Heat Flux Formula: Definition, Heat Flow Rate, Heat Transfer

‘Heat Flux’ – is a basic concept of thermodynamics. Heat flux is referred to as the amount of heat transferred per unit area per unit time to or from a surface. Meaning, it is basically a derived quantity since it involves the principle of two quantities viz. Heat Flux can simply be defined as Heat Transfer. The idea was first established back in 1822, by Joseph Fourier- a famous French mathematician and physicist, when he published his classic work “The Analytical Theory of Heat”. He is the one who established the Law of Heat Transfer- the ‘Fourier’s Law’.

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What is Heat Flux?

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Let me explain this with an example. Suppose you are enjoying a bonfire on a cold winter evening and your hands are freezing, what will you do? You will inevitably hold your hands out near the fire, right? This will help you warm your hands up. But have you ever wondered why and how does this happens?

The reason behind this my friend is the basic concept of heat transfer. Heat is the energy that transfers from one element or system to another. Hence, Heat Flux can be defined as –“the amount of heat transferred per unit area per unit time to or from a surface”.

Suppose, heat is transferring through a material of constant temperature, and at one side of the material, the temperature is higher than the other side; then through the process of transmission of heat, the material itself will try to balance the temperature.

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Different Ways of Heat Transfer

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Hopefully, we have understood the basic concept of heat flux or heat transfer by now. But have you wondered how the heat transfer takes place! Well, there are three ways of heat transfer-

1. Conduction
2. Convection
3. Radiation

Let’s discuss these methods in detail:

Conduction:

Definition: “The process in which heat flows from objects with higher temperature to objects with lower temperature.”

Real-Life Example: We all can observe this process while ironing our clothes. When we begin the process, the clothes, the surface of the iron machine, and the clothes represent different temperatures right? But, while ironing the temperature of the clothes somehow rises. That happens because of this process.

Equation: The conduction rate can be measured through-

Q = KA { T (hot) – T (cold) }/ d

Where,

Q = the transfer of heat per unit time

K = the thermal conductivity of the body

A = the area of heat transfer

T (hot) = the temperature of the hot region

T (cold) =the temperature of the cold region

d =the thickness of the body

Convection:

Definition: “The movement of fluid molecules from higher temperature regions to lower temperature regions.”

Real-Life Example: We can observe a perfect example of this process when we try to boil the water. The heat will be transferred through the molecules.

Equation: The convection rate can be measured through-

Q = hc A(Ts – Tf)

Where,

Q = the heat transferred per unit time

Hc = the coefficient of convective heat transfer

A = the area of heat transfer

Ts = the surface temperature

Tf = the fluid temperature

Radiation:

Definition: “Radiation heat transfer is a process where heatwaves are emitted that may be absorbed, reflected, or transmitted through a colder body. Sun heats the earth by electromagnetic waves”.

Real-Life Example: As we know, the Ultra Violet ray comes from the sun. This is an absolute example of the Radiation process.

Equation: The radiation rate can be measured through-

P =σeAT4 Q t = σ e A T 4

Where,

P = the net power of radiation

A = the area of radiation

Tr = the radiator temperature

Tc = the surrounding temperature

e = emissivity

σ = Stefan’s constant

But how will you measure the amount of heat that is being transferred from one surface to another? That’s where the Heat Flux Formula comes to our rescue.

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Heat Flux Formula

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Heat Flux can be represented as where the q represents heat flux. As per SI, heat flux density can be measured as Watts per meter square, i.e. (W/m 2). This is a vector quantity that includes magnitude and direction.

Therefore, the heat flux formula is – Фq = - k dT(x)/ dx

Where, Фq = heat flux

k = thermal conductivity

T = temperature

Fourier’s Law

“The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area, at right angles to that gradient, through which the heat flows.”

Hence, this law can be expressed as: 

\(JH_c = \lambda \frac{dT}{dZ}\)

Where,

JH_c =

conductive heat flux

T = temperature

λ = thermal conductivity constant

Heat Flow Rate Formula

The Heat Flow Rate can be defined as the amount of heat that is being transferred in the material as per the unit amount of time. This can be measured through the formula mentioned below-

\(Q = -k(\frac {A}{l}) (\Delta T)\)

Where,

Q= the transferred heat per unit

k = the thermal conductivity

A =the cross-sectional area

l = the length of the material

and ΔT= the temperature difference

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Things to Remember

• The idea was first established back in 1822, by Joseph Fourier.
• Heat Flux can be defined as –“the amount of heat transferred per unit area per unit time to or from a surface”.
• Conduction: “The process in which heat flows from objects with higher temperature to objects with lower temperature.”
• The conduction rate can be measured through- Q = KA { T (hot) – T (cold) }/ d
• Convection: “The movement of fluid molecules from higher temperature regions to lower temperature regions.”
• The convection rate can be measured through- Q = hc A(Ts – Tf)
•  Radiation: “Radiation heat transfer is a process where heatwaves are emitted that may be absorbed, reflected, or transmitted through a colder body. Sun heats the earth by electromagnetic waves”.
• The radiation rate can be measured through- P = σeAT4 Q t = σ e A T 4
• Heat Flux Formula: Фq = - k dT(x)/ dx
• Fourier’s Law: “The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and the area, at right angles to that gradient, through which the heat flows.”
• Fourier's Law can be expressed as-\(JH_c = \lambda \frac{dT}{dZ}\)
• Heat Flow Rate Formula:\(Q = -k(\frac {A}{l}) (\Delta T)\)

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