# Unsteady State Heat Transfer: Formula and Applications

By Deepak Yadav|Updated : January 23rd, 2023

Unsteady State Heat Transfer refers to the heat transfer process in which a system's temperature changes with time. This is in contrast to steady-state heat transfer, in which the temperature of a system remains constant over time. Unsteady state heat transfer can occur in various systems, including solid materials, fluids, and gases.

In unsteady state heat transfer, the heat transfer rate is dependent on the rate of temperature change. This can lead to complex behaviour and be challenging to model and predict. However, understanding unsteady state heat transfer is important in a wide range of applications, such as in the design of thermal systems and in the study of heat transfer in natural systems such as oceans and the atmosphere.

## What is Unsteady State Heat Transfer?

Unsteady state heat transfer refers to the process in which the temperature of a system or an object changes as a function of time. This is in contrast to steady-state heat transfer, in which the system's or object's temperature remains constant over time. This type of heat transfer can happen in different forms, such as conduction, convection, and radiation. It occurs in various systems, including solid materials, fluids, and gases. The heat transfer rate in an unsteady state is directly proportional to the rate of temperature change. This means that the heat transfer rate is not constant and can vary over time. It's an important aspect in the design and optimization of thermal systems, and understanding this process is crucial in many research areas, such as combustion, electronics, and aerospace.

## Types of Unsteady State Heat Transfer

There are three main types of unsteady state heat transfer:

1. One-dimensional heat conduction: This type of heat transfer occurs in materials where heat is transferred in only one direction. An example of this would be heat transfer through a metal rod.
2. Transient convection: This heat transfer occurs in fluids, such as liquids and gases, and is characterized by the movement of the fluid and the associated heat transfer. An example of transient convection would be heat transfer in a fluid flowing through a pipe.
3. Radiative heat transfer: This heat transfer occurs through the emission and absorption of electromagnetic radiation. An example of this would be heat transfer through a window.

Additionally, it's also possible to have a combination of these types of heat transfer in a system, for example, conduction through a solid material and convection through a fluid, known as "unsteady state conduction-convection heat transfer".

## Unsteady State Heat Transfer Formula

The formula for the unsteady state heat transfer equation is given by:

ΔQ/Δt = hA(Ts - T) + mcΔT

where:

• ΔQ/Δt = rate of heat transfer
• h = heat transfer coefficient
• A = surface area
• Ts = surface temperature
• T = ambient temperature
• m = mass flow rate
• c = specific heat
• ΔT = change in temperature.

This equation calculates the heat transfer rate in a system where the temperature changes over time.

## Applications of Unsteady State Heat Transfer

Unsteady state heat transfer has a wide range of applications, including:

1. Industrial processes commonly design heat exchangers, boilers, and reactors.
2. Automotive engineering: It is used to analyse cooling systems in automobiles, which are typically subjected to rapid changes in temperature and flow conditions.
3. Aerospace engineering analyses the thermal performance of aerospace vehicles such as missiles and spacecraft operating in rapidly changing environments.
4. Energy systems: It is used to model the performance of solar thermal, geothermal, and other renewable energy systems subject to changing temperature and flow conditions.
5. Building heating and cooling: It is used to model the performance of heating, ventilation, and air conditioning (HVAC) systems in buildings, which are typically subject to changing temperature and flow conditions.
6. Food processing: It is used in the food processing industry to model the heat transfer during the cooking, drying and freezing processes.
7. Biomedical Engineering: It is used to analyse temperature changes in the human body during medical procedures such as hyperthermia treatment for cancer.

## Limitations of Unsteady State Heat Transfer

There are several limitations of unsteady state heat transfer, including:

1. Complexity: Unsteady-state heat transfer problems are generally more complex than steady-state problems due to the need to track the changing temperature and flow conditions over time.
2. Solution methods: A limited number of analytical solutions are available for unsteady state heat transfer problems, and most problems require numerical solution methods.
3. Data requirements: Unsteady-state heat transfer problems typically require more detailed information about the initial and boundary conditions than steady-state problems.
4. Time-dependent: The heat transfer rate, temperature, and other parameters change with time, so it requires more data points to model the system accurately.
5. Difficulties in measuring: Measuring the unsteady heat transfer coefficient and other parameters is difficult, and it requires specialized techniques.
6. Modelling assumptions: Some unsteady state heat transfer problems may require simplifying assumptions, such as lumped system analysis, which may not be valid for all situations.
7. Thermal mass effect: The thermal mass effect, which is the ability of an object to store thermal energy, can cause delays in temperature changes in some cases.
 Important GATE Notes Open Channel Flow Free Convection First Law of Thermodynamics Helical Gear Triangle Law of Forces Connecting Rod Types of Support Constant Acceleration Mechanical Energy Constant Velocity

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• Unsteady state heat conduction refers to the transfer of heat through a solid material due to a temperature difference, while unsteady state heat convection refers to the transfer of heat through a fluid due to a temperature difference between the fluid and the surrounding surfaces.

• Like steady state heat transfer, the thermal mass effect refers to the ability of an object to store thermal energy, which can cause delays in temperature changes in unsteady state heat transfer. For example, a large thermal mass can absorb heat before the object's temperature rises.

• Unsteady state heat transfer is affected by changes in the flow rate because the heat transfer rate can be directly related to the mass flow rate of the fluid. An increase in flow rate will increase the heat transfer rate, while a decrease in flow rate will decrease the heat transfer rate.

• The heat transfer coefficient can vary with time in unsteady state heat transfer, depending on the conditions of the system. For example, the heat transfer coefficient will also change if the fluid's flow rate or temperature changes.

• Choosing boundary conditions is important in unsteady state heat transfer problems because it determines the system's boundaries' initial and final temperatures and heat fluxes. For example, if the system is insulated, the boundary conditions will be different than if the system is in contact with a heat source or sink.

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