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In this article we will learn about Significance of Dimensionless Numbers in Heat Transfer. before moving toward main topic we will learn about what is Dimensionless Numbers? What are different type of Dimensionless number? So let’s begin our journey towards Dimensionless Numbers.

What is Mean by Dimensionless Numbers?
Dimensionless numbers in heat transfer is a set of dimensionless quantities which play important role in analyzing the behavior of transfer of heat. The important dimensionless Number in heat transfer are Fourier number and Biot number.

Significance of Dimensionless Numbers in Heat Transfer:

1) Dimensionless numbers allow for comparisons between very different systems.
Let's say you are designing a stirrer to get a syrup vat and you also would like to test a model. It might make sense to make a mini of this system but you understand that size makes a difference. Well if you decrease the viscosity of the liquid you are stirring, then you can make certain that the Reynolds number is exactly the same between the two procedures and will take your decisions out of the tiny and use them to the huge system.

2) Dimensionless numbers tell you how the system will behave.
The classic example of this yet again involves the Reynolds number to predict the onset of turbulence in a system. Critical values to the Reynolds number for many different systems are tabulated and so that you may readily forecast the onset of turbulence. Other examples include using the Rayleigh number to forecast if or not a fluid's heat transfer will occur largely through natural convection or via conduction. In the same way, the Péclet number will inform you whether transportation will take place via advection (busy convection) or diffusion.

3) To Determine the influence of particular parameter on the system.
A classic example is discovering the way the thermal boundary layer increases together with the speed of the stream. It ends up that you can utilize the Peclet number again to signify the stream and the border depth, δ scales as δ∼Pe−1/3. Given a couple of data dimensions you can easily extrapolate temperature gradients to a fluid.

4) Dimensionless Numbers help to find solution quickly and easy.
Many alternative techniques ask that you non-dimensionalize your problem before proceeding ahead since the option of scale matters.A Similarity alternative is possible only when you're able to map 1 scale onto a different (say a timescale on a length scale). Other methods for approximating solutions like Asymptotic analysis frequently ask questions about what occurs when a parameter is either very big or very little. These parameters are conveniently dimensionless numbers so one may compare many different situations at the same time.

5) To solve Problem numerically, dimensionless groups assist to scale the problem.
Computers can not deal with broad ranges of numbers particularly when incorporating little numbers to very large numbers. In numerical procedures, problems which have specific terms which are much bigger than others are believed to have a sizable Condition number and are therefore both hard to solve and hard to solve correctly. By increasing the problem to proper scales, it is possible to make many conditions be of the exact same order to ensure it that the ramifications of numerical errors are minimized when calculating the remaining.

Difference Types Dimensionless Numbers in Heat Transfer:

Many equation in heat transfer are totally based on dimensionless numbers, which are used to establish similitude among cases which might seem very different. significant dimensionless numbers in heat transfer course are discussed below.

1. Reynolds Number:
The Reynolds number is the ratio of inertia force to viscous force.

The Reynolds number is used to determine whether flow is laminar or turbulent.
2. Nusselt Number:
Nusselt number is  a ratio of convective heat transfer coefficient to conductance.

Where, ‘h’ is the convective heat transfer coefficient of the flow,
‘L’ is the characteristic length,
‘k’ is the thermal conductivity of the fluid.

3. Prandtl Number:
The Prandtl number is the ratio of momentum diffusivity to thermal diffusivity of a fluid:

Where, ‘v‘ is kinematic viscosity,
‘∝’ is thermal diffusibility,
‘μ’ is dynamic viscosity,
‘ρ’ is density,
‘k’ is thermal conductivity,
‘cp‘ is specific heat.

4. Grashof number:
Grashof number ratio between the buoyancy forces and viscous forces. The Grashof number is used to determine the heat transfer coefficient under free convection conditions.

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