A long cylinder of 0.1-m-diameter has a surface temperature of 400 K. If it is immersed in a fluid at 350 K, natural convection will occur as a result of the temperature difference. Calculate the Grashof and Rayleigh numbers that will determine the Nusselt number if the fluid is
(a) Nitrogen
(b) Air
(c) Water
(d) Oil
(e) Mercury
GIVEN
• A long cylinder immersed in fluid
• Diameter (D) = 0.1 m
• Surface temperature (Ts) = 400 K
• Fluid temperature (T?) = 350 K
FIND
The Grashof number (Gr) and the Rayleigh number (Ra) if the fluid is
(a) Nitrogen (b) Air (c) Water (d) Oil (e) Mercury
ASSUMPTIONS
• The cylinder is in a horizontal position (the characteristic length is the diameter of the cylinder)
SKETCH
PROPERTIES AND CONSTANTS
The thermal expansion coefficients for oil and mercury can be estimated from
The Grashof number based on the cylinder diameter is
For nitrogen
The Rayleigh number is defined as
Calculating the GrD and RaD in a similar manner for the other fluids
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