Kara Sears
Newton's law of cooling, published by Isaac Newton in 1701, states that the rate at which an object cools is proportional to the difference in temperature between the object and its surroundings. In other words, a hot object will cool faster in a cold room than in a hot room. This law is frequently used in the study of heat transfer, particularly in convection cooling, where the heat transfer coefficient is independent or relatively independent of the temperature difference. However, it is important to note that Newton's law of cooling does not apply to thermal radiation and has limitations when the temperature difference is large. While the term Newton's law of cooling is commonly used, some sources suggest that it is more accurately described as a model of heat exchange rather than a law. The applicability of Newton's law of cooling in heating scenarios is an interesting question that warrants further exploration.
| Characteristics | Values |
|---|---|
| Type of Law | Physical Law |
| Purpose | Study of heat transfer |
| Applicability | Convection heat transfer, forced air or pumped fluid cooling |
| Governing Factor | Heat transfer coefficient |
| Temperature Difference | Small |
| Heat Transfer Mechanism | Remains the same |
| Heat Loss | Directly proportional to the difference in temperature |
| Heat Exchange | Proportional to the difference in temperature between the object and its surroundings |
| Heat Transfer Coefficient | A constant |
| Heat Conduction | Generally followed as a consequence of Fourier's Law |
| Thermal Conductivity | Weakly dependent on temperature |
| Fluid Velocity | Does not rise with increasing temperature difference |
| Natural Convection | Heat transfer coefficient is a function of the temperature difference |
| Validity | Approximate results, not a law but a model of heat exchange |
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What You'll Learn
Newton's law of cooling is a model of heat exchange
Newton's law of cooling is frequently qualified to include the condition that the temperature difference is small, and the nature of the heat transfer mechanism remains the same. The law is followed when the heat transfer coefficient is independent or relatively independent of the temperature difference between the object and the environment. The thermal conductivity of most materials is only weakly dependent on temperature, so the constant heat transfer coefficient condition is generally met.
Newton's law of cooling is often used for calculating heat transfer by convection. It is equivalent to stating that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant. The law is most closely obeyed in purely conduction-type cooling, such as forced air or pumped liquid cooling, where the fluid velocity does not increase with rising temperature differences.
Newton's law of cooling, however, has its limitations. It does not apply to thermal radiation, and in natural convective (buoyancy-driven) heat transfer, it only approximates the result when the temperature difference is relatively small. Newton himself was aware of this limitation, and a correction to the law concerning convection for larger temperature differentials was made in 1817 by Dulong and Petit.
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The law is valid for small temperature differences
Newton's law of cooling, or heating, states that the rate of heat loss or gain of a body is directly proportional to the difference in temperatures between the body and its environment. In other words, the greater the temperature difference, the faster the rate of heat transfer.
The law is frequently qualified to include the condition that the temperature difference is small. This is because the law is based on the assumption that the nature of the heat transfer mechanism remains the same, and that the heat transfer coefficient is independent or relatively independent of the temperature difference. In reality, the heat transfer coefficient can change with temperature differences, especially in natural convection (buoyancy-driven) heat transfer.
Newton himself realized this limitation, and a correction to his law concerning convection for larger temperature differentials was made in 1817 by Dulong and Petit. In the case of heat transfer by thermal radiation, Newton's law of cooling holds only for very small temperature differences. This is because the law is derived from studies of conduction-type cooling, where the fluid velocity does not increase with temperature difference, and forced air or pumped liquid cooling, where the properties of the fluid do not vary strongly with temperature.
In summary, while Newton's law of cooling can be applied to both heating and cooling, it is most accurate for small temperature differences. This is because the underlying assumptions of the law may break down when temperature differences are large, leading to changes in the heat transfer mechanism and the heat transfer coefficient.
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The law is used for convective heat transfer
Newton's law of cooling is frequently used in the study of heat transfer. It states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its environment. This law is often applied to convective heat transfer, where the heat transfer coefficient is independent or relatively independent of the temperature difference between the object and its surroundings.
Convection is the movement of fluids, including liquids and gases. An example of convection is when a fan is used for cooling, and the heat is carried from a person to the surrounding air. Newton's law of cooling can be used to describe this process, as the rate of heat exchange between an object and its surroundings is proportional to the difference in temperature.
In convective heat transfer, Newton's law is typically followed for forced air or pumped fluid cooling. The properties of the fluid do not vary significantly with temperature, and the fluid velocity does not increase with the temperature difference. This is often the case in industrial applications, where heat transfer processes may involve composite systems with both conduction and convection. For instance, heat transfer in a steam generator involves convection from the reactor coolant to the steam generator inner tube surface, conduction through the tube, and then convection from the outer tube surface to the secondary fluid.
Newton's law of cooling is also relevant in natural convective heat transfer, which is driven by buoyancy. However, in this case, the law only holds true when the temperature difference is relatively small. This limitation was recognized by Newton himself, and a correction for larger temperature differentials was made by Dulong and Petit in 1817.
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The law is not valid for thermal radiation
Newton's law of cooling is a physical law that is frequently used to study heat transfer. It states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its environment. However, this law has certain limitations and does not hold true in all scenarios. One important limitation is that Newton's law of cooling is not valid for thermal radiation.
Thermal radiation refers to the transmission of heat in the form of waves, such as the heat transmitted from the sun. This is distinct from convection, which involves the bulk movement of fluids, such as air or liquids, to transfer heat. While Newton's law of cooling can be applied to convective heat transfer, it does not accurately describe thermal radiation.
The reason for this discrepancy lies in the nature of thermal radiation and the underlying physics involved. In the case of thermal radiation, the rate of heat transfer is influenced by the absolute temperatures of the object and its environment, rather than just the temperature difference. This behaviour is better described by the Stefan-Boltzmann law, which accounts for the fourth powers of the absolute temperatures in the heat transfer equation.
Newton's law of cooling makes several simplifying assumptions, such as a low Biot number and temperature-independent heat capacity. These assumptions lead to a simple differential equation that describes an exponential decrease in temperature difference over time. However, these assumptions break down when considering thermal radiation, particularly at high temperatures or when dealing with materials that have temperature-dependent thermal conductivities.
Furthermore, the concept of a "heat transfer coefficient" is central to Newton's law of cooling. This coefficient mediates between heat losses and temperature differences and is assumed to be constant in Newton's law. However, in the case of thermal radiation, the heat transfer coefficient may vary, and other factors come into play, such as the emissivity and absorptivity of the materials involved. Therefore, the simple relationship between temperature difference and heat transfer rate described by Newton's law does not hold for thermal radiation.
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The law is used to calculate the heat transfer coefficient
Newton's law of cooling is a physical law that is frequently used in the study of heat transfer. It states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its environment. In other words, a glass of hot water will cool down faster in a cold room than in a hot room.
The law is often used to calculate the heat transfer coefficient, which is a crucial value in heat transfer mechanisms' calculations. The heat transfer coefficient, denoted as 'h', depends on the physical properties of the fluid and the situation in which convection occurs. It is a measure of how easily heat is transferred from a body to its surroundings.
In theoretical constructions, Newton's law of cooling is used alongside Fourier's law to calculate the heat transfer coefficient. This is because the thermal conductivity of most materials is only weakly dependent on temperature, so the constant heat transfer coefficient condition is generally met. In heat conduction, Newton's law is followed as a consequence of Fourier's law.
Newton's law is particularly applicable in forced air and pumped liquid cooling, where the fluid velocity does not increase with rising temperature differences. In these cases, the heat transfer coefficient is independent or relatively independent of the temperature difference, and Newton's law is closely obeyed.
However, it is important to note that Newton's law of cooling has limitations. It does not hold for radiative heat transfer, and in natural convective (buoyancy-driven) heat transfer, the heat transfer coefficient is a function of the temperature difference. In this case, Newton's law only provides an approximation when the temperature difference is relatively small.
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Frequently asked questions
Newton's Law of Cooling is a physical law that states that the rate of heat loss of a body is directly proportional to the difference in temperature between the body and its environment.
Yes, Newton's Law of Cooling can be used for heating as well. It can be used to determine how quickly a cold object heats up. The law states that the temperature of a body changes at a rate proportional to the difference in temperature between the body and its surroundings.
Newton's Law of Cooling holds well for forced air and pumped liquid cooling, where the fluid velocity does not rise with increasing temperature difference. The law is most closely obeyed in purely conduction-type cooling. The law does not apply to thermal radiation and is only valid for small temperature differences.
