escape more rapidly through a thin-walled cup than through a thick-walled cup. The rate of heat transfer is inversely proportional to the thickness of the cup. A similar statement can be made for heat being conducted through a layer of cellulose insulation in the wall of a home. The thicker that the insulation is, the lower the rate of heat transfer. Those of us who live in colder winter climates know this principle quite well. We are told to dress in layers before going outside. This increases the thickness of the materials through which heat is transferred, as well as trapping pockets of air (with high insulation ability) between the individual layers.
A Mathematical Equation
So far we have learned of four variables that affect the rate of heat transfer between two locations. The variables are the temperature difference between the two locations, the material present between the two locations, the area through which the heat will be transferred, and the distance it must be transferred. As is often the case in physics, the mathematical relationship between these variables and the rate of heat transfer can be expressed in the form of an equation. Let’s consider the transfer of heat through a glass window from the inside of a home with a temperature of T1 to the outside of a home with a temperature of T2. The window has a surface area A and a thickness d. The thermal conductivity valueof the window glass is k. The equation relating the heat transfer rate to these variables is
Rate = k•A•(T1 – T2)/d
The units on the rate of heat transfer are Joule/second, also known as a Watt. This equation is applicable to any situation in which heat is transferred in the same direction across a flat rectangular wall. It applies to conduction through windows, flat walls, slopes roofs (without any curvature), etc. A slightly different equation applies to conduction through curved walls such as the walls of cans, cups, glasses and pipes. We will not discuss that equation here.
To illustrate the use of the above equation, let’s calculate the rate of heat transfer on a cold day through a rectangular window that is 1.2 m wide and 1.8 m high, has a thickness of 6.2 mm, a thermal conductivity valueof 0.27 W/m/°C. The temperature inside the home is 21°C and the temperature outside the home is -4°C.
To solve this problem, we will need to know the surface area of the window. Being a rectangle, we can calculate the area as width • height.
Area = (1.2 m)•(1.8 m) = 2.16 m2.(Video) Heat Transfer: Crash Course Engineering #14
We will also need to give attention to the unit on thickness (d). It is given in units of cm; we will need to convert to units of meters in order for the units to be consistent with that of k and A.
d = 6.2 mm = 0.0062 m
Now we are ready to calculate the rate of heat transfer by substitution of known values into the above equation.
Rate = (0.27 W/m/°C)•(2.16 m2)•(21°C – -4°C)/(0.0062 m)
Rate = 2400 W (rounded from 2352 W)
It is useful to note that the thermal conductivity value of a house window is much lower than the thermal conductivity value of glass itself. The thermal conductivity of glass is about 0.96 W/m/°C. Glass windows are constructed as double and triple pane windows with a low pressure inert gas layer between the panes. Furthermore, coatings are placed on the windows to improve efficiency. The result is that there are a series of substances through which heat must consecutively pass in order to be transferred out of (or into) the house. Like electrical resistors placed in series, a series of thermal insulators has an additive effect on the overall resistance offered to the flow of heat. The accumulative effect of the various layers of materials in a window leads to an overall conductivity that is much less than a single pane of uncoated glass.
Lesson 1 of this Thermal Physics chapter has focused on the meaning of temperature and heat. Emphasis has been given to the development of a particle model of materials that is capable of explaining the macroscopic observations. Efforts have been made to develop solid conceptual understandings of the topic in the absence of mathematical formulas. This solid conceptual understanding will serve you well as you approach Lesson 2. The chapter will turn slightly more mathematical as we investigate the question: how can the amount of heat released from or gained by a system be measured? Lesson 2 will pertain to the science of calorimetry.
Check Your Understanding
1. Predict the effect of the following variations upon the rate at which heat is transferred through a rectangular object by filling in the blanks.
a. If the area through which heat is transferred is increased by a factor of 2, then the rate of heat transfer is ________________ (increased, decreased) by a factor of _________ (number).
b. If the thickness of the material through which heat is transferred is increased by a factor of 2, then the rate of heat transfer is ________________ by a factor of _________.
c. If the thickness of the material through which heat is transferred is decreased by a factor of 3, then the rate of heat transfer is ________________ by a factor of _________.
d. If the thermal conductivity of the material through which heat is transferred is increased by a factor of 5, then the rate of heat transfer is ________________ by a factor of _________.
e. If the thermal conductivity of the material through which heat is transferred is decreased by a factor of 10, then the rate of heat transfer is ________________ by a factor of _________.
f. If the temperature difference on opposite sides of the material through which heat is transferred is increased by a factor of 2, then the rate of heat transfer is ________________ by a factor of _________.
2. Use the information on this page to explain why the 2-4 inch thick layer of blubber on a polar bear helps to keep polar bears warm during frigid artic weather.
3. Consider the example problem above. Suppose that the area where the window is located is replaced by a wall with thick insulation. The thermal conductivity of the same area will be decreased to 0.0039 W/m/°C and the thickness will be increased to 16 cm. Determine the rate of heat transfer through this area of 2.16 m2.
Extra Information About what factors affect the rate of thermal energy transfer That You May Find Interested
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Rates of Heat Transfer – The Physics Classroom Tutorial
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Frequently Asked Questions About what factors affect the rate of thermal energy transfer
If you have questions that need to be answered about the topic what factors affect the rate of thermal energy transfer, then this section may help you solve it.
What factors affect the rate of thermal energy transfer?
The material through which heat is transferred determines the rate of heat transfer; this effect is frequently expressed in terms of a number known as the thermal conductivity, which is a numerical value that is determined through experiment.
What elements affect thermal performance and heat transfer?
According to experiments, a substance’s mass, its change in temperature, and some physical characteristics associated with its phase all affect how much heat is transferred to or away from it.
What three factors affect thermal energy?
If all other conditions are equal, substances in gas form have the most thermal energy, followed by liquids, then solids. A substance’s total thermal energy depends on its temperature, number of atoms, and physical state. More atoms and higher temperature mean more thermal energy.
What elements impact the conduction’s rate of energy transfer?
The temperature gradient, the cross section of the materials involved, their path length, and the properties of those materials are the four fundamental factors that determine the process of heat conduction.
What controls the thermal energy transfer?
When a substance is heated, its temperature rises because the molecules that make it up move more quickly and gain thermal energy through heat transfer. Thermal energy is the internal energy of a system as a result of its temperature.
What three factors are related to thermal energy?
Temperature, state, and mass are the three elements that have an impact on thermal energy.
What four different ways can thermal energy be transferred?
There are numerous ways to transfer heat, including evaporative cooling, thermal radiation, convection, and conduction.
What two things are necessary for thermal energy to exist?
Mass measures the amount of material in a sample of matter, so thermal energy depends on the mass and temperature of the object being measured. Thermal energy is a function of both the temperature of the sample of matter and the quantity of material in that sample of matter.
What influences the flow of energy?
The amount of energy that can be transferred between moving objects depends on their speed, and objects that are moving faster have a greater impact because they transfer more energy.
Does heat transfer change depending on the temperature?
The rate of heat transfer between two objects is therefore inversely proportional to the temperature difference between the objects and their surroundings, such as the air.
What causes the rate of heat transfer to decrease?
The answer is thermal insulation, which is the process of constructing a barrier between hot and cold objects that lessens heat transfer by either reflecting thermal radiation or reducing thermal conduction and convection between the objects.
What prevents the transfer of heat?
Insulation can be used to control and prevent heat transfer so that it doesn’t affect the surrounding environment.
Why do large temperature differences cause heat to transfer more quickly?
This is because a great deal of energy can be transferred from the “faster” to the “slower” molecules, which ultimately means a great deal of heat transfer, because the greater the temperature difference between two substances, the greater the difference in the kinetic energies of the respective molecules.
What expedites the transfer of heat?
The difference in temperature between two objects is referred to as a thermal gradient (gradient = slope) and the steeper the thermal gradient, the faster the flow of heat from the hotter to the cooler one.
What are the 3 factors that affect the rate of heat transfer by conduction? ›
The process of heat conduction depends on four basic factors: the temperature gradient, the cross section of the materials involved, their path length, and the properties of those materials.What effects thermal energy transfer? ›
Thermal energy typically flows from a warmer material to a cooler material. Generally, when thermal energy is transferred to a material, the motion of its particles speeds up and its temperature increases. There are three methods of thermal energy transfer: conduction, convection, and radiation.What 4 factors affect the rate of emission of thermal radiation? ›
- The temperature of the object (hotter = more radiation)
- The colour of the object (black = more radiation)
- The surface area of the object (greater surface area = more area for radiation to be emitted from)
- The temperature of the body rises if we provide extra heat to the body.
- The shape of the body may change. Some bodies expand on heating.
- Change in state of the body.
Temperature, moisture content, and density are the most important factors. Other factors include thickness, air velocity, pressing, and aging time. The relationship between main factors with thermal conductivity is presented.What are the factors affecting heat transfer and thermal performance? ›
Experiments show that the heat transferred to or from a substance depends on three factors—the change in the substance's temperature, the mass of the substance, and certain physical properties related to the phase of the substance.What are examples of thermal energy transfer? ›
For example, a lighted match (higher temperature object) will transfer heat to a large pan filled with lukewarm water (lower temperature object). Note that the actual amount of thermal energy each object has doesn't matter, as the pan of lukewarm water might have more thermal energy than the match.
The main factors influencing temperature include latitude, altitude, distance from oceans and lakes, and ocean currents.What are the 4 environmental factors affecting thermal comfort? ›
The main factors that influence thermal comfort are those that determine heat gain and loss, namely metabolic rate, clothing insulation, air temperature, mean radiant temperature, air speed and relative humidity.What three factors affect thermal stress? ›
- HEAT STRESS. Risk Factors.
- Workers should be aware of the many factors that can impact the risk of heat illness. Environment.
- • High temperatures, especially. with high humidity, which. ...
- • High exertion. • Not enough rest breaks. ...
- Medications. Heat tolerance can. ...
- Health. Conditions. ...
- Other Factors. • Age over 60. ...
- Prior Heat. Illness.
What is the best way to transfer thermal energy? ›
Thermal energy is transferred from hot places to cold places by convection. Convection occurs when warmer areas of a liquid or gas rise to cooler areas in the liquid or gas. Cooler liquid or gas then takes the place of the warmer areas which have risen higher.What are the three 3 methods of energy heat transfer give example for each? ›
1: Conduction: Heat transfers into your hands as you hold a hot cup of coffee. Convection: Heat transfers as the barista “steams” cold milk to make hot cocoa. Radiation: Reheating a cold cup of coffee in a microwave oven.What method transfers the most thermal energy? ›
A conductor is a material that allows internal (thermal) energy to be transmitted through it easily. Metals, such as copper and aluminium are the best conductors of heat. This is because metals have loosely held outer electrons surrounding the atoms called 'free' electrons.Does temperature difference affect heat transfer? ›
Rate of heat transfer between two objects
So the greater the temperature difference between an object and its surroundings (air for example), the greater the rate at which heat energy is transferred.
The transfer of heat always occurs from a body with greater potential and kinetic energy to a body of lower potential and kinetic energy, in other words, from high to low temperature.How does density affect heat transfer? ›
An increase in the bulk density will decrease the “heat transfer average distance,” and therefore decrease the thermal conductivity. Counteracting this effect is the increased mass within the same volume, which will increase the solid conduction.What two factors affect thermal energy Why? ›
The thermal energy of matter depends on how fast its particles are moving on average, which is measured by temperature, and also on how many particles there are, which is measured by mass.What are the three factors affecting thermal energy quizlet? ›
What are the three factors affecting thermal energy? Temperature, State, and Mass. What is Heat? The transfer of thermal energy from an object of higher temperature to an object of lower temperature.What are the factors affecting thermal efficiency? ›
Factors analysis of thermal efficiency
The key factors affecting the boiler heat loss and efficiency are superheating surface area, excess air coefficient, inlet gas and exhaust gas temperature, etc.
The larger the difference in temperature between two objects, the faster heat will transfer from the hotter one to the cooler one. The difference in temperature between two objects is called a thermal gradient (gradient = slope). The steeper the thermal gradient, the faster the flow of heat.
What are the 3 types of thermal energy? ›
Types of Thermal Energy
The thermal energy of the matter is increased by three methods, namely, conduction, convection and radiation.
- Solar Energy. Solar radiation (a form of thermal energy) heats up our atmosphere, that's why heat is felt on Earth.
- Geothermal Energy. ...
- Heat Energy From the Oceans. ...
- Fuel Cell Energy. ...
- A Glass of Cold Chocolate and a Cup of Hot Chocolate Milk. ...
- Melting Ice.
Thermal energy transfer involves the transfer of internal energy. The three types of thermal energy transfer are conduction, convection and radiation. Conduction involves direct contact of atoms, convection involves the movement of warm particles and radiation involves the movement of electromagnetic waves.What are the 3 most important factors that influence climate? ›
The most important natural factors are: distance from the sea. ocean currents. direction of prevailing winds.What are the 5 major factors that affect climate? ›
Hint:The five main factors which affect the climate of a region are Latitude, Altitude, relief, currents and winds and distance from the sea.What is the most important factor affecting temperature? ›
The Sun is the primary source of energy that influences any planet's temperature, including Earth.What are the six primary factors that affect thermal comfort? ›
- Air temperature.
- Radiant temperature.
- Air movement and speed.
- Clothing and PPE insulation.
- Work rate and metabolic heat.
The temperature characteristics of a region are influenced by natural factors such as latitude, elevation and the presence of ocean currents. The precipitation characteristics of a region are influenced by factors such as proximity to mountain ranges and prevailing winds.What are the factors of thermal? ›
- Input heat energy.
- Output heat energy.
The factors related to the polymer structure significantly affecting thermal stability are functional groups, molecular weight, branch degree, cross-linking, and crystallinity.
What three factors are important in thermal control and comfort? ›
The thermal comfort is one of the indoor environment factors that affect health and human performance, thus chiefly determined by temperature, humidity, and air movement.How can you increase or decrease the rate of thermal energy transfer? ›
a. If the area through which heat is transferred is increased by a factor of 2, then the rate of heat transfer is increased by a factor of 2. b. If the thickness of the material through which heat is transferred is increased by a factor of 2, then the rate of heat transfer is decreased by a factor of 2.What are the 3 main methods of heat transfer explain the difference between them? ›
In conduction, heat transfer occurs between objects by direct contact. In convection, the heat transfer takes within the fluid. In radiation, heat transfer occurs through electromagnetic waves without involving particles. The heat transfer takes place due to the difference in temperature.What are the 3 types of heat transfer and briefly describe each? ›
The first is conduction, which occurs in solids or fluids that are at rest, such as this metal bar. The second form of heat transfer is convection, which occurs in liquids or gases that are in motion. And the third form of heat transfer is radiation, which takes place with no material carrier.What are the 4 types of thermal energy transfer? ›
Various heat transfer mechanisms exist, including convection, conduction, thermal radiation, and evaporative cooling.What materials transfer thermal energy well? ›
In general, good conductors of electricity (metals like copper, aluminum, gold, and silver) are also good heat conductors, whereas insulators of electricity (wood, plastic, and rubber) are poor heat conductors.What factors affect the rate of energy transfer by conduction? ›
The rate at which an object transfers energy by heating depends on: the surface area, volume and material of the object and the nature of the surface with which the object is in contact. The bigger the temperature difference between a body and its surroundings, the faster the rate at which heat is transferred.What are the three 3 basic types of heat transfer mechanisms? ›
Heat can be transferred in three ways: by conduction, by convection, and by radiation. Conduction is the transfer of energy from one molecule to another by direct contact.What are three types of conduction of heat? ›
- Conduction is the transfer of energy from one atom to another through direct contact.
- There are three main types of conduction: ionic conduction, electric conduction, and thermal conduction.
Statement 1: There must be a heat-conducting material between two bodies for heat transfer. Statement 2: There must be a temperature difference between two bodies for heat transfer. Statement 3: The material must be made of metal between two bodies for heat flow.
What does the rate of heat transfer depend on? ›
The rate of heat transfer depends on the material through which heat is transferred. The effect of a material upon heat transfer rates is often expressed in terms of a number known as the thermal conductivity. Thermal conductivity values are numerical values that are determined by experiment.What factors affect the rate of energy? ›
There is a range of factors that affect the availability of energy, including physical factors, cost of exploitation and production, technology and political factors.What are the 4 primary modes of heat transfer? ›
Various heat transfer mechanisms exist, including convection, conduction, thermal radiation, and evaporative cooling.What are the 5 most modes of heat transfer? ›
- Convection vs. conduction.
Electronic conductivities are derived from currents obtained using electronically-conductive glassy carbon electrodes to contact the sample, whereas ionic conductivities are derived from currents obtained using ionically-conductive Nafion electrodes to contact the sample.How can you prevent the transfer of heat? ›
Heat transfer can be controlled and prevented by insulation so that it doesn't transfer to the environment. The purpose of the insulation is to prevent heat transfer from a higher temperature to a lower temperature and therefore all ways of heat transfer should be taken into account when designing the insulation.What is the essential condition for heat transfer? ›
Heat transfer occurs between states of matter whenever a temperature difference exists and heat transfer occurs only in the direction of decreasing temperature, meaning from a hot object to a cold object.What are the two important conditions for transfer of heat by conduction? ›
(i) The two objects should be in direct contact with each other. (ii) The temperature of the two objects should be different. Heat will flow from a hotter object to a cooler object.