Heat Conduction Through Slab

The applications of heat conduction through a slab and walls have significantly helped in recent development in technology. It can also be seen as an important phenomenon that allows the formulation and carrying out of thermal simulation. Although several factors influence the accuracy, it is important to understand the method’s efficiency to calculate the flow of heat.

Heat Conduction Through Slab

Let us now understand the heat conduction through slab with reference to our subject matter. As we know, the rate of heat transfer depends on the properties of the material that are defined in terms of coefficient of thermal conductivity. The included factors are often summarised in a simple equation generally deduced from experiments. 

However, on a microscopic scale, heat transfer takes place quickly through vibrating and moving atoms and molecules that come in contact with the nearby particles, which results in the transfer of some of their kinetic energy. The differential approach for the applications of heat conduction is one of the ways to represent numerical solutions. These are more relevant for cases where heat conduction takes place through slabs. 

The electrical analogy of heat conduction

The conduction of heat in the case of solids is quite identical to the conduction of electricity in the case of electrical conductors. In the case of conductors, the potential difference is mainly responsible for driving the flow of electricity. The same analogy applies in the case of the flow of heat, which is significantly driven by the difference in temperature.

 In electric conduction, the motion of electrons enables the electric charge to transport from one point in a conductor to the other. Moreover, heat is transported from one solid to another due to the vibration of molecules and increased energy in the case of thermal conduction. In such cases, heat conduction is regulated by Fourier’s law. 

The law implies that the heat transfer rate (Q) between two points in a medium is proportional to the difference in temperature between 2 points (T1-T2) divided by the separation (∆x) and area normal to the heat flow direction (A). 

Mathematically, it is expressed as Q = kA ( T1 – T2 )/Δx

Here, Q = heat transfer rate and k = material’s thermal conductivity.

Conduction of heat through a finite one layer slab

The first possible case in heat conduction through slab can be applicable on one layer slab. In this case, several arbitrary constants are kept for the calculation. Here, only the sample values and their discrete-time instance are applied rather than the analytical temperature function. 

Conduction of heat through semi finite 1-layer slabs

The equation Q = kA ( T1 – T2 )/Δx can also be applied to heat conduction use cases in semifinite regions. However, it is important to ensure that the solutions are bounded as x applies to infinity. As a result, any possible hyperbolic function will be reduced to exponential functions. 

While these are closely associated with the modified functions of the first category, modified functions of the third category can also be used to describe the exponential functions.

Conduction of heat through multilayer slabs

The relationship between the rate of heat flows and temperature on both sides of the wall are described by two-port parameters that act as transfer functions. These parameters are responsible for the slab being a region where only the inputs and outputs can be accessed. 

However, using two-port parameters is an easy way to represent the transfer functions, especially in the case of multi-layer walls. Thus, it is important to ensure that transfer of heat through multi-layer slabs is computed using the right method.

Conclusion

In conclusion, we can say that heat conduction through a slab is one of the generally known methods of conduction of heat. In this process, the generated heat is transferred equally towards both sides of the slab as it covers a distance, usually denoted by x. This quantity is measured from the centre of the slab along the x-direction. During the entire process, the temperature on both sides of the slab remains constant and is represented by T1 while the same amount of heat flows towards different sides of the slab from the centre.