# Graetz Number

on . Posted in Dimensionless Numbers

Graetz number, abbreviated as Ga, a dimensionless number, also known as the Graetz ratio or Graetz problem parameter, that characterizes laminar flow with heat transfer in a conduit.  This number is used to determine the thermal development on the entrance to ducts.  A Graetz number of 1000 and below is usually where a flow is considered thermally developed.  The Graetz number describes the relative significance of convective heat transfer and conductive heat transfer in the flow.  It indicates the extent to which the fluid flow influences the heat transfer process.  A high Graetz number indicates that convection dominates over conduction, while a low Graetz number suggests that conduction is more significant.

In practical applications, the Graetz number is commonly used to analyze and design heat exchangers, where heat is transferred between two fluids separated by a solid wall.  It helps engineers assess the efficiency and performance of the heat exchanger and determine the appropriate design parameters for optimal heat transfer.

## Graetz number formula

$$\large{ Gz = \frac {D_h}{l} \; Re \;Pr }$$     (Graetz Number)

$$\large{ D_h = \frac{ Gz \; l }{ Re \; Pr } }$$

$$\large{ l = \frac{ D_h }{ Gz \; Re \; Pr } }$$

$$\large{ Re = \frac{ Gz }{ \frac{ D_h }{ l \; Pr } } }$$

$$\large{ Pr = \frac{ Gz }{ \frac{ D_h }{ l } \; Re } }$$

### Solve for Gz

 hydraulic diameter, Dh length of the pipe, l Reynolds number, Re Prandtl number, Pr

### Solve for Dh

 Graetz number, Gz length of the pipe, l Reynolds number, Re Prandtl number, Pr

### Solve for l

 hydraulic diameter, Dh Graetz number, Gz Reynolds number, Re Prandtl number, Pr

### Solve for Re

 Graetz number, Gz hydraulic diameter, Dh length of the pipe, l Prandtl number, Pr

### Solve for Pr

 Graetz number, Gz hydraulic diameter , Dh length of the pipe, l Reynolds number, Re

Symbol English Metric
$$\large{ Gz }$$ = Graetz number $$\large{dimensionless}$$
$$\large{ D_h }$$ = hydraulic diameter of the pipe $$\large{ft}$$ $$\large{m}$$
$$\large{ l }$$ = length of the pipe $$\large{ft}$$ $$\large{m}$$
$$\large{ Re }$$ = Reynolds number $$\large{dimensionless}$$
$$\large{ Pr }$$ = Prandtl number $$\large{dimensionless}$$ 