GATE-CH-1994-4-g-ht-1mark

Match the following:

• I. Stanton number

Answer 1A. hD/kB. h/(Cp\rho v)C. Cpk/\muD. Cp\mu/k

• II. Prandtl number

Answer 2A. hD/kB. h/(Cp\rho v)C. Cpk/\muD. Cp\mu/k

GATE-CH-1994-4-j-ht-1mark

Match the following:

• I. Nusselt number

Answer 1D. Convective resistance / Solid conduction resistanceC. Solid conduction resistance / Convective resistanceA. Convective resistance / Fluid conduction resistanceB. Fluid conductance resistance / Convective resistance

• II. Biot number

Answer 2D. Convective resistance / Solid conduction resistanceC. Solid conduction resistance / Convective resistanceA. Convective resistance / Fluid conduction resistanceB. Fluid conductance resistance / Convective resistance

GATE-CH-1996-3-4-ht-2mark

Match the following:

• I. Graetz number

Answer 1C. product of Grashof and Prandtl numbersA. heat transfer in creeping flowB. thermally developing flowD. product of Reynolds and Prandtl numbers

• II. Rayleigh number

Answer 2C. product of Grashof and Prandtl numbersA. heat transfer in creeping flowB. thermally developing flowD. product of Reynolds and Prandtl numbers

GATE-CH-1989-4-i-b-ht-1mark

The rate of diffusion of momentum relative to the rate of diffusion of heat is:

• proportional to Prandtl number

• inversely proportional to Prandtl number

• proportional to the Colburn’s \(j_H\) factor

• proportional to Stanton number

GATE-CH-1989-4-i-c-ht-1mark

Heat transfer coefficient in a helical coil compared to that in a straight pipe is:

• Lower

• Higher

• Same

GATE-CH-1990-4-iii-ht-2mark-MANY

Grashof number is associated with:

• buoyancy effects

• free convection

• forced convection

• high temperature difference

GATE-CH-1991-5-ii-ht-2mark

The widely used Dittus-Boelter equation is valid provided

• \(2100 < \text {Re} < 10,000\) and the properties of the fluid are evaluated at the average film temperature

• \(\text {Re} < 2100\) and the properties of the fluid are evaluated at the bulk temperature

• \(10,000 < \text {Re} < 120,000\) and the fluid properties are evaluated at the bulk temperature

• none of the above

GATE-CH-1994-1-m-ht-1mark

For a laminar flow of fluid in a circular tube, \(h_1\) is the convective heat transfer coefficient at a velocity \(v_1\). If the velocity is reduced by half and assuming the fluid properties are constant, the new convective heat transfer coefficient at the thermally developing flow section is

• \(1.26h_1\)

• \(0.794h_1\)

• \(0.574h_1\)

• \(1.741h_1\)

GATE-CH-1996-1-11-ht-1mark

The non-dimensional temperature gradient in a liquid at the wall of a pipe is

• the heat flux

• the Nusselt number

• the Prandtl number

• the Schmidt number

GATE-CH-1996-1-9-ht-1mark

In natural convection heat transfer the correlating parameter is

• Graetz number

• Eckert number

• Grashof number

• Bond number

GATE-CH-1996-2-7-ht-2mark

The hydrodynamic and thermal boundary layers will merge when

• Prandtl number is one

• Schmidt number tends to infinity

• Nusselt number tends to infinity

• Archimedes number is greater than 10,000

GATE-CH-1996-2-8-ht-2mark

When the ratio of the Grashof number to the square of the Reynolds number is one, the dominant mechanism of heat transfer is

• free convection

• entry length problem in laminar forced convection (developing thermal boundary layer)

• mixed convection (both free and forced)

• forced convection

GATE-CH-1999-1-15-ht-1mark

In pipe flow, heat is transferred from hot wall to the liquid by

• conduction only

• forced convection only

• forced convection and conduction

• free and forced convection

GATE-CH-1999-1-16-ht-1mark

Heat transfer occurs by natural convection because change in temperature causes differences in

• viscosity

• density

• thermal conductivity

• heat capacity

GATE-CH-2000-1-12-ht-1mark

The Grashof number is defined as the ratio of

• buoyancy to inertial forces

• buoyancy to viscous forces

• inertial to viscous forces

• buoyancy to surface tension forces

GATE-CH-2001-1-10-ht-1mark

Heat transfer by natural convection is enhanced in systems with

• high viscosity

• high coefficient of thermal expansion

• low temperature gradients

• low density change with temperature

GATE-CH-2001-2-9-ht-2mark

The Sieder-Tate correlation for heat transfer in turbulent flow in a pipe gives \(\text {Nu} \propto \text {Re}^{0.8}\), where \(\text {Nu}\) is the Nusselt number and \(\text {Re}\) is the Reynolds number for the flow. Assuming that this relation is valid, the heat transfer coefficient varies with the pipe diameter (\(D\)) as

• \(D^{-1.8}\)

• \(D^{-0.2}\)

• \(D^{0.2}\)

• \(D^{1.8}\)

GATE-CH-2003-52-ht-2mark

Match the following dimensionless numbers with the appropriate ratio of forces:

	Dimensionless Number		Ratio of forces
P	Froude Number	1	Shear force / inertial force
Q	Reynolds Number	2	Convective heat transfer / conductive heat transfer
R	Friction factor	3	Gravitational force / viscous force
S	Nusselt Number	4	Inertial force / viscous force
		5	Inertial force / gravitational force

• P - 1, Q - 2, R - 5, S - 3

• P - 5, Q - 4, R - 3, S - 2

• P - 5, Q - 4, R - 1, S - 2

• P - 3, Q - 4, R - 5, S - 1

GATE-CH-2004-17-ht-1mark

In forced convection, the Nusselt number Nu is a function of

• Re and Pr

• Re and Gr

• Pr and Gr

• Re and Sc

GATE-CH-2005-13-ht-1mark

The thermal boundary layer is significantly thicker than the hydrodynamic boundary layer for

• Newtonian liquids

• polymeric liquids

• liquid metals

• gases

GATE-CH-2006-11-ht-1mark

Let \(d_h\) be the hydrodynamic entrance length for mercury in laminar flow in a pipe under isothermal conditions. Let \(d_t\) be its thermal entrance length under fully developed hydrodynamic conditions. Which ONE of the following is TRUE ?

• \(d_h > d_t\)

• \(d_h < d_t\)

• \(d_h = d_t\)

• \(d_h < d_t\) only if the pipe is vertical

GATE-CH-2006-12-ht-1mark

The Boussinesq approximation for the fluid density in the gravitational force term is given by ONE of the following ? (\(\rho _{\text {ref}}\) is the fluid density at the reference temperature \(T_{\text {ref}}\), and \(\beta \) is the thermal coefficient of volume expansion at \(T_{\text {ref}}\))

• \(\rho =\rho _{\text {ref}} + T_{\text {ref}}\beta (\rho -\rho _{\text {ref}})\)

• \(\rho =\rho _{\text {ref}} - T_{\text {ref}}\beta (\rho -\rho _{\text {ref}})\)

• \(\rho =\rho _{\text {ref}} - \rho _{\text {ref}}\beta (T-T_{\text {ref}})\)

• \(\rho =\rho _{\text {ref}} - T_{\text {ref}}\beta (\rho -\rho _{\text {ref}}) + \rho _{\text {ref}}(T-T_{\text {ref}})/T_{\text {ref}}\)

GATE-CH-2007-15-ht-1mark

The Grashof Number is

• thermal diffusivity / mass diffusivity

• inertial force / surface tension force

• sensible heat / latent heat

• buoyancy force / viscous force

GATE-CH-2009-10-ht-1mark

The Prandtl number of a fluid is the ratio of

• thermal diffusivity to momentum diffusivity

• momentum diffusivity to thermal diffusivity

• conductive resistance to convective resistance

• thermal diffusivity to kinematic diffusivity

GATE-CH-2010-2-ht-1mark

The ratio of Nusselt number to Biot number is

• conductive resistance of fluid / conductive resistance of solid

• conductive resistance of fluid / conductive resistance of fluid

• conductive resistance of solid / conductive resistance of fluid

• unity

GATE-CH-2012-16-ht-1mark

If the Nusselt number (Nu) for heat transfer in a pipe varies with Reynolds number (Re) as \(\text{Nu} \propto \text{Re}^{0.8}\), then for constant average velocity in the pipe, the heat transfer coefficient varies with the pipe diameter \(D\) as

• \(D^{-1.8}\)

• \(D^{-0.2}\)

• \(D^{0.2}\)

• \(D^{1.8}\)

GATE-CH-ME-2009-6-ht-1mark

A coolant fluid at 30^oC flows over a heated flat plate maintained at a constant temperature of 100^oC. The boundary layer temperature distribution at a given location on the plate may be approximated as \(T=30+70\exp (-y)\) where \(y\) (in m) is the distance normal to the plate and \(T\) is in ^oC. If thermal conductivity of the fluid is 1.0 W/m.K, the local convective heat transfer coefficient (in W/m².K) at that location will be

• 0.2

• 1

• 5

• 10

GATE-CH-1991-3-iii-ht-2mark

For \(5000 < \text {Re} < 200000\), the friction factor \(f=0.046(\text {Re})^{-0.2}\). Find the Colburn factor, \(j_H\) at \(\text {Re} = 10000\).

• Answer

GATE-CH-1994-3-d-ht-1mark

When a vertical plate is heated in an infinite air environment under natural convection conditions, the velocity profile in air, normal to the plate, exhibits a maximum. (True/False).

• True
• False

GATE-CH-2002-8-ht-5mark

Air flows through a smooth tube, 2.5 cm diameter and 10 m long, at 37\(^\circ \)C. If the pressure drop through the tube is 10000 Pa, estimate:

(a) the velocity of air (in m/s).

{#1}

(b) the heat transfer coefficient (in W/m\(^2\).K) using Colburn Analogy [\(j_H = (\text {St})(\text {Pr})^{0.67}\)], where \(\text {St}\) is the Stanton Number and \(\text {Pr}\) is the Prandtl Number.

{#2}

Gas constant, \(R\) = 82.06 cm\(^3\).atm/mol.K. Darcy friction factor \( = 0.184/\text {Re}^{0.2}\). Other relevant properties of air under the given conditions: viscosity = \(1.8\times 10^{-5}\) kg/m.s, density = 1.134 kg/m\(^3\), specific heat capacity, \(C_P\) = 1.046 kJ/kg.\(^\circ \)C, thermal conductivity = 0.028 W/m.\(^\circ \)C.

GATE-CH-2000-2-13-ht-2mark

For turbulent flow in a tube, the heat transfer coefficient is obtained from Dittus-Boelter correlation. If the tube diameter is halved and the flow rate is doubled, then the heat transfer coefficient will change by a factor of

• 1

• 1.74

• 6.1

• 37

GATE-CH-2003-59-ht-2mark

A fluid is flowing inside the inner tube of a double pipe heat exchanger with diameter '\(d\)’. For a fixed mass flow rate, the tube side heat transfer coefficient for turbulent flow conditions is proportional to

• \(d^{0.8}\)

• \(d^{-0.2}\)

• \(d^{-1}\)

• \(d^{-1.8}\)

GATE-CH-2005-59-ht-2mark

Consider the flow of a gas with density 1 kg/m³, viscosity \(1.5 \times 10^{-5}\) kg/(m.s), specific heat \(C_P = 846\) J/(kg.K) and thermal conductivity \(k = 0.01665\) W/(m.K), in a pipe of diameter \(D = 0.01\) m and length \(L = 1\) m, and assume the viscosity does not change with temperature. The Nusselt number for a pipe with \((L/D)\) ratio greater than 10 and Reynolds number greater than 20000 is given by \[ \text{Nu} = 0.026  \text{Re}^{0.8}\; \text{Pr}^{1/3} \] While the Nusselt number for a laminar flow for Reynolds number less than 2100 and \((\text {Re}\;  \text{Pr} \ D/L) < 10\) is \[ \text{Nu} = 1.86 [\text{Re}\; \text{Pr} \ (D/L) ]^{1/3}\] If the gas flows through the pipe with an average velocity of 0.1 m/s, the heat transfer coefficient is

• 0.68 W/(m².K)

• 1.14 W/(m².K)

• 2.47 W/(m².K)

• 24.7 W/(m².K)

GATE-CH-2006-42-ht-2mark

One dimensional steady state heat transfer occurs from, a flat vertical wall of length 0.1 m into the adjacent fluid. The heat flux into this fluid is 21 W/m². The wall thermal conductivity is 1.73 W/(m.K). If the heat transfer coefficient is 30 W/(m².K) and the Nusselt number based on the wall length is 20, then the magnitude of the temperature gradient at the wall on the fluid side (in K/m) is

• 0.7

• 12.14

• 120

• 140

GATE-CH-2006-44-ht-2mark

A fluid flows through a cylindrical pipe under fully developed, steady state laminar flow conditions. The tube wall is maintained at constant temperature. Assuming constant physical properties and negligible viscous heat dissipation, the governing equation for the temperature profile is (\(z\) - axial direction; \(r\) - radial direction).

• (a)

• (b)

• (c)

• (d)

GATE-CH-2008-45-ht-2mark

Hot liquid is flowing at a velocity of 2 m/s through a metallic pipe having an inner diameter of 3.5 cm and length 20 m. The temperature at the inlet of the pipe is 90^oC. Following data is given for liquid at 90^oC: 

Density = 950 kg/m³ 
Specific heat = 4.23 kJ/kg.^oC
Viscosity = \(2.55 \times 10^{-4}\) kg/m.s
Thermal conductivity = 0.685 W/m.^oC 

The heat transfer coefficient (in kW/m².^oC) inside the tube is

• 222.22

• 111.11

• 22.22

• 11.11

GATE-CH-2016-41-ht-2mark

In an experimental setup, mineral oil is filled in between the narrow gap of two horizontal smooth plates. The setup has arrangements to maintain the plates at desired uniform temperatures. At these temperatures, ONLY the radiative heat flux is negligible. The thermal conductivity of the oil does not vary perceptibly in this temperature range. Consider four experiments at steady state under different experimental conditions, as shown in the figure below. The figure shows plate temperatures and the heat fluxes in the vertical direction.

What is the steady state heat flux (in W/m²) with the top plate at 70^oC and the bottom plate at 40^oC?

• 26

• 39

• 42

• 63

GATE-CH-2017-40-ht-2mark

A fluid flows over a heated horizontal plate maintained at temperature \(T_w\). The bulk temperature of the fluid is \(T_{\infty }\). The temperature profile in the thermal boundary layer is given by: \[ T = T_w + (T_w-T_{\infty })\left [\frac {1}{2}\left (\frac {y}{\delta _t}\right )^3-\frac {3}{2}\left (\frac {y}{\delta _t}\right ) \right ], \qquad 0 \le y \le \delta _t \] Here, \(y\) is the vertical distance from the plate, \(\delta _t\) is the thickness of the thermal boundary layer and \(k\) is the thermal conductivity of the fluid.

The local heat transfer coefficient is given by

• \(\dfrac {k}{2\delta _t}\)

• \(\dfrac {k}{\delta _t}\)

• \(\dfrac {3}{2}\dfrac {k}{\delta _t}\)

• \(2\dfrac {k}{\delta _t}\)

GATE-CH-ME-2007-32-ht-2mark

The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observations of the change in plate temperature with time as it cools. Assume the plate temperature to be uniform at any instant of time and radiation heat exchange with the surroundings negligible. The ambient temperature is 25^oC, the plate has a total surface area of 0.1 m² and a mass of 4 kg. The specific heat of the plate material is 2.5 kJ/kg.K. The convective heat transfer coefficient in W/m².K, at the instant when the plate temperature is 225^oC and the change in plate temperature with time \(dT/dt=-0.02\) K/s, is

• 200

• 20

• 15

• 10

GATE-CH-ME-2015-S2-57-ht-2mark

For flow through a pipe of radius \(R\), the velocity and temperature distributions are as follows: \(u(r,x)=C_1\), and \(\displaystyle T(r,x)= C_2\left [1-\left (\dfrac {r}{R}\right )^3\right ]\), where \(C_1\) and \(C_2\) are constants. The bulk mean temperature is given by \(\displaystyle T_m=\frac {2}{u_m R^2}\int _0^R u(r,x)T(r,x) rdr\), with \(u_m\) being the mean velocity of flow. The value of \(T_m\) is

• \(\dfrac {0.5C_2}{u_m}\)

• \(0.5C_2\)

• \(0.6C_2\)

• \(\dfrac {0.6C_2}{u_m}\)

GATE-CH-1989-14-iii-ht-5mark

A liquid metal flows at a rate of 5 kg/s through a 5 cm diameter stainless steel tube. It enters at 425\(^\circ \)C and is heated to 450\(^\circ \)C as it passes through the tube. If a constant heat flux is maintained along the tube and the tube wall is at a temperature 20\(^\circ \)C higher than the liquid metal bulk temperature, calculate the area (in m\(^2\)) required to effect the heat transfer. At constant heat flux, the following relation holds good: \[ \text {Nu} = 4.82 + 0.0185\; \text {Pe}^{0.827} \] Properties of the compound:
\(\mu = 1.34 \times 10^{-3}\) kg/m.s; \(C_P\) = 0.149 kJ/kg.K; \(k\) = 15.6 W/m.K; \(\text {Pr}\) = 0.013.

• Answer

GATE-CH-2015-40-ht-2mark

Air is flowing at a velocity of 3 m/s perpendicular to a long pipe as shown in the figure below. The outside diameter of the pipe is \(d=6\) cm and temperature at the outside surface of the pipe is maintained at 100^oC. The temperature of the air far from the tube is 30^oC.

Data for air: Kinematic viscosity, \(\nu =18\times 10^{-6}\) m²/s;
Thermal conductivity, \(k=0.03\) W/(m.K)

Using the Nusselt number correlation: \(\displaystyle \text {Nu}=\frac {hD}{k}=0.024\times \text {Re}^{0.8}\), the rate of heat loss per unit length (W/m) from the pipe to air (up to one decimal place) is ____________

• Answer

GATE-CH-1989-4-ii-ht-2mark

Name the dimensionless numbers:

1. \(\dfrac {hL}{k_s}\)
2. \(\dfrac {kt}{\rho C_PL^2}\)
3. \(\dfrac {hL}{k_f}\)
4. \(\dfrac {h}{\rho v C_P}\)

• Answer

GATE-CH-1993-11-a-ht-2mark

A hot horizontal plate is exposed to air by keeping

• [(i)] the hot surface facing up
• [(ii)] the hot surface facing down

Heat transfer to the ambient air is primarily by natural convection. In which of the above cases, is the heat transfer coefficient higher and why? Answer in three or four lines.

• Answer

GATE-CH-2001-10-ht-5mark

A 200 W heater has a spherical casing of diameter 0.2 m. The heat transfer coefficient for conduction and convection from the casing to the ambient air is obtained from \(\text{Nu} = 2 + 0.6\; \text{Re}^{1/2} \text{Pr}^{1/3}\), with \(\text{Re}=10^4\) and \(\text{Pr}=0.69\). The temperature of the ambient air is 30\(^\circ\)C and the thermal conductivity of air is \(k\) = 0.02 W/m.K.

1. Find the heat flux from the surface at steady state.

2. Find the steady state surface temperature of the casing.

3. Find the temperature of the casing at steady state for stagnant air. Why is this situation physically infeasible?

• Answer