Question

Which one of the following options is correct?

For a solid immersed in a fluid, the convective heat transfer coefficient across the solid-fluid interface is NOT dependent on:

• A. Solid-fluid interfacial area
• B. Thermal conductivity of solid
• C. Roughness of solid surface
• D. Viscosity of fluid

Hint:

The convective coefficient h comes from a fluid-side correlation like Nu = f(Re, Pr); the solid's conductivity only enters conduction inside the solid, through the Biot number.

Answer 1

The Correct Option is B

The trick in this question is remembering that the convective heat transfer coefficient $h$ belongs to the fluid boundary layer, not to the solid it is sitting next to. Let's test each option against that idea.

1. Solid-fluid interfacial area: The shape and size of the surface set the characteristic length $L$ that goes into the Reynolds number, $Re = \rho V L/\mu$. A bigger or differently shaped surface changes $Re$, which changes $h$ through the correlation $Nu = f(Re, Pr)$. So area does affect $h$.
2. Thermal conductivity of solid: Look at the correlation used to find $h$, namely $Nu = hL/k_{fluid} = f(Re, Pr)$. Every term in it, $Re$, $Pr$, and $k_{fluid}$, belongs to the fluid. The solid's own conductivity never enters this formula. What the solid's conductivity does control is how fast heat moves once it is already inside the solid, which is a separate, internal conduction problem, tied together with $h$ only through the Biot number $Bi = hL/k_{solid}$.
3. Roughness of solid surface: A rough surface disturbs the fluid layer close to the wall and can push the flow into turbulence earlier than a smooth surface would, and turbulent flow carries heat away faster. So roughness changes $h$.
4. Viscosity of fluid: Viscosity sits directly inside $Re$, so it controls how thick the boundary layer is and how much resistance the fluid offers. It clearly affects $h$.

Three of the four options change the flow, the boundary layer, or the geometry the correlation depends on, so they all influence $h$. Only the solid's thermal conductivity plays no role in the correlation that defines $h$, since it governs conduction inside the solid rather than convection at its surface.

Let's summarize:

• $h$ comes from a fluid-side correlation $Nu = f(Re, Pr)$, so fluid viscosity, surface area/geometry, and surface roughness all matter.
• The solid's own thermal conductivity is a conduction property, tied to $h$ only through the Biot number, and does not set the value of $h$.

So the convective heat transfer coefficient is not dependent on the thermal conductivity of the solid.