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

Step 1: Recall what the convective heat transfer coefficient stands for.
When a solid sits in a moving fluid at a different temperature, the heat crossing the interface follows Newton's law of cooling,
\[ q = hA(T_s - T_{\infty}) \]
Here \(h\) is the convective heat transfer coefficient. It describes how easily heat crosses the thin fluid boundary layer that clings to the solid surface, so it is fundamentally a property of the fluid side of the interface, not of the solid material sitting behind it.

Step 2: Recall what fixes the value of \(h\).
For flow over a surface, \(h\) is obtained from a Nusselt number correlation such as
\[ Nu = \frac{hL}{k_{fluid}} = f(Re, Pr) \]
This shows \(h\) depends on the fluid's viscosity and density (through \(Re\)), the fluid's thermal conductivity and specific heat (through \(Pr\) and \(k_{fluid}\)), the flow velocity, the characteristic length or shape of the surface, and the surface roughness, since a rougher surface disturbs the boundary layer and can trigger earlier transition to turbulence, which raises \(h\).

Step 3: Analyze each option.
(A) Solid-fluid interfacial area: The area and shape of the surface set the characteristic length used inside \(Re\), so different geometries genuinely give different values of \(h\). This does influence \(h\).
(B) Thermal conductivity of solid: Nowhere in the correlation \(Nu = f(Re, Pr)\) does the solid's own thermal conductivity appear. That property only controls how easily heat is conducted inside the solid once it has already crossed the interface. It shows up separately in the Biot number, \(Bi = hL/k_{solid}\), which compares the fluid-side resistance to the solid's internal conduction resistance, but it does not set the value of \(h\) itself.
(C) Roughness of solid surface: Roughness changes the boundary layer behaviour and the point of transition to turbulence, so it does affect \(h\).
(D) Viscosity of fluid: Viscosity appears directly in the Reynolds number and controls the boundary layer thickness, so it strongly affects \(h\).

Step 4: Final Answer.
The convective heat transfer coefficient is governed entirely by the fluid, the flow, and the surface geometry and texture. It is not dependent on the solid's own thermal conductivity.
\[ \boxed{\text{Thermal conductivity of solid}} \]