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The Graetz number (Gr) is a dimensionless parameter used in fluid mechanics and heat transfer to characterize the thermal development length in a pipe or duct when there is heat transfer due to forced convection. The formula for the Graetz number depends on the specific context in which it is being used. In general, it is defined as the product of the Reynolds number (Re) and the Prandtl number (Pr) divided by the square of the pipe diameter (D). Mathematically, it can be expressed as: Graetz number (Gr)=Re⋅PrD2Graetz number (Gr)=D2Re⋅Pr​ Where:

• Re is the Reynolds number,
• Pr is the Prandtl number,
• D is the characteristic length scale of the flow (such as the diameter of the pipe).

The Graetz number is used to determine the extent of thermal development in a fluid flow, particularly in cases where there is a significant temperature difference along the length of the pipe or duct. It helps to predict how quickly the fluid reaches a fully developed temperature profile.