# Using Prandtl Number to Assess Heat Transfer Fluid Options

The Prandtl number (Pr) is a dimensionless parameter that puts the viscosity of a fluid in correlation with its thermal conductivity. It shows the relationship between momentum transport (viscous diffusion rate) and thermal transport capacity (thermal diffusion rate) of a fluid. It can be used to compare the performance of heat transfer fluids for a particular application when engineers are considering multiple fluid options. In this article, we explore Prandtl Number (Pr) from theoretical and practical perspectives.

Prandtl Number (Pr) is defined as follows:

μ = dynamic viscosity

Cp = Specific Heat of the fluid taken into consideration

k = Thermal Conductivity of the fluid

ν = Kinematic viscosity

α = Thermal diffusivity

ρ = Density of the fluid

Prandtl number (Pr) is independent of length. It depends upon the property, type and state of a heat transfer fluid.

##### Practical significance of Prandtl Number

In Fluid Mechanics and Thermodynamics, boundary layer theory is often used to describe the mechanism of heat transfer in fluids. Let us consider the heat transfer that occurs between a wall and a flowing fluid as seen in a typical heat exchanger. Heat is transported from the bulk of a fluid through a momentum boundary layer and a thermal boundary layer. The momentum boundary layer consists of the bulk fluid and a transition layer in which heat is transported via convection. The thermal boundary layer consists of stagnant film in which heat transport occurs by fluid conduction. The Prandtl number (Pr) of a fluid gives the relative importance of the momentum boundary layer to the thermal boundary layer in the transfer of heat.

When Prandtl number (Pr) has low values, (for instance, Pr << 1), it represents that thermal diffusivity dominates over momentum diffusivity. Similarly, for large values of Prandtl number, (Pr >> 1), the momentum diffusivity dominates over thermal diffusivity. If you consider the physical properties of most organic heat transfer fluids, momentum diffusivity is the significant parameter. For gases, the Prandtl number (Pr) is about 1. Thermal boundary layer has equal thickness relative to velocity boundary layer.

As viscosity increases, Prandtl number (Pr) increases and thus heat conduction capacity of a thermal fluid decreases. When compared to water or air, heat transfer oils have higher Prandtl number (Pr). Therefore, they possess poorer heat transport characteristics comparatively . In other words, the thermal boundary layer has lower thickness relative to velocity boundary layer in this case. However, heat transfer oils have other desirable properties that air, and water do not have, making them a necessity in many industrial applications. Such properties include high temperature capabilities/stability and low pour points/low temperature pumpability. That said, Engineers are often faced with multiple heat transfer fluid choices and the Prandtl Number (Pr) can be used to determine an optimal fluid choice amongst other parameters.

##### Summary

Prandtl number signifies the thickness of thermal boundary layer and thickness of hydrodyanamic boundary layer i.e the ratio of momentum diffusivity to thermal diffusivity. It can be equal to one, more than one or less than one. If it is equal to one, it signifies that thickness of thermal boundary layer is equal to that of velocity boundary layer. If Pr is less than one, it tells us that thermal diffusion is dominant in comparison to momentum diffusion and vice versa.

For a given fluid flow scenario, the flow conditions remaining the same, if a higher heat transfer rate is desirable, it is advisable to choose a heat transfer fluid that has a lower Prandtl number. If you have any questions regarding the optimal heat transfer fluid to select for your application, the Thermal Fluid Engineers at Relatherm Heat Transfer Fluids are always ready to help. Give us a call anytime.