List of top Fluid Mechanics and Thermal Sciences Questions

Consider a slab of 20mm thickness. There is a uniform heat generation of \(\dot{q}\) = 100MW/m³ inside the slab. The left and right faces of the slab are maintained at 150°C and 110°C, respectively. The plate has a constant thermal conductivity of 200W/(m.K). Considering a 1-D steady state heat conduction, the location of the maximum temperature from the left face will be at (answer in integer).

A condenser is used as a heat exchanger in a large steam power plant in which steam is condensed to liquid water. The condenser is a shell and tube heat exchanger which consists of 1 shell and 20,000 tubes. Water flows through each of the tubes at a rate of 1kg/s with an inlet temperature of 30°C. The steam in the condenser shell condenses at the rate of 430kg/s at a temperature of 50°C. If the heat of vaporization is 2.326MJ/kg and specific heat of water is 4kJ/(kg.K), the effectiveness of the heat exchanger is _____ (rounded off to 3 decimal places).

A furnace can supply heat steadily at 1200 K at a rate of 24000 kJ/min. The maximum amount of power (in kW) that can be produced by using the heat supplied by this furnace in an environment at 300 K is

Which one of the following statements regarding a Rankine cycle is FALSE?

The velocity field of a two-dimensional, incompressible flow is given by
\(\overrightarrow{V} = 2 sinh\ x\ \vec{i} + v(x, y)\vec{j}\)
where \(\vec{i}\ \text{and}\ \vec{j}\) denote the unit vectors in x and y directions, respectively. If v(x, 0) = cosh x, then v(0, -1) is

Consider incompressible laminar flow over a flat plate with freestream velocity of u_∞. The Nusselt number corresponding to this flow velocity is Nu₁. If the freestream velocity is doubled, the Nusselt number changes to Nu₂. Choose the correct option for Nu₂/Nu₁.

Given below are two statements:
Statement I: Viscosity of liquids decreases with increase in temperature.
Statement II: Viscosity of liquids is appreciably affected by change in pressure.
In the light of the above statements, choose the correct answer from the options given below:

Match List I with List II

List I		List II
A.	Number of transfer units	I	Boiler
B.	Periodic flow of heat exchanger	II	Deposition on heat exchanger
C.	Phase change	III	A measure of size of heat exchanger
D.	Fouling factor	IV	Regenerators

Choose the correct answer from the options given below:

An engine running on an air standard Otto cycle has a displacement volume of 250 cm\(^3\) and a clearance volume of 35.7 cm\(^3\). The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ________________ kPa (round off to the nearest integer).

A steady two-dimensional flow field is specified by the stream function \[ \psi = k x^3 y, \] where \( x \) and \( y \) are in meter and the constant \( k = 1 \, \text{m}^2 \text{s}^{-1} \). The magnitude of acceleration at a point \( (x, y) = (1 \, \text{m}, 1 \, \text{m}) \) is ________________ m/s² (round off to 2 decimal places).

Consider a solid slab (thermal conductivity, \( k = 10 \, \text{W}\cdot\text{m}^{-1}\cdot\text{K}^{-1} \)) with thickness 0.2 m and of infinite extent in the other two directions as shown in the figure. Surface 2, at 300 K, is exposed to a fluid flow at a free stream temperature (\( T_{\infty} \)) of 293 K, with a convective heat transfer coefficient (\( h \)) of 100 W\( \cdot\text{m}^{-2}\cdot\text{K}^{-1} \). Surface 2 is opaque, diffuse and gray with an emissivity (\( \varepsilon \)) of 0.5 and exchanges heat by radiation with very large surroundings at 0 K. Radiative heat transfer inside the solid slab is neglected. The Stefan-Boltzmann constant is \( 5.67 \times 10^{-8} \, \text{W}\cdot\text{m}^{-2}\cdot\text{K}^{-4} \). The temperature \( T_1 \) of Surface 1 of the slab, under steady-state conditions, is ________________ K (round off to the nearest integer).

During open-heart surgery, a patient’s blood is cooled down to 25°C from 37°C using a concentric tube counter-flow heat exchanger. Water enters the heat exchanger at 4°C and leaves at 18°C. Blood flow rate during the surgery is 5 L/minute.
Use the following fluid properties: \[ \begin{array}{|c|c|c|} \hline \text{Fluid} & \text{Density (kg/m}^3\text{)} & \text{Specific heat (J/kg-K)}
\hline \text{Blood} & 1050 & 3740
\text{Water} & 1000 & 4200
\hline \end{array} \] Effectiveness of the heat exchanger is ________________ (round off to 2 decimal places).

In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________________ kJ/kg (round off to 2 decimal places).

Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80°C, and the heat transfer rate per unit area to low temperature side B is 4.5 kW/m². The thermal conductivity of the slab is 15 W/m·K. The rate of entropy generation per unit area during the heat transfer process is ________________ W/m²·K (round off to 2 decimal places).

Consider a rod of uniform thermal conductivity whose one end \( (x = 0) \) is insulated and the other end \( (x = L) \) is exposed to the flow of air at temperature \( T_{\infty} \) with convective heat transfer coefficient \( h \). The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as \[ \dot{q} = \cos \left( \frac{2 \pi x}{L} \right). \] The steady-state temperature at the mid-location of the rod is given as \( T_A \). What will be the temperature at the same location, if the convective heat transfer coefficient increases to \( 2h \)?

Consider steady, one-dimensional compressible flow of a gas in a pipe of diameter 1 m. At one location in the pipe, the density and velocity are 1 kg/m\(^3\) and 100 m/s, respectively. At a downstream location in the pipe, the velocity is 170 m/s. If the pressure drop between these two locations is 10 kPa, the force exerted by the gas on the pipe between these two locations is ________________ N.

A solid spherical bead of lead (uniform density = 11000 kg/m\(^3\)) of diameter \( d = 0.1 \) mm sinks with a constant velocity \( V \) in a large stagnant pool of a liquid (dynamic viscosity = \( 1.1 \times 10^{-3} \) kg·m\(^{-1}\)·s\(^{-1}\)). The coefficient of drag is given by \[ C_D = \frac{24}{Re}, \] where the Reynolds number \( Re \) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as \[ D = (C_D)(0.5 \rho V^2)\left( \frac{\pi d^2}{4} \right), \] where \( \rho \) is the density of the liquid. Neglect the buoyancy force. Using \( g = 10 \) m/s\(^2\), the velocity \( V \) is ________________ m/s.

The figure shows a purely convergent nozzle with a steady, inviscid compressible flow of an ideal gas with constant thermophysical properties operating under choked condition. The exit plane shown in the figure is located within the nozzle. If the inlet pressure (P0) is increased while keeping the back pressure (Pback) unchanged, which of the following statements is/are true?

A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m³ to a final volume of 2.5 m³. The polytropic index is given by \( n = 1.2 \). The absolute value of the work done during the process is ________________ kJ (round off to 2 decimal places).

A flat plate made of cast iron is exposed to a solar flux of 600 W/m² at an ambient temperature of 25°C. Assume that the entire solar flux is absorbed by the plate. Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant = \( 5.669 \times 10^{-8} \, \text{W/m}^2 \text{K}^4 \). Neglect all other modes of heat transfer except radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is ________________ °C (round off to the nearest integer).

In the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature \( T_\infty \) (g is the gravitational acceleration, \( \beta \) is the volumetric thermal expansion coefficient, \( \nu \) is the kinematic viscosity, \( u \) and \( v \) are the velocities in \( x \) and \( y \) directions, respectively, and \( T \) is the temperature) \[ u \frac{\partial u}{\partial x} + v \frac{\partial u}{\partial y} = g \beta (T - T_\infty) + \nu \frac{\partial^2 u}{\partial y^2}, \] the term \( g \beta (T - T_\infty) \) represents

A tiny temperature probe is fully immersed in a flowing fluid and is moving with zero relative velocity with respect to the fluid. The velocity field in the fluid is \[ \mathbf{V} = (2x) \hat{i} + (y + 3t) \hat{j}, \] and the temperature field in the fluid is \[ T = 2x^2 + xy + 4t, \] where \(x\) and \(y\) are the spatial coordinates, and \(t\) is the time. The time rate of change of temperature recorded by the probe at \( (x = 1, y = 1, t = 1) \) is ________________.

The Clausius inequality holds good for

Wien's law is stated as \( \lambda_m T = C \), where \( C = 2898\ \mu\text{mK} \) and \( \lambda_m \) is the wavelength at which the emissive power of a black body is maximum for a given temperature T. The spectral hemispherical emissivity curve shows a maximum at \( \lambda_m \approx 6000\ \text{\AA} \). The temperature at which the total hemispherical emissivity is highest is ________________ K (nearest integer).

At steady state, 500 kg/s of steam enters a turbine with specific enthalpy \(h_1 = 3500\ \text{kJ/kg}\) and entropy \(s_1 = 6.5\ \text{kJ . kg}^{-1}\text{K}^{-1}\). It expands reversibly in the turbine at 500 K. Exit properties: \(h_2 = 2500\ \text{kJ/kg}\), \(s_2 = 6.3\ \text{kJ . kg}^{-1}\text{K}^{-1}\). Find turbine work output (MW, integer).