GATE ME 2014 Set 4 — Question 25

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MCQ+1 / -0.33EasyDimensionless NumbersDimensional Analysis & SimilitudeFluid MechanicsBiot & Fourier NumbersConductionHeat TransferDimensionless ParametersConvection

Fluid Mechanics → Conduction → Biot & Fourier Numbers

Last updated 5 September 2026

Question

Match Group A with Group B Group A Group B P: Biot number 1: Ratio of buoyancy to viscous force Q: Grashof number 2: Ratio of inertia force to viscous force R: Prandtl number 3: Ratio of momentum to thermal diffusivities S: Reynolds number 4: Ratio of internal thermal resistance to boundary layer thermal resistance

Group A	Group B
P: Biot number	1: Ratio of buoyancy to viscous force
Q: Grashof number	2: Ratio of inertia force to viscous force
R: Prandtl number	3: Ratio of momentum to thermal diffusivities
S: Reynolds number	4: Ratio of internal thermal resistance to boundary layer thermal resistance

Correct answer (A) P-4, Q-1, R-3, S-2 Solution Let's match the dimensionless numbers in Group A with their definitions in Group B: P: Biot number (Bi) The Biot number is a dimensionless quantity used in heat transfer calculations. It is the ratio of the heat transfer resistance inside a body to the heat transfer resistance at the surface of the body. More precisely, it is the ratio of internal thermal resistance to boundary layer thermal resistance. So, P-4 . Q: Grashof number (Gr) The Grashof number is a dimensionless number in fluid dynamics and heat transfer that approximates the ratio of the buoyancy force to the viscous force acting on a fluid. It is often used in natural convection problems. So, Q-1 . R: Prandtl number (Pr) The Prandtl number is a dimensionless number, approximately the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It relates the relative thickness of the hydrodynamic and thermal boundary layers. So, R-3 . S: Reynolds number (Re) The Reynolds number is a dimensionless quantity that is used to predict flow patterns in different fluid flow situations. It is the ratio of inertia forces to viscous forces. So, S-2 . Combining these matches: P-4 Q-1 R-3 S-2 This corresponds to option (A). Turn this into a strength. Explore AI-powered practice and doubt support with Success Tracker.

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Correct answer (A) P-4, Q-1, R-3, S-2 Solution Let's match the dimensionless numbers in Group A with their definitions in Group B: P: Biot number (Bi) The Biot number is a dimensionless quantity used in heat transfer calculations. It is the ratio of the heat transfer resistance inside a body to the heat transfer resistance at the surface of the body. More precisely, it is the ratio of internal thermal resistance to boundary layer thermal resistance. So, P-4 . Q: Grashof number (Gr) The Grashof number is a dimensionless number in fluid dynamics and heat transfer that approximates the ratio of the buoyancy force to the viscous force acting on a fluid. It is often used in natural convection problems. So, Q-1 . R: Prandtl number (Pr) The Prandtl number is a dimensionless number, approximately the ratio of momentum diffusivity (kinematic viscosity) to thermal diffusivity. It relates the relative thickness of the hydrodynamic and thermal boundary layers. So, R-3 . S: Reynolds number (Re) The Reynolds number is a dimensionless quantity that is used to predict flow patterns in different fluid flow situations. It is the ratio of inertia forces to viscous forces. So, S-2 . Combining these matches: P-4 Q-1 R-3 S-2 This corresponds to option (A).

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GATE ME 2014 Set 4 — Question 25

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