Concept:
Convection is the transfer of heat between a solid surface and an adjacent moving fluid (liquid or gas). The rate of this transfer is governed by Newton's Law of Cooling ($Q = hA\Delta T$), where '$h$' is the convective heat transfer coefficient.
Step 1: Unlike thermal conductivity ($k$), which is a strict physical property of a solid material, the convective coefficient ($h$) is a flow property. It describes the complex interaction at the boundary layer between the solid and the fluid.
Step 2: How well a fluid can absorb and carry away heat depends heavily on its intrinsic properties: density ($\rho$), dynamic viscosity ($\mu$), specific heat ($C_p$), and thermal conductivity ($k_{fluid}$).
Step 3: How fast the fluid is moving (Velocity, $V$) dictates how quickly fresh, cool fluid replaces heated fluid at the surface. Faster flow creates a thinner boundary layer, drastically increasing '$h$'.
Step 4:
* While surface roughness can affect turbulence (and thus '$h$'), it is not the main or only factor.
* Temperature difference ($\Delta T$) is the driving force for heat rate ($Q$), not the determining factor for the coefficient '$h$' itself.
* The thermal conductivity of the solid governs conduction inside the wall, not convection outside it.