2. Determine the heat transfer coefficient and the linear heat flux in the transverse air flow for a pipe with a diameter of d=25 mm, if its surface temperature is t_(s)= 80^circ C the air temperature is t_(a)=-15^circ C and the wind speed is w=9m/s

To determine the heat transfer coefficient and the linear heat flux in the transverse airflow for a pipe, we can use the Dittus-Boelter equation, which is a commonly used empirical correlation for convective heat transfer. The Dittus-Boelter equation is given by: where:- is the heat transfer coefficient,- is the Reynolds number,- is the Prandtl number,- is the specific heat capacity of the fluid,- is the dynamic viscosity of the fluid,- is the diameter of the pipe.First, we need to calculate the Reynolds number ( ) and the Prandtl number ( ).The Reynolds number is given by: where:- is the wind speed,- is the diameter of the pipe,- is the kinematic viscosity of the fluid.The Prandtl number is given by: where:- is the specific heat capacity of the fluid,- is the dynamic viscosity of the fluid,- is the thermal conductivity of the fluid.Given:- mm = 0.025 m,- ,- ,- m/s.Assuming air as the fluid, we can find the properties at the film temperature ( ) which is approximately the average of and : Using standard air properties at :- J/(kg·K),- Pa·s,- m²/s,- W/(m·K).Now, calculate : Next, calculate : Now, substitute these values into the Dittus-Boelter equation: Calculate each term: \[ h \approx 0.023 \cdot 1.34 \times 10^4 \cdot 0.45 \cdot 7.92 \times 10