# Calculation of Heat Transfer Coefficient for Internal Flow

## Determination of Heat Transfer Coefficient for Internal Flow

### Laminar Flow

• The heat transfer rate for laminar flow can be calculated using the following equation:

Q =  A * h*ΔT

where

• Q is the heat transfer rate, k is the thermal conductivity of the fluid
•  A is the cross-sectional area of the pipe
• ΔT = (Ts  – Tref) is the mean temperature difference between the fluid and the pipe wall
• For laminar flow, the Nusselt number (Nu) can be calculated using the following equation:

Nu = 3.66

• Using the Nusselt number, the average heat transfer coefficient (h) can be calculated as:

h = (Nu * k) / h

where h is the hydraulic diameter of the pipe.

•  Once the average heat transfer coefficient (h) is known, the heat transfer rate (Q) can be calculated using the first equation mentioned above.
•  The assumption of laminar flow is only valid for low Reynolds numbers (less than 2300).

### Turbulent Flow

• The Dittus-Boelter equation is a widely used empirical equation that relates the average heat transfer coefficient for forced convection to the fluid properties, the flow conditions, and the geometric properties of the system.

• The equation for heat transfer coefficients  is given by:

h = Nu * k/d

where h is the average heat transfer coefficient, k is the thermal conductivity and D is the hydraulic diameter of the pipe or duct.

• The Reynolds number is defined as:

Re =ρ* V * D/ μ

where, ρ is the fluid density, V is the fluid velocity, D is the hydraulic diameter, and μ is the dynamic viscosity of the fluid.

• The Prandtl number is defined as:

Pr = μ*Cp / k

• where Cp is the specific heat at a constant pressure of the fluid.

### The assumption for Equations Dittus -Boelter equation

•  The Dittus – Boelter equation is valid for
• Fully developed for thermal and fluid flows
• Turbulent flow in a circular pipe, Reynolds numbers > 2300
• Constant Wall Temperature.
• However, it has been found to give reasonably accurate results for a wide range of geometries and flow conditions.

## Calculator For Internal Heat Transfer

### Validation with CFD Results

• The heat transfer from the experimntal correlations need to be comparedCFD Results for validation of any internal heat transfer problems as presented in the post.
• Difference up to 20% is acceptable depending on complexicity of case