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Momentum Transfer(11)Heat Transfer(11)Mass Transfer and Dimensional Analysis(3)Dimensional Analysis(5)

Momentum Transfer

11 Questions

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q1

NAT[1 Mark]

Two parallel plates, with Newtonian incompressible liquid in between, are 2 mm apart. The upper plate is stationary and the lower plate moves with a velocity of $4\text{ m/s}$. A force per unit area of $5\text{ N/m}^2$ is applied parallel to the lower plate to maintain its motion. The viscosity of the liquid (rounded off to two decimal places) is ___ $\times 10^{-3}\text{ N}\cdot\text{s/m}^2$.

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q2

MCQ[2 Marks]

The equation below represents steady-state laminar flow of a fluid through a horizontal tube: $$\eta \frac{1}{r} \frac{d}{dr}\left(r \frac{dv_z}{dr}\right) - \frac{dP}{dz} = 0$$\nWhich one of the following statements related to the above case is NOT correct? (A) The fluid is Newtonian (B) Shear stress is maximum at the center ($r=0$) (C) Radial velocity is zero (D) There is no variation of $v_z$ in $z$-direction

(A)

The fluid is Newtonian

(B)

Shear stress is maximum at the center (r=0)

(C)

Radial velocity is zero

(D)

There is no variation of v_{z} in z-direction

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Momentum Transfer

Q3

MSQ[2 Marks]

Choose the correct option(s). Permeability of a porous bed made of spherical particles is/are: (A) Independent of particle size (B) Increases with increase in particle size (C) Decreases with increase in particle size (D) Affected by particle size distribution

(A)

Independent of particle size

(B)

Increases with increase in particle size

(C)

Decreases with increase in particle size

(D)

Affected by particle size distribution

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Momentum Transfer

Q4

MCQ[1 Mark]

At high temperatures, which one of the following empirical expressions correctly describes the variation of dynamic viscosity $\mu$ of a Newtonian liquid with absolute temperature $T$? Given: $A$ and $B$ are positive constants. (A) $\mu = A + BT$ (B) $\mu = A \exp\left(-\frac{B}{T}\right)$ (C) $\mu = A \exp(BT)$ (D) $\mu = A \exp\left(\frac{B}{T}\right)$

(A)

\mu = A + BT

(B)

\mu = A \exp(-B/T)

(C)

\mu = A \exp(BT)

(D)

\mu = A \exp(B/T)

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Momentum Transfer

Q5

MSQ[1 Mark]

Consider a fully developed, steady, one-dimensional, laminar flow of a Newtonian liquid through a pipe. The maximum velocity in the pipe is proportional to which of the following quantities?\nGiven: $\Delta P$ is the pressure drop, $\mu$ is dynamic viscosity, and $R$ and $L$ are radius and length of the pipe, respectively. (A) $\Delta P$ (B) $1/R^2$ (C) $1/\mu$ (D) $1/L$

(A)

\Delta P

(B)

1/R^{2}

(C)

1/\mu

(D)

1/L

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Momentum Transfer

Q6

MCQ[1 Mark]

For laminar fluid flow through a smooth circular tube, the relation between friction factor ($f$) and Reynolds number ($Re$) is (A) $f = \frac{16}{Re}$ (B) $f = \frac{24}{Re}$ (C) $f = \frac{16}{\sqrt{Re}}$ (D) $f = \frac{24}{\sqrt{Re}}$

(A)

f=\frac{16}{Re}

(B)

f=\frac{24}{Re}

(C)

f=\frac{16}{\sqrt{Re}}

(D)

f=\frac{24}{\sqrt{Re}}

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Momentum Transfer

Q7

NAT[1 Mark]

A liquid of density $900\text{ kg m}^{-3}$ is flowing over a flat plate with a free stream velocity of $0.1\text{ m s}^{-1}$. The laminar boundary layer thickness at a distance of $0.2\text{ m}$ from the leading edge of the plate is $0.007\text{ m}$. The viscosity of the liquid in centipoise is ___ (round off to 2 decimal places). (Given: $1\text{ centipoise} = 10^{-3}\text{ kg m}^{-1}\text{s}^{-1}$)

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Momentum Transfer

Q8

NAT[2 Marks]

A chimney as shown in the figure requires to have natural draft (pressure difference between the furnace and the bottom of chimney, $P_{0}-P_{1}$) of $1.0133\times 10^{3}\text{ Pa}$. If the density difference between the air and flue is $0.5\text{ kg m}^{-3}$, the minimum height ($h$) of the chimney in meters is ___ (round off to nearest integer). (Given: acceleration due to gravity, $g = 9.81\text{ m s}^{-2}$)

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q9

NAT[1 Mark]

A Newtonian incompressible liquid is contained between two parallel metal plates separated by $10^{-3}\text{ m}$. A stress of $5\text{ Pa}$ is required to maintain the upper plate in motion with a constant speed of $2\text{ m s}^{-1}$ in the horizontal direction relative to the bottom plate. The viscosity of liquid contained between the plates is ___ $\times 10^{-3}\text{ Pa-s}$ (answer rounded off to 1 decimal place).

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q10

MSQ[2 Marks]

A non-rotating smooth solid spherical object is fixed in the stream of an inviscid incompressible fluid of density $\rho$. The flow is horizontal, slow, steady, and fully developed far from the object as shown by the streamline arrows near point O. Which of the following statement(s) is (are) TRUE? (A) The velocity of the fluid at the point A is zero (B) The fluid pressure at the point A exceeds that at point O by the amount $\frac{\rho v^2}{2}$, where $v$ is the fluid velocity at point O (C) Fluid moving precisely along OA will turn perpendicular to OA to circumvent the object (D) On each side of the central streamline OA, the flow will be deflected round the object

(A)

The velocity of the fluid at the point A is zero

(B)

The fluid pressure at the point A exceeds that at point O by the amount \frac{\rho v^2}{2}, where v is the fluid velocity at point O

(C)

Fluid moving precisely along OA will turn perpendicular to OA to circumvent the object

(D)

On each side of the central streamline OA, the flow will be deflected round the object

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Momentum Transfer

Q11

NAT[2 Marks]

A spherical gas bubble of radius $0.01\text{ mm}$ is entrapped in molten steel held at $1773\text{ K}$. If the pressure outside the bubble is $1.5\text{ bar}$, the pressure inside the bubble is ___ $\text{bar}$ (round off to 1 decimal place).\nGiven: $1\text{ bar} = 10^5\text{ Pa}$ and the surface tension of the steel at $1773\text{ K}$ is $1.4\text{ N m}^{-1}$.

Explanation

Heat Transfer

11 Questions

GATE→2026→Transport Phenomena and Rate Processes→Heat Transfer

Q12

MCQ[1 Mark]

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

(A)

Solid-fluid interfacial area

(B)

Thermal conductivity of solid

(C)

Roughness of solid surface

(D)

Viscosity of fluid

Explanation

GATE→2026→Transport Phenomena and Rate Processes→Heat Transfer

Q13

NAT[2 Marks]

For a cylindrical furnace with $0.1\text{ m}$ diameter and $0.2\text{ m}$ height operating at $1873\text{ K}$, power needed is ___ W.

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Heat Transfer

Q14

MCQ[2 Marks]

Radiative heat flux $\dot{q}$ at a hot surface at a temperature $T_s$ can be expressed as $\dot{q} = A \cdot f(T_s, T_\infty)(T_s - T_\infty)$ where $A$ is a constant and $T_\infty$ is the temperature of the surroundings. The function $f(T_s, T_\infty)$ is given by (A) $(T_s + T_\infty)^2(T_s - T_\infty)$ (B) $(T_s^2 + T_\infty^2)(T_s + T_\infty)$ (C) $(T_s^2 - T_\infty^2)(T_s + T_\infty)$ (D) $(T_s - T_\infty)^2(T_s + T_\infty)$

(A)

(T_{s}+T_{\infty})^{2}(T_{s}-T_{\infty})

(B)

(T_{s}^{2}+T_{\infty}^{2})(T_{s}+T_{\infty})

(C)

(T_{s}^{2}-T_{\infty}^{2})(T_{s}+T_{\infty})

(D)

(T_{s}-T_{\infty})^{2}(T_{s}+T_{\infty})

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Heat Transfer

Q15

NAT[2 Marks]

Temperatures at two sides of a $0.4\text{ m}$ thick copper plate are $1000^{\circ}\text{C}$ and $500^{\circ}\text{C}$. Assuming steady state, one-dimensional conductive heat transfer through the wall and ignoring end-effects, the magnitude of the heat flux through the wall is ___ $\times 10^5\text{ W m}^{-2}$ (in integer). (Given: Thermal conductivity of copper is $400\text{ W m}^{-1}\text{K}^{-1}$)

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q16

MCQ[1 Mark]

As shown in the figure, two rods of different metals of equal lengths $L/2$, diameter $d$, and constant thermal conductivities $k_1$ and $k_2$ (with $k_1 > k_2$) are connected perfectly. Which one of the graphs represents the steady-state temperature distribution?

(A)

Option A

(B)

Option B

(C)

Option C

(D)

Option D

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q17

MCQ[2 Marks]

As shown in the figure, the right end of a slender, long solid cylindrical metal rod of thermal conductivity $k$, length $L$ and diameter $d$ is in contact with an infinite liquid heat sink at $T_0$. At steady-state, temperatures are $T_2$ at the right end and $T_0$ at the heat sink, with convection coefficient $h$. The temperature of the left end $T_1$ at steady-state is determined by fin/rod heat transfer balances.

(A)

T_{1}=T_{2}+(T_{2}-T_{0})\frac{hL}{k}

(B)

T_{1}=T_{2}-(T_{2}-T_{0})\frac{hL}{k}

(C)

T_{1}=T_{2}-(T_{2}-T_{0})\frac{k}{hL}

(D)

T_{1}=T_{2}+(T_{2}-T_{0})\frac{k}{hL}

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Heat Transfer

Q18

NAT[2 Marks]

A long metallic cylindrical rod of radius $r$, length $L$ and electrical resistivity $\rho_e$ is kept in vacuum and is carrying an electric current of $I$. The only way it loses heat to the ambient is via radiation. If the ambient temperature is $T_0$, then the steady-state temperature of the rod is ___ $\text{K}$ (Round off to the nearest integer).\nGiven: Stefan-Boltzmann constant $= 5.667 \times 10^{-8}\text{ W m}^{-2}\text{K}^{-4}$, $r = 0.1\text{ mm} = 10^{-4}\text{ m}$, $I = 0.3\text{ A}$, $L = 1\text{ m}$, $\rho_e = 10^{-8}\text{ }\Omega\text{m}$, $T_0 = 300\text{ K}$.

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Heat Transfer

Q19

NAT[2 Marks]

Two circular surfaces A and B with the values of emissivity $\varepsilon$, temperature $T$, and respective view factors are shown in the figure. Surface A: radius $1\text{ m}$ (area $A_1 = \pi\text{ m}^2$), $\varepsilon_1 = 0.7$, $T_1 = 800\text{ K}$, $F_{AB} = 0.172$. Surface B: radius $1\text{ m}$ (area $A_2 = \pi\text{ m}^2$), $\varepsilon_2 = 0.8$, $T_2 = 500\text{ K}$, $F_{BA} = 0.172$. Net heat flow rate by radiation from surface A in kW is ___ (round off to 1 decimal place). Given: Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W m}^{-2}\text{K}^{-4}$

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q20

MSQ[2 Marks]

Which of the following statement(s) is (are) TRUE about black body radiation? (A) Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum (B) The total emissive power of an ideal black body is proportional to the square of its absolute temperature (C) The emissive power of an ideal black body peaks at a wavelength $\lambda$ which is inversely proportional to its absolute temperature (D) The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above $0\text{ K}$

(A)

Among all radiation emitted by an ideal black body at room temperature, the most intense radiation falls in the visible light spectrum

(B)

The total emissive power of an ideal black body is proportional to the square of its absolute temperature

(C)

The emissive power of an ideal black body peaks at a wavelength \lambda which is inversely proportional to its absolute temperature

(D)

The radiant energy emitted by an ideal black body is greater than that emitted by the non-black body at all temperatures above 0 K

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q21

NAT[2 Marks]

A rectangular block made of Material I and Material II of identical cross sections has a temperature ($T$) of $435\text{ K}$ and $400\text{ K}$ at the bottom and top surfaces, respectively. Assuming purely steady state conductive heat transfer, the temperature at the interface is ___ $\text{K}$ (round off to nearest integer). (Given: The two parts of the block made of Material I and Material II have equal thickness of $25\text{ mm}$ each. The thermal conductivities of Material I and Material II are $50\text{ W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}$ and $200\text{ W}\cdot\text{m}^{-1}\cdot\text{K}^{-1}$ respectively.)

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Heat Transfer

Q22

NAT[2 Marks]

Air at $300\text{ K}$ is passed at a mass flow rate of $1.5\text{ kg}\cdot\text{s}^{-1}$ through a metallic tube of inner diameter $0.08\text{ m}$. Inner wall temperature of the tube is maintained at $700\text{ K}$. Temperature of the air leaving the tube is $600\text{ K}$. Assuming that heat transfer occurs entirely by steady state convection, length of the tube is ___ $\text{m}$ (round off to 2 decimal places).\nGiven: convective heat transfer coefficient $h = 500\text{ W}\cdot\text{m}^{-2}\cdot\text{K}^{-1}$, specific heat $C_p = 1080\text{ J}\cdot\text{kg}^{-1}\cdot\text{K}^{-1}$, $\pi = 3.14$.

Explanation

Mass Transfer and Dimensional Analysis

3 Questions

GATE→2026→Transport Phenomena and Rate Processes→Mass Transfer and Dimensional Analysis

Q23

MCQ[1 Mark]

Which one of the following options is correct? In convective heat transfer for laminar flow over a flat plate, Nusselt number is a function of Reynolds and Prandtl numbers. Similarly, in convective mass transfer, Sherwood number is a function of: (A) Schmidt number and Reynolds number (B) Weber number and Reynolds number (C) Schmidt number and Weber number (D) Weber number and Prandtl number

(A)

Schmidt number and Reynolds number

(B)

Weber number and Reynolds number

(C)

Schmidt number and Weber number

(D)

Weber number and Prandtl number

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Mass Transfer and Dimensional Analysis

Q24

MCQ[1 Mark]

Match the laws listed in Column I with the corresponding material properties listed in Column II:\nColumn I:\nP. Hooke's law\nQ. Fick's law\nR. Fourier's law\nS. Darcy's law\nColumn II: 1. Thermal conductivity 2. Young's modulus 3. Permeability 4. Diffusivity (A) P-2, Q-1, R-4, S-3 (B) P-4, Q-3, R-1, S-2 (C) P-2, Q-4, R-1, S-3 (D) P-4, Q-3, R-2, S-1

(A)

P-2, Q-1, R-4, S-3

(B)

P-4, Q-3, R-1, S-2

(C)

P-2, Q-4, R-1, S-3

(D)

P-4, Q-3, R-2, S-1

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Mass Transfer and Dimensional Analysis

Q25

MCQ[2 Marks]

Match the transport processes in Column I with the relationships in Column II.\nColumn I: (P) Molecular momentum transport (Q) Molecular mass transport (R) Molecular energy transport (S) Radiation energy transport\nColumn II: (1) Stefan-Boltzmann law (2) Newton's law of viscosity (3) Fick's law (4) Fourier law (A) P-2, Q-3, R-4, S-1 (B) P-4, Q-3, R-2, S-1 (C) P-3, Q-1, R-4, S-2 (D) P-2, Q-1, R-4, S-3

(A)

P-2, Q-3, R-4, S-1

(B)

P-4, Q-3, R-2, S-1

(C)

P-3, Q-1, R-4, S-2

(D)

P-2, Q-1, R-4, S-3

Explanation

Dimensional Analysis

5 Questions

GATE→2025→Transport Phenomena and Rate Processes→Dimensional Analysis

Q26

NAT[1 Mark]

For an application where the Reynolds number is to be kept constant, a liquid with a density of $1\text{ g cm}^{-3}$ and viscosity $0.01\text{ Poise}$ results in a characteristic speed of $1\text{ cm s}^{-1}$. If this liquid is replaced by another with a density of $1.25\text{ g cm}^{-3}$ and viscosity of $0.015\text{ Poise}$, the characteristic velocity will be ___ $\text{cm s}^{-1}$ (rounded off to one decimal place).

Explanation

GATE→2025→Transport Phenomena and Rate Processes→Dimensional Analysis

Q27

NAT[2 Marks]

The reaction represented by $A \rightarrow B$ follows first order kinetics. At a given temperature, $20\%$ of the reaction is completed in $223\text{ s}$. The time taken to complete $50\%$ of the reaction at the same temperature is ___ $\text{s}$ (rounded off to the nearest integer).

Explanation

GATE→2024→Transport Phenomena and Rate Processes→Dimensional Analysis

Q28

MCQ[2 Marks]

Match the dimensionless numbers listed in Column I with their applications to transport phenomena listed in Column II.\nColumn I:\nP. Reynolds number\nQ. Schmidt number\nR. Prandtl number\nS. Biot number\nColumn II: 1. Momentum and mass transfer 2. Momentum and heat transfer 3. Convective and conductive heat transfer 4. Laminar to turbulent flow (A) P-4, Q-1, R-3, S-2 (B) P-3, Q-2, R-4, S-1 (C) P-4, Q-1, R-2, S-3 (D) P-2, Q-3, R-1, S-4

(A)

P-4, Q-1, R-3, S-2

(B)

P-3, Q-2, R-4, S-1

(C)

P-4, Q-1, R-2, S-3

(D)

P-2, Q-3, R-1, S-4

Explanation

GATE→2023→Transport Phenomena and Rate Processes→Dimensional Analysis

Q29

NAT[1 Mark]

The rate constant of a reaction at $400\text{ K}$ is three times the value at $300\text{ K}$. The activation energy of the reaction in $\text{kJ mol}^{-1}$ is ___ (round off to 1 decimal place). Given: Universal gas constant, $R = 8.314\text{ J mol}^{-1}\text{K}^{-1}$

Explanation

GATE→2022→Transport Phenomena and Rate Processes→Dimensional Analysis

Q30

MCQ[1 Mark]

In fluid flow, the dimensionless number that describes the transition from laminar to turbulent flow is (A) Reynolds number (B) Schmidt number (C) Biot number (D) Prandtl number

(A)

Reynolds number

(B)

Schmidt number

(C)

Biot number

(D)

Prandtl number

Explanation