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All About the Heat Flux Equation

Key Takeaways

  • Heat flux is defined as the amount of heat energy transferred through a surface in a unit area in unit time. 

  • The heat flux density is measured in SI unit-Watts per square meter. 

  • The heat flux in a system is dependent on the temperature gradient and heat transfer coefficient.

Heat flux

Depending on the medium, heat transfer mechanisms are classified into conduction, convection, or radiation

The demand for energy encourages us to explore opportunities in renewable energy sources. Among non-conventional energy sources, solar energy is critical due to its abundance. Solar power is used for utility power generation as well as heating. Concentrated solar power plants meet today’s energy requirements. In the design of concentrated solar power plants, especially solar receivers, heat flux and temperature are two primary design parameters. Understanding heat flux aids in determining the efficiency of solar receivers.

In most thermodynamic applications, heat flux is a fundamental quantity of importance, as it influences efficiency and performance. Theoretically, the heat flux equation is utilized for calculating heat flux. However, in practicality, a range of calorimeters, gauges, and radiometers are used.

Let’s explore heat flux and its equations.

Heat Flow and Heat Transfer Mechanisms

In a given system, heat flows from one point to another only if there is a temperature difference between them. The heat flows from a warmer location to a colder location. Heat flow occurs only if there is a medium for the heat to travel between points with different temperatures.

The heat flow or heat transfer phenomenon is complex and multi-dimensional. Depending on the medium or the set of media where there is a temperature gradient, heat transfer mechanisms can be classified into:

  1. Conduction - In conduction, heat flow takes place through solid materials.

  2. Convection - When heat flows through gases and liquids, the heat transfer mechanism is called convection.

  3. Radiation - When electromagnetic waves carry heat energy, it forms the radiation mechanism of heat transfer.

In the above heat transfer mechanisms, heat is transferred from one point to another through a medium. The rate of heat energy transferred gives the idea of heat flux in conduction, convection, and radiation.

What Is Heat Flux?

Heat flux is the amount of heat energy transferred through a surface in a unit area in unit time. The heat flux can be the amount of heat transferred from or dissipated on the surface of consideration.  Heat flux is also known as thermal flux, heat flow density, heat flux density, or heat flow rate intensity.

Heat flux is evaluated based on two fundamental quantities:

  1. The amount of heat transfer per unit area (Q)

  2. The area where the heat transfer takes place (A)

 (Alt text:  Generalized heat flux equation)             

Since the heat flux is based on these two quantities, it is considered a derived quantity.

Unit of Heat Flux Density 

The amount of heat energy transferred, or the heat transfer rate, can be measured in Joule per second or Watt. Heat flux can be calculated as the heat transfer rate per unit area, otherwise known as the heat flux density. Heat flux density is measured in SI unit-Watts per square meter (W/m2).

The heat flux is a vector quantity with both magnitude and direction.

Factors Influencing Heat Flux

The heat flux in a system is dependent on:

  1. Temperature difference - The temperature difference or gradient is necessary for any heat transfer to take place. The heat flux shares a direct relationship with the temperature gradient. As the temperature gradient increases, the heat flux magnitude increases.

  2. Thermal transfer coefficient or heat transfer coefficient - The thermal transfer coefficient is introduced through Newton’s law of cooling. According to this law, the heat flux associated with a surface is linearly related to the temperature gradient. The proportionality constant linking heat flux and temperature gradient is called the heat transfer coefficient.

Heat Flux Equation

The heat flux equation can be obtained from the law of thermal conduction or the law of thermal conductivity, popularly known as Fourier’s law. The law is also referred to as the law of heat conduction.

According to Fourier’s law, the heat flux is directly proportional to the thermal or temperature gradient. Mathematically, the heat flux equation can be expressed as: 

Heat flux equation for conduction heat transfer

 q is the heat flux 

Q is the heat transfer rate 

A is the area of the cross-section of the surface 

T is the temperature gradient 

K is the heat transfer coefficient 

Heat Flux Equation for Convection and Radiation Heat Transfer

The heat flux equation for conduction heat transfer can be utilized for convection, provided the convective heat transfer coefficient is used in the place of constant K. To determine the heat flux in radiative heat transfer, the equation is given by the Stefan-Boltzmann law.

The heat flux equation for radiation heat transfer is:

Heat flux equation for radiation heat transfer

σ is the Stefan-Boltzmann constant 

ϵ is the emissivity

T is the temperature in (K)

The calculation of heat flux is crucial in chemical processes, thermodynamic systems, and the aviation industry, among other things. Cadence’s CFD solver can support multi-dimensional heat flux problems. With the proper CFD tools, solving complex problems involving heat flux equations is a breeze. 

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About the Author

With an industry-leading meshing approach and a robust host of solver and post-processing capabilities, Cadence Fidelity provides a comprehensive Computational Fluid Dynamics (CFD) workflow for applications including propulsion, aerodynamics, hydrodynamics, and combustion.

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