Heat Transfer Coefficient in Turbulent Flow in Pipe

In turbulent flow, the heat transfer coefficient can be obtained from the Dittus-Boelter equation. The Dittus-Boelter equation is widely used to calculate the heat transfer coefficient for turbulent flow in pipes. It relates the heat transfer coefficient (h) to the fluid flow rate (m_dot), fluid properties (such as density and viscosity), and the inner diameter of the pipe (D).

The Dittus-Boelter Equation:
The Dittus-Boelter equation is given as follows:
h = (0.023 * Re^0.8) * (Pr^0.4) * (k/D)

Where:
h is the heat transfer coefficient,
Re is the Reynolds number,
Pr is the Prandtl number,
k is the thermal conductivity of the fluid, and
D is the inner diameter of the pipe.

The Reynolds number (Re) is a dimensionless quantity that characterizes the flow regime in a pipe. It is defined as the ratio of inertial forces to viscous forces and is given by the equation:
Re = (m_dot * D) / μ

Where:
m_dot is the fluid mass flow rate, and
μ is the dynamic viscosity of the fluid.

Effect of Halving the Tube Diameter:
If the tube diameter is halved, the Reynolds number of the flow will increase. This is because the Reynolds number is directly proportional to the fluid velocity, which in turn is inversely proportional to the cross-sectional area of the pipe. As the pipe diameter decreases, the fluid velocity increases, resulting in a higher Reynolds number.

Effect of Doubling the Flow Rate:
If the flow rate is doubled, the Reynolds number will also increase. This is because the Reynolds number is directly proportional to the fluid velocity, which is determined by the flow rate and the cross-sectional area of the pipe. Increasing the flow rate will increase the velocity and consequently, the Reynolds number.

Overall Effect on the Heat Transfer Coefficient:
Both halving the tube diameter and doubling the flow rate will increase the Reynolds number. According to the Dittus-Boelter equation, the heat transfer coefficient is directly proportional to the Reynolds number raised to the power of 0.8. Therefore, doubling the Reynolds number will increase the heat transfer coefficient.

Conclusion:
When the tube diameter is halved and the flow rate is doubled in turbulent flow in a pipe, the heat transfer coefficient will increase by a factor of approximately 1.68. This is because both changes result in an increase in the Reynolds number, which in turn increases the heat transfer coefficient according to the Dittus-Boelter equation.