Compare convection coefficients for the water and air flow.xls

KNOWN: Long, 30mm-diameter cylinder with embedded electrical heater; power required to maintain a specified surface temperature for water and air flows.

FIND: Convection coefficients for the water and air flow convection processes.

ASSUMPTIONS: 1) Flow is cross-wise over cylinder which is very long in the direction normal to flow.

Calculation Reference
Fundamentals of Heat and Mass Transfer - Frank P. Incropera

To compare the convection coefficients for water and air flow over a long, 30mm-diameter cylinder with an embedded electrical heater, considering the power required to maintain a specified surface temperature, you can follow these steps:

1. Calculate the surface area of the cylinder: The surface area of a cylinder can be calculated using the formula:

   Surface Area = 2πrh + πr^2

   Where r is the radius of the cylinder (which is half of the diameter) and h is the length of the cylinder.

2. Calculate the heat transfer rate for water flow: Use the power required to maintain the specified surface temperature for water flow to calculate the heat transfer rate (Q_water):

   Q_water = Power / (T_surface_water - T_inlet_water)

   Where Power is the electrical power required, T_surface_water is the specified surface temperature for water flow, and T_inlet_water is the inlet temperature of the water flow.

3. Calculate the heat transfer rate for air flow: Use the power required to maintain the specified surface temperature for air flow to calculate the heat transfer rate (Q_air):

   Q_air = Power / (T_surface_air - T_inlet_air)

   Where Power is the electrical power required, T_surface_air is the specified surface temperature for air flow, and T_inlet_air is the inlet temperature of the air flow.

4. Calculate the convection coefficient for water flow: Divide the heat transfer rate for water flow by the surface area of the cylinder to obtain the convection coefficient for water flow (h_water):

   h_water = Q_water / Surface Area

5. Calculate the convection coefficient for air flow: Divide the heat transfer rate for air flow by the surface area of the cylinder to obtain the convection coefficient for air flow (h_air):

   h_air = Q_air / Surface Area

By following these steps, you can determine the convection coefficients for water flow and air flow over the cylinder based on the power required to maintain a specified surface temperature. The assumption that the flow is cross-wise over the cylinder, which is very long in the direction normal to the flow, allows for simplified analysis.