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What is the importance of graetz number in heat transfer

What is the importance of Graetz number in heat transfer?




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The Graetz number (Gz) is a dimensionless number that plays a crucial role in analyzing laminar flow heat transfer in ducts and pipes, especially when the flow is developing thermally. It essentially represents the ratio of the heat transfer rate by convection to the heat transfer rate by axial conduction.

Its importance stems from its ability to characterize the thermal entry length and predict the temperature profile development within a fluid flowing through a conduit.

Here's a breakdown of its significance:

  1. Indication of Thermal Development:

    • Large Graetz Number (Gz1): This indicates that convective heat transfer dominates over axial conduction. The fluid has not yet reached a fully developed thermal profile. In this thermal entry region, the temperature profile is still changing significantly along the length of the duct. This is common in situations with high flow rates, short ducts, or fluids with low thermal conductivity.
    • Small Graetz Number (Gz1): This suggests that axial conduction becomes significant, and the fluid has likely reached a thermally fully developed region. In this region, the dimensionless temperature profile no longer changes with axial distance. The heat transfer coefficient becomes constant.
    • Intermediate Graetz Number (Gz1): Both convection and axial conduction are comparable in importance.
  2. Predicting Heat Transfer Performance:

    • The Graetz number helps engineers determine whether a heat exchanger or pipe system is operating in a thermally developing or fully developed regime. This distinction is critical because the heat transfer coefficient is generally higher in the entry region than in the fully developed region.
    • For example, in compact heat exchangers where laminar flow is common and short passages are used, the flow is often thermally developing, and the Graetz number is essential for accurately predicting heat transfer rates.
  3. Design and Optimization of Heat Exchangers:

    • Mechanical engineers use the Graetz number to design and optimize heat exchange equipment. By understanding the thermal development, they can determine the optimal length of a heat transfer section, select appropriate flow rates, and ensure efficient energy transfer.
    • It helps in determining if increasing the length of a heat exchanger will actually lead to a proportional increase in heat transfer (less effective in fully developed flow) or if other methods (like increasing surface area or flow rate) would be more beneficial.
  4. Relationship with Other Dimensionless Numbers:

    The Graetz number is related to other important dimensionless numbers:

    Gz=L/DRe⋅Pr​=L/D(ρvD/μ)⋅(cp​μ/k)​=kLρvD2cp​​

    Where:

    • Re is the Reynolds number (indicates flow regime).
    • Pr is the Prandtl number (ratio of momentum diffusivity to thermal diffusivity).
    • L is the length of the duct.
    • D is the hydraulic diameter of the duct.
    • ρ is density, v is velocity, μ is dynamic viscosity, cp is specific heat capacity, k is thermal conductivity.

    This relationship highlights how fluid properties, flow conditions, and geometric dimensions collectively influence the thermal development of the flow.

In essence, the Graetz number is a fundamental tool for understanding and quantifying the interplay between convection and conduction in laminar internal flows, which is vital for the accurate design and analysis of various heat transfer systems in mechanical and chemical engineering.


Answered By

ortan

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