Thermal conductance and resistance

In heat transfer, thermal engineering, and thermodynamics, thermal conductance and thermal resistance are fundamental concepts that describe the ability of materials or systems to conduct heat and the opposition they offer to the heat current. The ability to manipulate these properties allows engineers to control temperature gradient, prevent thermal shock, and maximize the efficiency of thermal systems. Furthermore, these principles find applications in a multitude of fields, including materials science, mechanical engineering, electronics, and energy management. Knowledge of these principles is crucial in various scientific, engineering, and everyday applications, from designing efficient temperature control, thermal insulation, and thermal management in industrial processes to optimizing the performance of electronic devices.
Thermal conductance measures the ability of a material or system to conduct heat. It provides insights into the ease with which heat can pass through a particular system. It is measured in units of watts per kelvin. It is essential in the design of heat exchangers, thermally efficient materials, and various engineering systems where the controlled movement of heat is vital.
Conversely, thermal resistance measures the opposition to the heat current in a material or system. It is measured in units of kelvins per watt and indicates how much temperature difference is required to transfer a unit of heat current through the material or object. It is essential to optimize the building insulation, evaluate the efficiency of electronic devices, and enhance the performance of heat sinks in various applications.
Objects made of insulators like rubber tend to have very high resistance and low conductance, while objects made of conductors like metals tend to have very low resistance and high conductance. This relationship is quantified by resistivity or conductivity. However, the nature of a material is not the only factor as it also depends on the size and shape of an object because these properties are extensive rather than intensive. The relationship between thermal conductance and resistance is analogous to that between electrical conductance and resistance in the domain of electronics.
Thermal insulance is a measure of a material's resistance to the heat current. It quantifies how effectively a material can resist the transfer of heat through conduction, convection, and radiation. It has the units square metre kelvins per watt in SI units or square foot degree Fahrenheit–hours per British thermal unit in imperial units. The higher the thermal insulance, the better a material insulates against heat transfer. It is commonly used in construction to assess the insulation properties of materials such as walls, roofs, and insulation products.

Practical applications

Thermal conductance and resistance have several practical applications in various fields:

Building insulation: Understanding thermal resistance helps in designing energy-efficient buildings with effective insulation materials to reduce heat transfer.
Electronics cooling: Thermal resistance is crucial for designing heat sinks and thermal management systems in electronic devices to prevent overheating. Calculating thermal conductance is crucial for designing effective heat sinks and cooling systems in electronic devices.
Automotive design: Automotive engineers use thermal resistance to optimize the cooling system and prevent overheating in engines and other vehicle components. Evaluating thermal resistance helps in designing engine components and automotive cooling systems.
Cookware design: Thermal conductance is important for designing cookware to ensure even heat distribution and cooking efficiency. Assessing thermal conductance is important in designing cookware for even heat distribution.
Heat exchangers: In industries like HVAC and chemical processing, heat exchangers use thermal conductance to efficiently transfer heat between fluids.
Aerospace: In spacecraft and aircraft, thermal resistance and conductance are critical for managing temperature variations in extreme environments. Designing spacecraft and aviation systems require considerations of thermal conductance and resistance to manage temperature extremes.
Cryogenics: Understanding thermal properties is vital for the design of cryogenic systems used in superconductors and medical applications.
Energy efficiency: In the energy sector, thermal resistance and conductance play a role in designing efficient heat exchangers for power plants and energy-efficient appliances.
Medical devices: Thermal management is crucial for medical equipment like magnetic resonance imaging machines and laser systems to maintain precise operating temperatures. Ensuring proper thermal management is crucial for the safety and performance of medical devices and laser systems.
Food processing: The food industry uses knowledge of thermal conductance to optimize processes like pasteurization and cooking and design equipment for food processing, such as ovens and refrigeration units.
Materials science: Researchers use thermal conductance data to develop new materials for various applications, including energy storage and advanced coatings.
Environmental science: Thermal resistance is considered in climate studies to understand heat transfer in Earth's atmosphere and oceans. Evaluating thermal resistance is useful in studying soil temperature profiles for environmental and agricultural research.
Heating, ventilation, and air conditioning : Understanding thermal resistance aids in optimizing heating, ventilation, and air conditioning systems for better energy efficiency.
Thermal packaging: Ensuring proper thermal conductance and resistance is crucial for protecting sensitive goods during transport.
Solar energy systems: Understanding thermal resistance is important in the design of solar collectors and thermal energy storage systems.
Manufacturing processes: Controlling thermal conductance is essential in processes like welding, heat treatment, and metal casting.
Geothermal energy: Assessing thermal conductance is important in geothermal heat exchangers and energy production.
Thermal imaging: Infrared cameras and thermal imaging devices use principles of thermal conductance to detect temperature variations.
Absolute thermal resistance

Absolute thermal resistance is the temperature difference across a structure when a unit of heat energy flows through it in unit time. It is the reciprocal of thermal conductance. The SI unit of absolute thermal resistance is kelvins per watt or the equivalent degrees Celsius per watt – the two are the same since the intervals are equal: ΔT = 1 K = 1 °C.
The thermal resistance of materials is of great interest to electronic engineers because most electrical components generate heat and need to be cooled. Electronic components malfunction or fail if they overheat, and some parts routinely need measures taken in the design stage to prevent this.

Analogies and nomenclature

Electrical engineers are familiar with Ohm's law and so often use it as an analogy when doing calculations involving thermal resistance. Mechanical and structural engineers are more familiar with Hooke's law and so often use it as an analogy when doing calculations involving thermal resistance.

type	structural analogy	hydraulic analogy	thermal	electrical analogy
quantity	impulse	volume	heat	charge
potential	displacement	pressure	temperature	potential
flux	load or force	flow rate	heat transfer rate	current
flux density	stress	velocity	heat flux	current density
resistance	flexibility	fluid resistance	thermal resistance	electrical resistance
conductance	...	fluid conductance	thermal conductance	electrical conductance
resistivity	flexibility	fluid resistivity	thermal resistivity	electrical resistivity
conductivity	stiffness	fluid conductivity	thermal conductivity	electrical conductivity
lumped element linear model	Hooke's law	Hagen–Poiseuille equation	Newton's law of cooling	Ohm's law
distributed linear model	...	...	Fourier's law	Ohm's law

Explanation from an electronics point of view

Equivalent thermal circuits

The heat flow can be modelled by analogy to an electrical circuit where heat flow is represented by current, temperatures are represented by voltages, heat sources are represented by constant current sources, absolute thermal resistances are represented by resistors and thermal capacitances by capacitors.
The diagram shows an equivalent thermal circuit for a semiconductor device with a heat sink.

Example calculation

Consider a component such as a silicon transistor that is bolted to the metal frame of a piece of equipment. The transistor's manufacturer will specify parameters in the datasheet called the absolute thermal resistance from junction to case, and the maximum allowable temperature of the semiconductor junction. The specification for the design should include a maximum temperature at which the circuit should function correctly. Finally, the designer should consider how the heat from the transistor will escape to the environment: this might be by convection into the air, with or without the aid of a heat sink, or by conduction through the printed circuit board. For simplicity, let us assume that the designer decides to bolt the transistor to a metal surface that is guaranteed to be less than above the ambient temperature. Note: T_HS appears to be undefined.
Given all this information, the designer can construct a model of the heat flow from the semiconductor junction, where the heat is generated, to the outside world. In our example, the heat has to flow from the junction to the case of the transistor, then from the case to the metalwork. We do not need to consider where the heat goes after that, because we are told that the metalwork will conduct heat fast enough to keep the temperature less than above ambient: this is all we need to know.
Suppose the engineer wishes to know how much power can be put into the transistor before it overheats. The calculations are as follows.
where is the absolute thermal resistance of the bond between the transistor's case and the metalwork. This figure depends on the nature of the bond - for example, a thermal bonding pad or thermal transfer grease might be used to reduce the absolute thermal resistance.
We use the general principle that the temperature drop across a given absolute thermal resistance with a given heat flow through it is:
Substituting our own symbols into this formula gives:
and, rearranging,
The designer now knows, the maximum power that the transistor can be allowed to dissipate, so they can design the circuit to limit the temperature of the transistor to a safe level.
Let us substitute some sample numbers:
The result is then:
This means that the transistor can dissipate about 18 watts before it overheats. A cautious designer would operate the transistor at a lower power level to increase its reliability.
This method can be generalized to include any number of layers of heat-conducting materials, simply by adding together the absolute thermal resistances of the layers and the temperature drops across the layers.