Compare convection coefficients for the water and air flow.xls
Description
KNOWN: Long, 30mmdiameter 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 crosswise 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, 30mmdiameter cylinder with an embedded electrical heater, considering the power required to maintain a specified surface temperature, you can follow these steps:

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.

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.

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.

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

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 crosswise over the cylinder, which is very long in the direction normal to the flow, allows for simplified analysis.
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