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# Heat Transfer Efficiency

"If you can't handle the heat, stay out of the kitchen". This is a commonly used idiom - but if you think about this more literally, you know that when a pot or pan is placed on a hot stove it is still possible to feel the temperature rise in the surrounding air as the kitchen gets hotter. Surely this means that not all of the electrical energy from the stove, which is being converted into heat energy, is being used to cook the food in the pot or pan. This process is not 100% efficient, and unfortunately, no process ever is. We will discuss heat transfer efficiency in this article and find out how to keep our kitchen cool.

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## Heat Transfer Efficiency Meaning

Thermal energy is defined as the energy that is associated with the temperature of an object. Warmer objects will typically have a greater amount of thermal energy than cooler objects. Thermal energy can be transformed from other forms of energy via friction, electrical currents and even air resistance.

Heat transfer is the flow of thermal energy from high-temperature regions to lower-temperature regions. That means that thermal energy is transferred from hot objects to cold objects that are near each other. You are probably already familiar with this phenomenon; we use ice to keep drinks cool on hot days. The liquid transfers thermal energy to the cold ice, which increases in temperature and melts. This process extracts thermal energy from the liquid, cooling the drink down.

Heat transfer efficiency is the ratio of the useful output heat energy transfer to the total input heat energy transfer.

When energy is transferred between different forms, a proportion of the energy is usually lost to an unwanted form of energy during the conversion and is wasted in the surroundings. Due to the conservation of energy, the total energy output of the system includes both the useful energy output and the dissipated (lost) energy. The efficiency can be calculated as a percentage and cannot exceed 100% efficiency, as this would imply more energy came out of the transfer than went in! The formula used to calculate heat transfer efficiency is shown below, where either energy or power can be used. The higher the efficiency the smaller the proportion of wasted energy and vice versa.

## The Equation for Heat Transfer Efficiency

We can write the definition for heat transfer efficiency mathematically as follows:

$\begin{array}{rcl}\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}& =& \frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{input}}\end{array}$

We can note from this equation that the numerator and denominator are both quantities that are measured in the unit of joules$\left(\mathrm{J}\right)$. It is clear then that the efficiency does not have a unit and is simply a number. Using this equation we can identify how much heat energy is transferred usefully from one system to another. Recall that energy transferred per unit time is the power output of the system; it follows then that we can write the heat transfer efficiency in another way:

$\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}=\frac{\mathrm{useful}\mathrm{heat}\mathrm{power}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{power}\mathrm{input}}$

## Mechanisms to Consider for Heat Transfer Efficiency

Heat transfer occurs through three main mechanisms: conduction, convection and radiation. Energy is transferred via each mechanism but the processes are different. The efficiency of heat transfer can be calculated irrespective of the mechanism responsible for the heat transfer, as in most real-life situations heat will be transferred using a combination of these mechanisms.

### Conduction

Conduction is the mechanism of heat transfer between two substances in direct contact. The substance at a higher temperature has more energetic atom collisions, which gradually transfer heat energy to the cooler substance. Conduction is the flow of thermal energy through one object and into another, and also the mechanism by which heat diffuses through a solid object. The image below shows the conduction of heat energy of a metal rod from a candle's flame.

The image shows heat being transferred from a candle's flame to a metal rod via conduction. Conduction occurs when thermal energy is transferred between objects, Wikimedia Commons CC BY-SA 4.0

### Convection

Convection is a mechanism of heat transfer which occurs in liquids and gases that expand when heated. The hot particles become less dense than their surroundings causing them to rise, and colder particles to move to take their place. These cooler particles are then heated, and the process repeats. This creates a convection current that transfers heat from one particle to another.

An example of convection is the heat transfer that occurs in the mantle of the earth. The extremely hot layers of the mantle closest to the core move toward the earth's surface as they are less dense than the cooler layers of rock in the higher regions of the mantle. The cooler rock sinks closer to the core and then gets heated enough until the process repeats itself. A convection current is produced which moves the material back and forth in the mantle very slowly. The figure below illustrates this effect.

This image shows the convection currents that arise from the difference in density of the material in different regions of the earth's mantle, Wikimedia Commons CC BY-SA 4.0

Radiation is the energy emitted in the form of infrared electromagnetic radiation by heated surfaces. The properties of the thermal radiation depend on the type of surface of the material and its temperature. It occurs when moving charges within an object are decelerated, and their energy is converted into electromagnetic waves. The image below shows an example of thermal radiation being emitted by a fire.

The figure shows thermal radiation that is created by a fire when infrared waves are emitted by the movement of electrons and protons in the surrounding air, adapted from image by Kmecfiunit CC BY-SA 4.0

The principle of conservation of energy states that energy cannot be created or destroyed, but can only change form from one energy to another within a system. However, in practice when energy is transferred from one form to another, some of the energy transferred is almost always lost to the surroundings. This energy cannot be used by the system hence this energy is known as wasted or dissipated energy. There is always some heat loss in all heat transfer systems. If we reduce the amount of thermal energy a system loses, we can increase the efficiency of that system.

## Heat Transfer Efficiency Calculations

A kettle is used to heat water. Thermal energy of$1000\mathrm{J}$is transferred from the heating element to the kettle, and $820\mathrm{J}$of thermal energy is transferred from the kettle to the water. Find the efficiency of energy transferred to the water.

Answer: We can apply the equation for heat transfer efficiency as follows:

$\begin{array}{rcl}\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}& =& \frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{output}}×100%\\ & =& \frac{820}{1000}×100%\\ & =& 82%\end{array}$

We multiply by 100 to convert the fraction into a percentage. In the end, only 82% of the heat energy of the kettle goes into heating the water. The rest has been lost to the surrounding air and body of the kettle via conduction and convection.

A motor receives$450\mathrm{J}$of electrical energy from a power supply.$20%$of this energy is wasted. Find the efficiency of the motor.

Answer: We can first write the equation for heat transfer efficiency as:

$\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}=\frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{input}}×100%\phantom{\rule{0ex}{0ex}}$

We find the amount of useful energy output by subtracting the total energy input of$450\mathrm{J}$by the amount of wasted energy.

$\begin{array}{rcl}\mathrm{useful}\mathrm{heat}\mathrm{output}& =& 450-\left(450×\frac{20}{100}\right)\\ & =& 450-90\\ & =& 360\mathrm{J}\end{array}$

Finally, we substitute the useful energy output and total energy output into the efficiency equation.

$\begin{array}{rcl}\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}& =& \frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{input}}×100%\\ & =& \frac{360}{450}×100%\\ & =& 80%\end{array}$

Q. Find the energy wasted in a system if the useful heat ouput is$350\mathrm{J}$while the total heat input is$900\mathrm{J}$. What is the efficiency of the system?

A. To find the wasted energy we subtract the useful heat output from the total heat input. This gives us$550\mathrm{J}$as shown below.

$\mathrm{Wasted}\mathrm{Energy}=900\mathrm{J}-350\mathrm{J}=550\mathrm{J}$

Next, to find the heat transfer efficiency we use the formula.

$\begin{array}{rcl}\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}& =& \frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{input}}×100%\\ & =& \frac{350}{900}×100%\\ & =& 40%\end{array}$

## Factors Affecting the Efficiency of Heat Transfer

In different applications, we may want to design devices to improve or restrict the efficiency of heat transfer in a system depending on the objective. Below we describe some applications that improve heat transfer and some others that restrict heat transfer.

### Improving Heat Transfer Efficiency

#### Cooling fins

Cooling fins use conduction and convection to transfer heat away from objects that generate heat and need to remain cool. They increase the surface area over which heat can be transferred to the surrounding fluid via conduction and convection, and are an efficient method of improving heat transfer. The image below shows an example of cooling fins on a motorbike, used to keep the engine cool.

The engine of a motorbike is surrounded by cooling fins to transfer heat away from it over a larger surface area, and hence keep it cool.

#### Copper-based Saucepans

If you're lucky enough to have a high-quality set of saucepans in your kitchen, you may find they have a copper base. This is because the primary method of heat transfer a saucepan uses to transfer heat from the stove into the food is conduction. You might already know that copper is an excellent conductor of electricity, and it's also a great conductor of heat! By using copper in the section of the pan that contacts the stove, there is less thermal resistance to the heat transferring from the stove into the pan. This means the pan can warm up faster and is better to cook with.

### Restricting Heat Transfer Efficiency

#### Double-glazing

Double-glazed windows consist of two panes of glass rather than one. The panes are separated by a layer of gas, usually argon, which is a poor conductor of heat. The two panes are also positioned close enough to each other that a convection current cannot form in the gas between them. The double-glazing is intended to prevent conduction or convection from occurring between the inside of the home and the outside. Double-glazing is an efficient method of restricting heat transfer.

#### Oven Gloves

When handling hot objects from an oven, we often use oven gloves to protect our hands from being burnt. These work by separating the hot object and your skin using a thick layer of insulating material such as cotton or silicone. These materials increase the thermal resistance to heat transfer by conduction, which decreases the rate that heat energy is transferred through the glove.

## Heat Transfer Efficiency - Key takeaways

• Heat transfer efficiency is the ratio of the useful output heat energy transfer to the total input heat energy transfer.
• The definition of heat transfer efficiency can be written mathematically as follows

$\begin{array}{rcl}\mathrm{heat}\mathrm{transfer}\mathrm{efficiency}& =& \frac{\mathrm{useful}\mathrm{heat}\mathrm{output}}{\mathrm{total}\mathrm{heat}\mathrm{input}}\\ & & \end{array}$

• Heat transfer occurs through three mechanisms; conduction, convection and radiation.
• Conduction is the mechanism of heat transfer between two substances at different temperatures in direct contact with atomic collisions transferring heat between the substances.
• Convection is the mechanism of heat transfer via liquid and gases which expand when heated.
• Radiation is the energy emitted in the form of infrared electromagnetic radiation by heated surfaces.

#### Flashcards in Heat Transfer Efficiency 15

###### Learn with 15 Heat Transfer Efficiency flashcards in the free StudySmarter app

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What is heat transfer efficiency?

It is the ratio of useful heat energy transfer to total heat energy transfer.

How do you calculate heat transfer efficiency?

Heat transfer efficiency = Useful heat output / total heat input.

What are the factors that can affect the efficiency of heat transfer?

The factors include the type of materials used, the thickness of the insulation used, the thermal conductivity of materials and the temperature gradient between materials.

What is an example of heat transfer efficiency?

A kettle that requires 1000 J of energy to transfer 800 J of thermal energy to the water in it, has a heat transfer efficiency of 80%.

What is the heat transfer efficiency formula?

Heat transfer efficiency = Useful heat output / total heat input.

## Test your knowledge with multiple choice flashcards

Conduction is the mechanism of heat transfer that occurs in liquid and gases which expand when heated.

A system can have a heat transfer efficiency that is greater than 100%.

Convection is the mechanism of heat transfer of liquid and gas particles which expand when heated.

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