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QUESTION: 1

For the fluid flowing over a flat plate with Prandtl number greater than unity, the thermal boundary layer for laminar forced convection.

[1988]

Solution:

QUESTION: 2

A fluid flowing over a flat plate has the following properties: dynamic viscosity = 25 × 10^{–6} kg/ ms, specific heat = 2.0 kJ/kgK, thermal conductivity 0.05 W/mK. The hydrodynamic boundary layer thickness is measured to be 0.5 mm. The thickness of the thermal boundary layer would be

[1992]

Solution:

Now, δ = 0.5 mm

∴ δ = δ_{t} = 0.5mm

QUESTION: 3

Water (Prandtl number = 6) flows over a flat plate which is heated over the entire length. Which one of the following relationship between the hydrodynamic boundary layer thickness (δ) and thermal boundary layer thickness (δ_{t}) is true

[2001]

Solution:

Here, P_{r} = 6 > 1

or

∴ δ > δ_{t}

QUESTION: 4

Consider a laminar boundary layer over a heated flat plate. The free stream velocity is U_{∝}. At some distance x from the leading edge the velocity boundary layer thickness is δ_{v} and the thermal boundary layer thickness is δ_{T}. If the Prandtl number is greater than 1, then

[2003]

Solution:

Prandtl number

From question, since prandtl number > 1

∴ Velocity boundry thickness (δ_{v}) > thermal boundary thickness (δ_{t})

QUESTION: 5

An un-insulated air conditioning duct of rectangular cross section 1 m × 0.5 m, carrying air at 20°C with a velocity of 10 m/s, is exposed to an ambient of 30°C. Neglect the effect of duct construction material. For air in the range of 20 – 30°C, data is as follows: thermal conductivity = 0.025 W/mK; viscosity = 18 μPa.s; Prandtl number = 0.73; density =1.2 kg/m^{3}. For laminar flow Nusselt number is 3.4 for constant wall temperature conditions and , for turbulent flow, Nu = 0.023 Re^{0.8}Pr^{0.33}.The Reynolds number for the flow is

[2005]

Solution:

Reynolds number,

QUESTION: 6

An un-insulated air conditioning duct of rectangular cross section 1 m × 0.5 m, carrying air at 20°C with a velocity of 10 m/s, is exposed to an ambient of 30°C. Neglect the effect of duct construction material. For air in the range of 20 – 30°C, data is as follows: thermal conductivity = 0.025 W/mK; viscosity = 18 μPa.s; Prandtl number = 0.73; density =1.2 kg/m^{3}. For laminar flow Nusselt number is 3.4 for constant wall temperature conditions and , for turbulent flow, Nu = 0.023 Re^{0.8}Pr^{0.33}.

The heat transfer per meter length of the duct, in watts, is

[2005]

Solution:

As Re > 4000, the flow is turbulent

Surface area of duct

A = 2 × al + 2 × bl

where, l = length of duct

∴ A = 3l

Heat transfer rate, Q = h A(T_{0} – T)

Q = 25.60 × 3l × (30 – 20)

Q/I = 769W

QUESTION: 7

The temperature distribution with in the thermal boundary layer over a heated isothermal flat plate is given by where T_{W} and T_{∝} are the temperatures of plate and free stream respectively, and y is the normal distance measured from the plate. The local Nusselt number based on the thermal boundary layer thickness δ_{t} is given by

[2007]

Solution:

Only (b) satisfies the conditions

QUESTION: 8

For flow of fluid over a heated plate , the following fluid properties are known: viscosity = 0.001 Pa.s; specific heat at constant pressure = 1 kJ/kgK; thermal conductivity = 1 W/mK.

The hydrodynamic boundary layer thickness at a specified location on the plate is 1 mm. The thermal boundary layer thickness at the same location is

[2008]

Solution:

Given:

(Fluid thermal conductivity)

Hydrodynamic boundary layer thickness, δ = 1 mm

QUESTION: 9

A pipe of 25 mm outer diameter carries steam. The heat transfer coefficient between the cylinder and surroundings is 5 W/m^{2}K. It is proposed to reduce the heat loss from the pipe by adding insulation having a thermal conductivity of 0.05 W/mK. Which one of the following statements is TRUE?

[2011]

Solution:

Critical radius of insulation = (k/h)

= 10mm

(r_{outer}) > r_{critical}

Thus, adding insulation shall decrease H.T. Rate.

QUESTION: 10

The ratios of the laminar hydrodynamic boundary layer thickness to thermal boundary layer thickness of flows of two fluids P and Q on a flat plate are 1/2 and 2 respectively. The Reynolds number based on the plate length for both the flows is 10^{4}. The Prandtl and Nusselt numbers for P are 1/8 and 35 respectively. The Prandlt and Nusselt numbers for Q are respectively

[2011]

Solution:

For fluid Q :

⇒ P_{r} = 8

For fluid P : Laminar flow over flat plate

Similarly for fluid Q:

QUESTION: 11

Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.

The free stream velocity is U_{∝} and the freestream temperature T_{∝} is lower than the cylinder surface temperature T_{∝}. The local heat transfer coefficient is minimum at point

[2014]

Solution:

For laminar flow, the heat transfer coefficient is minimum where the boundary layer thickness is maximum and vice versa. For turbulentregion boundary layer thickness is maximum at 3 but for laminar boundary layer thickness is maximum at 2 so minimum heat transfer coefficient.

QUESTION: 12

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by where y is measured perpendicular to the plate, L is the plate length, and a, b and c are arbitrary constants. T_{W} and T_{∝} are wall and ambient temperatures, respectively. If the thermal conductivity of the fluid is k and the wall heat flux is q', the Nusselt number Nu is equal to

[2014]

Solution:

at y = 0

∴ N_{u} = b.

QUESTION: 13

For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is

[2015]

Solution:

QUESTION: 14

The Blausius equation related to boundary layer theory is a

[2015]

Solution:

Blausius equation :

This order non-linear D.E.

QUESTION: 15

For flow through a pipe of radius R, the velocity and temperature distribution are as follows: where C_{1} and C_{2} are constants. The bulk temperature is given by with U_{m} being the mean velocity of flow. The value of T_{m} is

[2015]

Solution:

Since u(r, x) is constant, u_{m} = C_{1}

∴ t_{m} = 0.6C_{2}

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