Difference between Eckert number and Brinkmann Number

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This means that the Eckert number is a more comprehensive measure of the fluid's ability to transfer both kinetic and thermal energy, while the Brinkmann number focuses solely on the thermal energy transfer. In summary, the Eckert number and Brinkmann number are both measures of the fluid's ability to transfer energy, but the Eckert number takes into account both kinetic and thermal energy, while the Brinkmann number only considers thermal energy.
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Urmi Roy
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So I do know that Br (Brinkmann number)=Ec.Pr (Eckert times Prandtl number)

However, looking at the expressions for them,

Ec=(U^2)/(Cp*(Tw-Tinf))

Br=(μ*U^2)/(k*(Tw-Tinf))

So What does (μ*U^2) (numerator for Brinkmann number) signify? Also, for the denominator in the Ec, Cp*(Tw-T) seems to be maximum enthalpy stored in the fluid. However, in Br we have (k*(Tw-Tinf)) in the denominator...which is basically the same amount of energy being conducted in...So what is the difference?
 
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The numerator for the Brinkmann number, μ*U^2, is a measure of the kinetic energy of the fluid. The denominators for both the Eckert number and the Brinkmann number, Cp*(Tw-Tinf) and k*(Tw-Tinf), respectively, are measures of the thermal energy stored in the fluid, or the amount of energy being conducted in and out of the system. The difference between them is that the Eckert number takes into account the specific heat capacity of the fluid, while the Brinkmann number only takes into account the thermal conductivity.
 

1. What is the definition of Eckert number and Brinkmann Number?

Eckert number is a dimensionless parameter used to measure the ratio of kinetic energy to thermal energy in a fluid flow. Brinkmann number is a dimensionless parameter used to measure the ratio of viscous forces to thermal diffusion in a fluid flow.

2. How are Eckert number and Brinkmann Number calculated?

Eckert number (Ec) is calculated by dividing the kinetic energy per unit mass by the thermal energy per unit mass, while Brinkmann number (Br) is calculated by dividing the viscous force per unit volume by the thermal diffusion coefficient.

3. What is the significance of Eckert number and Brinkmann Number in fluid mechanics?

Eckert number and Brinkmann number are important parameters in fluid mechanics as they help to characterize the dominant mode of heat transfer in a fluid flow. A high Eckert number indicates that the flow is dominated by kinetic energy, while a high Brinkmann number indicates that the flow is dominated by viscous forces.

4. How do Eckert number and Brinkmann Number affect heat transfer in a fluid flow?

A high Eckert number leads to a higher rate of heat transfer in a fluid flow, as the kinetic energy of the flow is able to overcome thermal diffusion. On the other hand, a high Brinkmann number leads to a lower rate of heat transfer, as the viscous forces inhibit the flow of heat in the fluid.

5. What are some practical applications of Eckert number and Brinkmann Number?

Eckert number and Brinkmann number are commonly used in the design of heat exchangers, combustion systems, and other engineering applications involving fluid flow and heat transfer. They are also used in research studies to better understand the behavior of fluids in different scenarios.

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