List of top Fluid Mechanics and Thermal Sciences Questions on Thermodynamics asked in GATE ME

During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, 85% of the power is absorbed within a circle of radius 5 mm while 65% is absorbed within an inner concentric circle of radius 3 mm. The power density in the shaded area is _________ W mm^-2 (rounded off to 2 decimal places).

Let a spherical block of ice at -7 °C be exposed to atmospheric air at 30 °C with the gravitational direction as shown in the figure below. What will be the overall direction of air flow in this situation?

Consider a cylindrical furnace of 5 m diameter and 5 m length with bottom, top, and curved surfaces maintained at uniform temperatures of 800 K, 1500 K, and 500 K, respectively. The view factor between the bottom and top surfaces, \( F_{12} \), is 0.2. The magnitude of net radiation heat transfer rate between the bottom surface and the curved surface is _________ kW (rounded off to 1 decimal place).
[All surfaces of the furnace can be assumed as black.]
[The Stefan-Boltzmann constant, \( \sigma = 5.67 \times 10^{-8} \, {W m}^{-2} \, {K}^{-4} \)] 

Water enters a tube of diameter, \( D = 60 \, {mm} \) with mass flow rate of 0.01 kg/s\(^{-1}\) as shown in the figure below. The inlet mean temperature is \( T_{{in},i} = 293 \, {K} \) and the uniform heat flux at the surface of the tube is 2000 W/m\(^{-2}\). For the exit mean temperature of \( T_{{m},o} = 353 \, {K} \), the length of the tube, \( L \) is _________m (rounded off to 1 decimal place).
Use the specific heat of water as 4181 J kg\(^{-1}\) K\(^{-1}\).

A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are 3344 kJ/kg and 6.5 kJ/kg·K, respectively. The turbine isentropic efficiency is 0.9, and the mass flow rate of steam at the turbine inlet is 102 kg/s. The turbine power output is _________ MW (rounded off to 1 decimal place).

A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ. During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is _________ kJ (rounded off to 1 decimal place). Specific heat of hydrogen at constant pressure = 14.56 kJ kg\(^{-1}\) K\(^{-1}\)
Specific heat of hydrogen at constant volume = 10.4 kJ kg\(^{-1}\) K\(^{-1}\)

A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).

During a welding operation, thermal power of 2500 W is incident normally on a metallic surface. As shown in the figure below (figure is NOT to scale), the heated area is circular. Out of the incident power, 85% of the power is absorbed within a circle of radius 5 mm while 65% is absorbed within an inner concentric circle of radius 3 mm. The power density in the shaded area is _________ W mmsuperscript{-2 (rounded off to 2 decimal places).}

 

Consider a cylindrical furnace of 5 m diameter and 5 m length with bottom, top and curved surfaces maintained at uniform temperatures of 800 K, 1500 K and 500 K, respectively. The view factor between the bottom and top surfaces, \( F_{12} \), is 0.2. The magnitude of net radiation heat transfer rate between the bottom surface and the curved surface is _________ kW (rounded off to 1 decimal place).
\[ {All surfaces of the furnace can be assumed as black.} \] \[ {The Stefan-Boltzmann constant, } \sigma = 5.67 \times 10^{-8} \, {W m}^{-2} \, {K}^{-4} \] 

 

Water enters a tube of diameter, \( D = 60 \, {mm} \) with mass flow rate of 0.01 kg/s\(^{-1}\) as shown in the figure below. The inlet mean temperature is \( T_{{in},i} = 293 \, {K} \) and the uniform heat flux at the surface of the tube is 2000 W/m\(^{-2}\). For the exit mean temperature of \( T_{{m},o} = 353 \, {K} \), the length of the tube, \( L \) is _________m (rounded off to 1 decimal place). \[ {Use the specific heat of water as 4181 J kg}^{-1} \, {K}^{-1} \]

 

A thermal power plant is running with no reheat or regeneration. The specific enthalpy and specific entropy of steam at the turbine inlet are 3344 kJ/kg and 6.5 kJ/kg·K, respectively. The turbine isentropic efficiency is 0.9, and the mass flow rate of steam at the turbine inlet is 102 kg/s. The turbine power output is _________ MW (rounded off to 1 decimal place).