# Heat Flux Formula

## Heat Flux

Heat flux is the amount of heat transferred per unit area per unit time to or from a surface. Basically, it is a derived quantity since it involves the principle of two quantities viz. the amount of heat transfer per unit time and the area to or from which the heat transfer occurs.

The derived SI unit of heat rate is joule per second or watt. Heat flux density describes the heat rate per unit area. In SI unit of heat flux density is measured in Watts per meter square (W/m2). Heat flux is a vector quantity that has both magnitude and direction.

Fourier’s law is an important application of these concepts. For a pure solid substance, the conductive heat flux JHc in one dimension is expressed by Fourier’s law.

 $$JH_{c}=\lambda \frac{dT}{dZ}$$

Where,

• JHc = conductive heat flux
• T = temperature
• λ = thermal conductivity constant

## Heat Flow Rate Formula

The heat flow rate is defined as the amount of heat transferred per unit time in the material. The heat flow rate in a rod depends on the cross-sectional area of the rod, the temperature difference between both the ends and the length of the rod. Following is the formula used to calculate the heat flow rate of any material:

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

Where,

• Q is the heat transfer per unit time
• k is the thermal conductivity
• A is the cross-sectional area
• l is the length of the material
• ∆T is the temperature difference

### Solved Example

Example 1

One face of a copper plate is 5 cm thick and maintained at 500C, and the other face is maintained at 100C. Calculate the heat transferred through the plate.

Solution:

Given parameters are,
coefficient of thermal conductivity of copper, λ = 385,
dT = 500 – 100= 400
dx = 5

Substitute the values in the given formula
JHc = λ dT / dZ
JHc= 385 x 400 / 5
JHc = 30,800 MW

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