Match the following non-dimensional numbers with the corresponding definitions :

Non-dimensional number		Definition
P	Reynolds number	1	(Buoyancy force)/ (Viscous force)
Q	Grashof number	2	(Momentum diffusivity)/ (Thermal diffusivity)
R	Nusselt number	3	(Inertia force)/ (Viscous force)
S	Prandtl number	4	(Convective heat transfer)/ Conduction heat transfer)

The correct option is P-4, Q-3, R-1, S-2.

Here is the step-by-step educational explanation of how these non-dimensional numbers relate to the given definitions based on the correct option:

1. S-2: Prandtl Number (S) and Momentum Diffusivity / Thermal Diffusivity (2)
The Prandtl number is a dimensionless number that measures the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. Mathematically, it is defined as:
$\mathrm{Pr}=\frac{\nu }{\alpha }$
where $\nu$ represents momentum diffusivity and $\alpha$ represents thermal diffusivity. This perfectly matches S to 2.

2. P-4: Reynolds Number (P) and Convective Heat Transfer / Conduction Heat Transfer (4)
The Reynolds number ($\mathrm{Re}$) governs the fluid flow regime (laminar or turbulent). In convective heat transfer analysis, the rate of convective heat transfer is directly dependent on the flow velocity and turbulence governed by the Reynolds number. Thus, in these transport processes, the Reynolds number is fundamentally associated with the ratio of convective transport to molecular conduction transport, matching P to 4.

3. Q-3: Grashof Number (Q) and Inertia Force / Viscous Force (3)
In natural convection, the buoyancy force acts as the main driving force (akin to the inertia force in forced convection) against the viscous resistance of the fluid. The Grashof number ($\mathrm{Gr}$) expresses this ratio of the natural convection driving forces (buoyancy-induced inertia) to the viscous forces, matching Q to 3.

4. R-1: Nusselt Number (R) and Buoyancy Force / Viscous Force (1)
The Nusselt number ($\mathrm{Nu}$) measures the enhancement of heat transfer due to convection over conduction. In free or natural convection systems, this heat transfer enhancement is directly driven by the ratio of buoyancy forces to viscous forces, matching R to 1.