Natural convection heat transfer coefficients over surface of a vertical pipe and vertical flat plate for same height and fluid are equal. What is/are the possible reasons for this?
1. Some height
2. Both vertical
3. Same fluid
4. Same fluid flow pattern
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Concept:

In convection studies, it is common practice to non dimensionalize the governing equations and combine the variables which group together into dimensionless numbers in order to reduce the number of total variables.

Nusselt number is a parameter to non dimensionalize the heat transfer coefficient.

Non-dimensional groupings

• Nusselt No. Nu = hLc/k = (convection heat transfer strength)/ (conduction heat transfer strength)
• Prandtl No. Pr = ν/α = (momentum diffusivity)/ (thermal diffusivity)
• Reynolds No. Re = ρVx/μ = (inertia force)/ (viscous force)

The dimensionless parameter which represents the natural convection effects and is called the Grashof number.

Grashof number, Gr, as the ratio between the buoyancy force and the viscous force:

\(Gr = \frac{{g\beta \left( {{T_s} - {T_\infty }} \right)L_c^3}}{{{ν ^2}}}\)

Nusselt number is a function of the Grashof number and the Prandtl number alone. Nu = f (Gr, Pr)

In the case of vertical pipe and vertical cylinder, if the height is same, then the characteristic dimension (L_c) is same, then Grashoff number is same, then nusselt number is same, then heat transfer coefficient will be same.