GATE Mechanical Engineering

Consider incompressible laminar flow over a flat plate with freestream velocity of $u_{\infty}$. The Nusselt number corresponding to this flow velocity is $Nu_1$. If the freestream...

Consider a hydrodynamically fully developed laminar flow through a circular pipe with the flow along the axis (i.e., z direction). In the following statements, $T$ is the temperatu...

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...

Consider incompressible laminar flow of a constant property Newtonian fluid in an isothermal circular tube. The flow is steady with fully-developed temperature and velocity profile...

Consider a laterally insulated rod of length L and constant thermal conductivity. Assuming one-dimensional heat conduction in the rod, which of the following steady-state temperatu...

Consider a counter-flow heat exchanger with the inlet temperatures of two fluids (1 and 2) being T 1, in = 300 K and T 2, in = 350 K. The heat capacity rates of the two fluids are...

A cylindrical rod of length ℎ and diameter 𝑑 is placed inside a cubic enclosure of side length 𝐿. 𝑆 denotes the inner surface of the cube. The view-factor F S-S is

A flat plate made of cast iron is exposed to a solar flux of 600 W/m 2 at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate. Cast iron has...

Consider a rod of uniform thermal conductivity whose one end (x = 0) is insulated and the other end (x = L) is exposed to flow of air at temperature T ∞ with convective heat transf...

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 l...

Which of the following non-dimensional terms is an estimate of Nusselt number?

Saturated vapor at 200 °C condenses to saturated liquid at the rate of 150 kg/s on the shell side of a heat exchanger (enthalpy of condensation h fg = 2400 kJ/kg). A fluid with C p...

Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of...

Saturated steam at $${100^ \circ }C$$ condenses on the outside of a tube. Cold fluid enters the tube at $${20^ \circ }C$$ and exits at $${50^ \circ }C.$$ The value of the Log Mean...

A metal ball of diameter $$60mm$$ is initially at $${220^ \circ }C.$$ The ball is suddenly cooled by an air jet of $${20^ \circ }C.$$ The heat transfer coefficient is $$200\,W/{m^2...

In a counter-flow heat exchanger, water is heated at the rate of $$1.5kg/s$$ from $$\,40{}^ \circ C\,$$ to $$\,80{}^ \circ C\,$$ by an oil entering at $$\,120{}^ \circ C\,$$ and le...

The heat loss from a fin is $$6W.$$ The effectiveness of the fin are $$3$$ and $$0.75,$$ respectively. The heat loss (in $$W$$) from the fin, keeping the entire fin surface at base...

Heat is generated uniformly in a long solid cylindrical rod ( diameter $$ = 10\,\,mm$$) at the rate of $$4 \times {10^7}\,\,W/{m^3}.$$ The thermal conductivity of the rod material...

The emissive power of a blackbody is $$P.$$ If its absolute temperature is doubled, the emissive power becomes

Grashof number signifies the ratio of

A steel ball of $$10$$ $$mm$$ diameter at $$1000$$ $$K$$ is required to be cooled to $$350$$ $$K$$ by immersing it in a water environment at $$300$$ $$K.$$ The convective heat tran...

A hollow cylinder has length $$L,$$ inner radius $${{r_1}}$$, outer radius $${{r_2}}$$, and thermal conductivity $$k.$$ The thermal resistance of the cylinder for radial conduction...

Two large parallel plates having a gap of $$10$$ $$mm$$ in between them are maintained at temperatures $${T_1} = 1000\,\,K$$ and $${T_2} = 400\,\,K$$ Given emissivity values, $${\v...

Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $${R_0}$$ and that of the inner cylinder is $...

Consider a parallel-flow heat exchanger with area $${A_p}$$ and a counter-flow heat exchanger with area $${A_c}.$$ In both the heat exchangers, the hot stream flowing at $$1$$ $$kg...

For a heat exchanger, $$\Delta {T_{\max }}$$ is the maximum temperature difference and $$\Delta {T_{\min }}$$ is the minimum temperature difference between the two fluids. $$LMTD$$...

A cylindrical steel rod, $$0.01$$ $$m$$ in diameter and $$0.2$$ $$m$$ in length is first heated to $${750^ \circ }C$$ and then immersed in a water bath at $${100^ \circ }C.$$ The h...

A fluid (Prandtl number, $$Pr=1$$) at $$500$$ $$K$$ flows over a flat plate of $$1.5$$ $$m$$ length, maintained at $$300$$ $$K.$$ The velocity of the fluid is $$10\,\,m/s.$$ Assumi...

A plastic sleeve of outer radius $${r_0} = 1\,\,mm$$ covers a wire (radius $$r = 0.5$$ $$mm$$) carrying electric current. Thermal conductivity of the plastic is $$0.15\,\,W/m$$-$$K...

The ratio of momentum diffusivity $$\left( \upsilon \right)$$ to thermal diffusivity $$\left( \alpha \right),$$ is called

In the laminar flow of air $$(Pr=0.7)$$ over a heated plate, if $$\delta $$ and $${\delta _T}$$ denote, respectively the hydrodynamic and thermal boundary layer thickness, then

A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of $$4 \times {10^7}\,\,W/{m^3}.$$ The rod is cooled by a liquid (convective heat...

The total emissive power of a surface is $$500$$ $$W/{m^2}$$ at a temperature $${T_1}$$ and $$1200$$ $$W/{m^2}$$ at a temperature $${T_2}$$, where the temperatures are in Kelvin. A...

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

The Blasius equation related to boundary layer theory is a

For flow through a pipe of radius $$R,$$ the velocity and temperature distribution are as follows: $$U\left( {r,x} \right) = {C_1}$$ and $$T\left( {r,x} \right) = {C_2}\left[ {1 -...

A $$10$$ $$mm$$ diameter electrical conductor is covered by an insulation of $$2$$ $$mm$$ thickness. The conductivity of the insulation is $$0.08$$ $$W/m$$-$$K$$ and the convection...

Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $${c_r} = {{{c_{\min }}} \over {{c_{\max }}}}.$$ The effectiveness $$(s)$$ of the conden...

A balanced counter-flow heat exchanger has a surface area of $$20\,\,{m^2}$$ and overall heat transfer coefficient of $$20$$ $$W/{m^2}$$-$$K$$. Air $$\left( {{C_p} = 1000J/kg - K}...

A brick wall $$\,\left( {k = 0.9{W \over {m.K}}} \right)$$ of thickness $$0.18$$ $$m$$ separates the warm air in a room from the cold ambient air. On a particular winter day, the o...

A double-pipe counter-flow heat exchanger transfers heat between two water streams. Tube side water at $$19$$ liter/s is heated from $${10^ \circ }C$$ to $${38^ \circ }C$$. Shell s...

Consider a long cylindrical tube of inner and outer radii, $${r_i}$$ and $${r_0}$$ , respectively, length, $$L$$ and thermal conductivity, $$k.$$ Its inner and outer surfaces are m...

Two infinite parallel plates are placed at a certain distance apart. An infinite radiation shield is inserted between the plates without touching any of them to reduce heat exchang...

Biot number signifies the ratio of

In a concentric counter flow heat exchanger, water flows through the inner tube at $${25^ \circ }C$$ and leaves at $${42^ \circ }C$$. The engine oil enters at $${100^ \circ }C$$ an...

In a heat exchanger, it is observed that $$\Delta {T_1} = \Delta {T_2},$$ where $$\Delta {T_1}$$ is the temperature difference between the two single phase fluid streams at one end...

For laminar forced convection over a flat plate, if the free stream velocity increases by a factor of $$2,$$ the average heat transfer coefficient

As the temperature increases, the thermal conductivity of a gas

Match Group $$A$$ with Group $$B$$ Group-A $$P:$$$$\,\,\,\,\,\,\,$$ Biot number $$Q:$$$$\,\,\,\,\,\,\,$$ Grashof number $$R:$$$$\,\,\,\,\,\,\,$$ Prandtl number $$S:$$$$\,\,\,\,\,\,...

A plane wall has a thermal conductivity of $$1.15$$ $$W/m.K.$$ If the inner surface is at $${1100^ \circ }C$$ and the outer surface is at $${350^ \circ }C$$, then the design thickn...

Water flows through a tube of diameter $$25mm$$ at an average velocity of $$1.0m/s.$$ The properties of water are $$\rho = 1000\,\,kg/{m^3},$$ $$\mu = 7.25 \times {10^{ - 4}}\,\,N....

A hemispherical furnace of $$1$$ $$m$$ radius has the inner surface (emissivity, $$\varepsilon = 1$$) of its roof maintained at $$800K,$$ while its floor $$\left( {\varepsilon = 0....

The non-dimensional fluid temperature profile near the surface of a convectively cooled flat plate is given by $${{{T_w} - T} \over {{T_w} - {T_\infty }}} = a + b{y \over L} + c{\l...

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of $$400$$ $$K$$ and $$300$$ $$K.$$ If the emissivities of the surfaces are $$0.8$$...

Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length...

Consider one-dimensional steady state heat conduction along x-axis $$\left( {0 \le x \le L} \right),$$ through a planewall with the boundary surfaces $$(x=0$$ and $$x=L)$$ maintain...

Water (specific heat, $${c_p} = 4.18\,\,kJ/kgK$$ ) enters a pipe at a rate of $$0.01$$ $$kg/s$$ and temperature of $${20^ \circ }C.$$ The pipe, of diameter $$50$$ $$mm$$ and length...

A steel ball of diameter $$60$$ $$mm$$ is initially in thermal equilibrium at $${1030^ \circ }C$$ in a furnace. It is suddenly removed from the furnace and cooled in ambient air at...

Which one of the following configurations has the highest fin effectiveness?

Water $$\left( {{C_p} = 4.18\,kJ/kg.K} \right)$$ at $${80^ \circ }C$$ enters a counter flow heat exchanger with a mass flow rate of $$0.5kg/s.$$ Air $$\left( {{C_p} = 1\,kJ/kg.\,K}...

For an opaque surface, the absorptivity $$\left( \alpha \right),$$ transmissivity $$\left( \tau \right)$$ and reflectivity $$\left( \rho \right)$$ are related by the equation:

A pipe of $$25$$ $$mm$$ outer diameter carries steam. The heat transfer coefficient between the cylinder and surrounding is $$5$$ $$W/{m^2}K.$$ It is propsed to reduce the heat los...

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 $${1 \over 2}$$ and $...

In a condenser of a power plant, the steam condenses at a temperature of $${60^ \circ }C.$$ The cooling water enters at $${30^ \circ }C$$ and leaves at $${45^ \circ }C.$$ The logar...

A spherical steel ball of $$12mm$$ diameter is initially at $$100K.$$ It is slowly cooled in a surrounding of $$300K.$$ The heat transfer coefficient between the steel ball and the...

Match the following List-$${\rm I}$$ $$P.$$ Compressible flow $$Q.$$ Free surface flow $$R.$$ Boundary layer flow $$S.$$ Pipe flow $$T.$$ Heat convection List-$${\rm II}$$ $$U.$$ R...

A fin has $$5mm$$ diameter and $$100mm$$ length. The thermal conductivity of fin material is $$400W/m K.$$ One end of the fin is maintained at $${130^ \circ }C$$ and its remaining...

In a parallel flow heat exchanger operating under steady state, the heat capacity rates (product of specific heat at constant pressure and mass flow rate) of the hot and cold fluid...

Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black sur...

A coolant fluid at $${30^ \circ }C$$ flows over a heated flat plate maintained at a constant temperature of $${100^ \circ }C$$. The boundary layer temp distribution at a given loca...

Radiative heat transfer is intended between the inner surfaces of two very largen isothermal parallel metal plates. While the upper plate (designated as plate $$1$$) is a black sur...

A hollow enclosure is formed between two infinitely concentric cylinders of radii $$1m$$ and $$2m$$ respectively. Radiative heat exchange takes place between the inner surface of t...

For flow of fluid over a heated plate, the following fluid properties are known: Viscosity $$=0.001Pa.s;$$ Specific heat at constant pressure $$=1$$ $$kJ/kgK;$$ Thermal conductivit...

The $$LMTD$$ of a counter flow heat exchanger is $${20^ \circ }C$$. The cold fluid enters at $${20^ \circ }C$$ and the hot fluid enters at $${100^ \circ }C$$. Mass flow rate of the...

The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by $$\left( {T - {T_w}} \right)/\left( {{T_\infty } - {T_w}} \right) =...

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 coo...

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatu...

In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass flow rate of the hot fluid is $$1$$ $$Kg/s$$ and that of co...

Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3}.$$ The left and right faces are kept at constant temperatu...

Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp under these conditions is $${10.17^0}C$$. The outside temp is $...