#### GATE Notes-Internal Convection Fully Developed Flow

# GATE Notes-Internal Convection Fully Developed Flow

**Laminar Flow in Circular Tube: Analytical**

- Local Nusselt number is constant in fully developed region and depends on surface thermal condition
- For constant heat flux,
- For constant surface temperature,

**Turbulent Flow in a Circular Tube: Empirical**

- Smooth surface and fully turbulent flow: (): Dittius-Boelter Correlation ,
- Rough surface and transitional turbulent flow: (): Gnielinski Correlation Smooth surface:

**Non-Circular Tubes:**

- Use hydraulic diameter as the characteristic length:
- Since the local convection coefficient varies around the periphery of a tube, approaching zero at its corners, correlations for the fully developed are associated with convection coefficients averaged over the periphery of the duct.
**Laminar Flow:**Local Nusselt number is constant but a function of duct geometry and surface thermal condition.**Turbulent Flow:**use Dittius-Boetler correlation or Gnielinski correlation as a first approximation for any surface thermal condition.- The manner in which the Nusselt number decays from the inlet to fully developed conditions for laminar flow depends on the nature of thermal and velocity boundary layer development in the entry region, as well as the surface thermal condition.
- It affects the average Nusselt number across the length of the tube.

For all internal flows, the effect of variable properties of the average Nusselt number may be considered by evaluating all properties at average mean temperature,

**Concentric Tube Annulus:**

- Fluid flow through region formed by concentric tubes.
- Convection heat transfer may be from or to: (a) inner surface of outer tube, (b) outer surface of inner tube.
- Standard surface thermal conditions (uniform temperature or heat flux) are typically considered.