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# Heat Flux Formula

Heat flux is the rate of thermal energy flow per unit surface area of the heat transfer surface, e.g, in a heat exchanger. The main parameter while calculating heat transfer is heat flux. There are 3 types of generalized classification is there that helps to distinguish between heat fluxes by convection, heat conduction, and radiation. We will further study the types of Heat Flux and the heat flux formula.

## What is Heat Flux?

Heat flux also named as thermal flux, is referred to as heat flux density, heat-flow density is a flow of energy per unit of area per unit of time. In SI its units are watts per square meter $$\left (\frac{W}{m^{2}} \right)$$. As heat flux has both a direction and a magnitude, and so it is a vector quantity.

Heat flux by the convection process is directly proportional to the temperature difference between solid, liquid, or gaseous media participating in heat transfer. Under the conduction process, the heat flux vector is directly proportional to and usually parallel to the temperature gradient vector. The heat flux formation due to radiation is a flux of electromagnetic radiation. In contrast to convection and heat conduction, it may occur without any intervening medium.

Source: en.wikipedia.org

### What is the formula for Heat Flux?

Joule per second or watt is the SI unit of heat rate. Heat flux density is the heat rate per unit area. In SI units, the heat flux density is measured in $$\frac{W}{m^{2}}.$$

Fourierâ€™s law and its application are very important regarding Heat flux. For a pure solid substance, the conductive heat flux JHc in one dimension is expressed by Fourierâ€™s law.

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

Where, $$JH_{c}$$ is conductive heat flux. T is temperature, $$\lambda$$ is thermal conductivity constant.

### Methods:

We can measure heat flux mainly by the following two methods:

1. The most common but often impractical, the method is by measuring a temperature difference over a piece of material with known thermal conductivity. This method is not proper and very difficult to perform since the thermal resistance of the material being tested is often not known.
2. The second most accurate method of measuring heat flux is by using a heat flux sensor, or heat flux transducer. It measures the amount of heat being transferred to/from the surface that the heat flux sensor is mounted to. A common type of heat flux sensor is a differential temperature thermopile. This method of thermal resistance/conductivity does not need a known parameter.

### Application:

The Heat flux value has many applications. It helps to evaluate heat transfer performance in many industrial applications, such as thermal protection of space shuttles, thermal management of electronic devices, metal heat treatment, maintenance of boilers, and nuclear reactors, spray cooling, geophysics, etc.

## Solved Examples forÂ Heat Flux Formula

Q.1. A 15 x 20 cm circuit board holds 120 closely spaced logic chips, each dissipating 0.12W. If the heat transfer from the back surface of the board is negligible, determine usingÂ Heat Flux Formula:

1. In 10 hours, how much amount of heat this board dissipates.
2. The heat flux on the surface of the board in $$\frac{W}{m^{2}}.$$

Ans- We can calculate Heat flux from the equation, $$\dot{q}= \frac{Q}{A}.$$

where Q is the heat transfer rate, A is the cross-sectional through which the heat transfer is taking place, $$\dot{q}$$ is the heat flux.

Area of the board, $$A= 0.15 \ast .2= .03m^{2}$$

Heat dissipated by each chip = 0.12 W

Total count of chips on the circuit board = 120

Heat dissipated by all chips on the circuit board, $$Q= 120\ast 0.12= 14.4 W$$

Heat dissipated in $$10 hours = 14.4 \ast 3600 \ast 10 = 518,400 J = 518.4 kJ$$

Thus, Heat flux on the surface of the board,

$$\dot{q}= \frac{14.4}{0.03}= 480 \frac{W}{m^{2}}$$

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