Hot questions in Heat Transfer / GO Mechanical

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GATE2015-2-43
A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convective heat transfer coefficient $1000 \: W/m^2-K$) at $25^{\circ}C$. At steady state, the surface temperature (in $K$) of the rod is $308$ $398$ $418$ $448$

A cylindrical uranium fuel rod of radius $5 \: mm$ in a nuclear reactor is generating heat at the rate of $4 \times 107 \: W/m^3$. The rod is cooled by a liquid (convecti...

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GATE2015-3-53
One side of a wall is maintained at $400 \: K$ and the other at $300 \: K$. The rate of heat transfer through the wall is $1000 \: W$ and the surrounding temperature is $25^\circ C$. Assuming no generation of heat within the wall, the irreversibility (in $W$) due to heat transfer through the wall is ________

One side of a wall is maintained at $400 \: K$ and the other at $300 \: K$. The rate of heat transfer through the wall is $1000 \: W$ and the surrounding temperature is $...

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GATE2016-3-15
Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the figure, where $k_A$ , $k_B$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $T_2$ (in $^\circ C$) is __________

Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the fig...

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GATE2016-1-45
For water at $25^\circ C$, $dp_s/dT_s = 0.189 \: kPa/K$ ($p_s$ is the saturation pressure in $kPa$ and $T_s$ is the saturation temperature in $K$) and the specific volume of dry saturated vapour is $43.38 \: m^3/kg$. Assume that the ... vapour. Using the Clausius-Clapeyron equation, an estimate of the enthalpy of evaporation of water at $25^\circ C$ (in $kJ / kg$) is __________

For water at $25^\circ C$, $dp_s/dT_s = 0.189 \: kPa/K$ ($p_s$ is the saturation pressure in $kPa$ and $T_s$ is the saturation temperature in $K$) and the specific volum...

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GATE2016-1-43
An infinitely long furnace of $0.5\:m\times 0. 4 \:m$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom walls are maintained at temperature $T_1=T_3=927^\circ C$ ... loss or gain on side $1$ is_________ $W/m$. Stefan-Boltzmann constant = $5.67 \times 10^{-8}$ $W/m^2-K^4$

An infinitely long furnace of $0.5\:m\times 0. 4 \:m$ cross-section is shown in the figure below. Consider all surfaces of the furnace to be black. The top and bottom wal...

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GATE2015-2-54
A project consists of $7$ activities. The network along with the time durations (in days) for various activities is shown in the figure. The minimum time (in days) for completion of the project is_________

A project consists of $7$ activities. The network along with the time durations (in days) for various activities is shown in the figure.The minimum time (in days) for com...

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GATE2015-1-50
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 coefficient at the insulation surface is $10$ $W/m^2-K$. Addition of ... heat loss continuously increase heat loss to a maximum and then decrease heat loss decrease heat loss to a minimum and then increase heat loss

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 coeffi...

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GATE2015-2-46
For the same values of peak pressure, peak temperature and heat rejection, the correct order of efficiencies for Otto, Dual and Diesel cycles is $\eta _{\text{Otto}}> \eta _{\text{Dual}}> \eta _{\text{Diesel}}$ ... $\eta _{\text{Diesel}}> \eta _{\text{Otto}}> \eta _{\text{Dual}}$

For the same values of peak pressure, peak temperature and heat rejection, the correct order of efficiencies for Otto, Dual and Diesel cycles is$\eta _{\text{Otto}} \eta ...

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GATE2016-1-42
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 transfer coefficient is $1000\:W/m^2-K$. Thermal conductivity of steel is $40\:W/m-K$. The time constant for the cooling process $\tau$ is $16\:s$. The time required (in $s$) to reach the final temperature is __________

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 transfer coeff...

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GATE2016-2-42
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 $1 \: kg/s$ cools from $80^\circ C$ to $50^\circ C$. For the cold stream ... exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio $A_c/A_p$ 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 \: k...

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GATE2015-2-13
Which of the following statements regarding a Rankine cycle with reheating are TRUE? increase in average temperature of heat addition reduction in thermal efficiency drier steam at the turbine exit only $(i)$ and $(ii)$ are correct only $(ii)$ and $(iii)$ are correct only $(i)$ and $(iii)$ are correct $(i)$, $(ii)$ and $(iii)$ are correct

Which of the following statements regarding a Rankine cycle with reheating are TRUE?increase in average temperature of heat additionreduction in thermal efficiencydrier s...

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GATE2016-3-17
The INCORRECT statement about the characteristics of critical point of a pure substance is that there is no constant temperature vaporization process it has point of inflection with zero slope the ice directly converts from solid phase to vapor phase saturated liquid and saturated vapor states are identical

The INCORRECT statement about the characteristics of critical point of a pure substance is thatthere is no constant temperature vaporization processit has point of inflec...

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GATE2015-3-40
A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{2-1}$ is $1/12$ $1/2$ $2$ $12$

A solid sphere $1$ of radius ‘$r$’ is placed inside a hollow, closed hemispherical surface $2$ of radius ‘$4r$’. The shape factor $F_{2-1}$ is$1/12$$1/2$$2$$12$

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GATE2016-2-45
A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat rejected (in $kJ$) to the heat sink at $47^ \circ C$ is __________

A reversible cycle receives $40 \: kJ$ of heat from one heat source at a temperature of $127^ \circ C$ and $37 \: kJ$ from another heat source at $97^ \circ C$. The heat ...

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GATE2015-3-12
Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $C_r = \displaystyle{\frac{C_{\text{min}}}{C_{\text{max}}}}$. The effectiveness $(\varepsilon)$ of the condenser is $\displaystyle{\frac{1-\text{exp}[-NTU(1+C_r)]}{1+C_r}} \\$ ... $\displaystyle{\frac{NTU}{1+NTU}} \\$ $1 - \text{exp}(-NTU)$

Saturated vapor is condensed to saturated liquid in a condenser. The heat capacity ratio is $C_r = \displaystyle{\frac{C_{\text{min}}}{C_{\text{max}}}}$. The effectivenes...

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GATE2016-2-16
Consider the radiation heat exchange inside an annulus between two very long concentric cylinders. The radius of the outer cylinder is $R_o$ and that of the inner cylinder is $R_i$ . The radiation view factor of the outer cylinder onto itself is $1-\sqrt{\dfrac{R_i}{R_o}}\\$ $\sqrt{1-\dfrac{R_i}{R_o}} \\$ $1-\dfrac{R_i}{R_o}^{1/3} \\$ $1-\dfrac{R_i}{R_o}$

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

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GATE2016-1-49
Heat is removed from a molten metal of mass $2$ $kg$ at a constant rate of $10$ $kW$ till it is completely solidified.The cooling curve is shown in the figure Assuming uniform temperature throughout the volume of the metal during solidification,the latent heat of fusion of metal ( in $kJ$/$kg$) is _________

Heat is removed from a molten metal of mass $2$ $kg$ at a constant rate of $10$ $kW$ till it is completely solidified.The cooling curve is shown in the figureAssuming uni...

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GATE2015-1-8
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 thinner than the velocity boundary layer thicker than the velocity boundary layer of the same thickness as the velocity boundary layer not formed at all

For flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer isthinner than the velocity boundar...

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GATE2016-3-18
For a heat exchanger, $\triangle T_{\text{max}}$ is the maximum temperature difference and $\triangle T_{\text{min}}$ is the minimum temperature difference between the two fluids. LMTD is the log mean temperature difference. $C_{\text{min}}$ and $C_{\text{max}}$ are the minimum ... $C_{\text{max}} \triangle T_{\text{max}}$ $C_{\text{max}} \triangle T_{\text{min}}$

For a heat exchanger, $\triangle T_{\text{max}}$ is the maximum temperature difference and $\triangle T_{\text{min}}$ is the minimum temperature difference between the tw...

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GATE2016-2-35
A circular metallic rod of length $250 \: mm$ is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left side and there is a gap of $0.2 \: mm$ between the rod and the wall on the right side. If the ... material of the rod is $200 \: GPa$ and the coefficient of thermal expansion is $10^{−5}$ per $_{}^{\circ}\textrm{C}$.

A circular metallic rod of length $250 \: mm$ is placed between two rigid immovable walls as shown in the figure. The rod is in perfect contact with the wall on the left ...

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GATE2016-3-42
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, $\epsilon _1 = 0.5$, $\epsilon _2=0.25$ and Stefan-Boltzmann constant $\sigma =5.67 \times 10^{−8} \: W/m^2-K^4$, the heat transfer between the plates (in $kW/m^2$) is __________

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, $\ep...

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GATE2015-1-9
For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy, it is sufficient to know only the temperature both temperature and pressure are required to be known both temperature and volume are required to be known both temperature and mass are required to be known

For an ideal gas with constant values of specific heats, for calculation of the specific enthalpy,it is sufficient to know only the temperatureboth temperature and pressu...

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GATE2015-3-11
The ratio of momentum diffusivity $(ν)$ to thermal diffusivity $(\alpha)$, is called Prandtl number Nusselt number Biot number Lewis number

The ratio of momentum diffusivity $(ν)$ to thermal diffusivity $(\alpha)$, is calledPrandtl numberNusselt numberBiot numberLewis number

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GATE Mechanical 2014 Set 2 | Question: 42
A hemispherical furnace of $1$ m radius has the inner surface (emissivity, $\varepsilon =1$) of its roof maintained at $800$ $K$, while its floor ($\varepsilon =5.0$) is kept at $600 K$. Stefan-Boltzmann constant is $5.668 \times 10^−8$ $W / m^2$.$K^4$. The net radiative heat transfer (in $kW$) from the roof to the floor is _______

A hemispherical furnace of $1$ m radius has the inner surface (emissivity, $\varepsilon =1$) of its roof maintained at $800$ $K$, while its floor ($\varepsilon =5.0$) is...

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GATE Mechanical 2014 Set 4 | Question: 48
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 exchange between the plates. Assume that the emissivities of plates and radiation shield are equal ... exchange between the plates with and without the shield is $1/2$ $1/3$ $1/4$ $1/8$

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 he...

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GATE Mechanical 2014 Set 4 | Question: 46
Two identical metal blocks L and M (specific heat = $0.4$ $kJ/kg.K$), each having a mass of $5$ $kg$, are initially at $313$ $K$. A reversible refrigerator extracts heat from block L and rejects heat to block M until the temperature of block L reaches $293$ $K$. The final temperature (in $K$) of block M is _______

Two identical metal blocks L and M (specific heat = $0.4$ $kJ/kg.K$), each having a mass of $5$ $kg$, are initially at $313$ $K$. A reversible refrigerator extracts heat ...

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GATE Mechanical 2014 Set 1 | Question: 41
$1.5$ kg of water is in saturated liquid state at $2$ bar $(vf = 0.001061 \: m^3/kg, uf = 504.0 \: kJ/kg,$ $hf = 505 kJ/kg$). Heat is added in a constant pressure process till the temperature of water reaches $400^ \circ C (v = 1.5493 \: m^3/kg, u = 2967.0 kJ/kg,$ $h = 3277.0 \: kJ/kg)$. The heat added (in $kJ$) in the process is _______

$1.5$ kg of water is in saturated liquid state at $2$ bar $(vf = 0.001061 \: m^3/kg, uf = 504.0 \: kJ/kg,$ $hf = 505 kJ/kg$). Heat is added in a constant pressure proces...

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GATE ME 2013 | Question: 42
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 $0.8$ and the Stefan-Boltzmann constant is $5.67$ × $10^{-8}$ $W$/$m^2$ $K^4$, the net radiation heat exchange rate in $kW$/$m^2$ between the two plates is $0.66$ $0.79$ $0.99$ $3.96$

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 $0.8$...

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GATE Mechanical 2014 Set 4 | Question: 42
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 thickness (in meter) of the wall to maintain a steady heat flux of $2500$ $W/m^2$ should be _______

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...

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GATE Mechanical 2014 Set 1 | Question: 14
Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below. The free stream velocity is $U_\infty$ and the free stream temperature $T_\infty$ is lower than the cylinder surface temperature $T_S$. The local heat transfer coefficient is minimum at point $1$ $2$ $3$ $4$

Consider a two-dimensional laminar flow over a long cylinder as shown in the figure below.The free stream velocity is $U_\infty$ and the free stream temperature $T_\infty...

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GATE ME 2013 | Question: 19
Consider one-dimensional steady state heat conduction along $x$-axis ($0 \leq x \leq L$), through a planewall with the boundary surfaces ($x = 0$ and $x = L$) maintained at temperatures of $0^{\circ} C$ and $100^{\circ}C$. ... . The temperature distribution is linear within the wall. The temperature distribution is symmetric about the mid-plane of the wall.

Consider one-dimensional steady state heat conduction along $x$-axis ($0 \leq x \leq L$), through a planewall with the boundary surfaces ($x = 0$ and $x = L$) maintained...

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GATE Mechanical 2014 Set 1 | Question: 47
In an air-standard Otto cycle, air is supplied at $0.1$ $MPa$ and $308$ $K$. The ratio of the specific heats $(γ)$ and the specific gas constant $(R)$ of air are $1.4$ and $288.8$ $J/kg.K$, respectively. If the compression ratio is $8$ and the maximum temperature in the cycle is $2660$ $K$, the heat (in $kJ/kg$) supplied to the engine is _______

In an air-standard Otto cycle, air is supplied at $0.1$ $MPa$ and $308$ $K$. The ratio of the specific heats $(γ)$ and the specific gas constant $(R)$ of air are $1.4$ a...

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GATE ME 2013 | Question: 51
Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01$ $kg$/$s$ and a temperature of $20^0$ $C$.The pipe, of diameter $50$ $mm$ and length $3$ $m$, is subjected to a wall heat flux ${q_{w}}''$ in $W$/$m^2$: ... $ $W$/$m^2$K$, the temperature in $_{}^{0}\textrm{C}$ at the inner surface of the pipe at the outlet is $71$ $76$ $79$ $81$

Water (specific heat, $c_p$ = $4.18$ $kJ$/$kgK$) enters a pipe at a rate of $0.01$ $kg$/$s$ and a temperature of $20^0$ $C$.Thepipe, of diameter $50$ $mm$ and length $3$ ...

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GATE Mechanical 2014 Set 3 | Question: 42
An amount of $100 \: kW$ of heat is transferred through a wall in steady state. One side of the wall is maintained at $127^{\circ} \: C$ and the other side at $27^{\circ} \: C$. The entropy generated (in $W/K$) due to the heat transfer through the wall is _______

An amount of $100 \: kW$ of heat is transferred through a wall in steady state. One side of the wall is maintained at $127^{\circ} \: C$ and the other side at $27^{\circ}...

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GATE Mechanical 2014 Set 3 | Question: 44
Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $(l)$. The conductivity of one section is $k$ and that of the other is $2k$. The left face of the wall is at $600$ $K$ and the right face is at $300$ $K$. The interface temperature $T_i$ (in $K$) of the composite wall is _______

Heat transfer through a composite wall is shown in figure. Both the sections of the wall have equal thickness $(l)$. The conductivity of one section is $k$ and that of th...

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GATE Mechanical 2014 Set 3 | Question: 48
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 side water at $25$ $litre/s$ is entering at $46^{\circ} \: C$. Assume ... density is $1000 \: kg/m^3$ and specific heat is $4186 \: J/kg.K$. The LM TD (in $^{\circ}C$) is _______

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 $38^{\circ} \: C$....

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GATE Mechanical 2014 Set 1 | Question: 42
Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $30$ $mm$ and thermal conductivity $15$ $W/m.K$. At $x$ = $0$, a constant heat flux, ${q}''$ = $1 105$ $W$/$m^2$ is applied. On ... $250$ $W$/$m^2.K$. The temperature (in $°C$), at $x$ = $0$ is _______

Consider one dimensional steady state heat conduction across a wall (as shown in figure below) of thickness $30$ $mm$ and thermal conductivity $15$ $W/m.K$. At $x$ = $0$,...

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GATE ME 2013 | Question: 9
Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by $k$ = $k_0$ + $bT$ ; where $k_0$ and $b$ are positive ... $x$ increases, the temperature gradient ( $dT$/ $dx$ ) will remain constant be zero increase decrease

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity o...

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GATE ME 2013 | Question: 44
The pressure, temperature and velocity of air flowing in a pipe are $5$ $bar$, $500$ $K$ and $50$ $m$/$s$, respectively. The specific heats of air at constant pressure and at constant volume are $1.005$ $kJ$/$kgK$ and $0.718$ $kJ$/$kgK$, respectively. ... $bar$ and $300$ $K$, respectively, the available energy in $kJ$/$kg$ of the air stream is $170$ $187$ $191$ $213$

The pressure, temperature and velocity of air flowing in a pipe are $5$ $bar$, $500$ $K$ and $50$ $m$/$s$, respectively. The specific heats of air at constant pressure an...

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GATE Mechanical 2014 Set 2 | Question: 48
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 $100^\circ C$ and flows in the annular flow passage. The exit temperature of the engine ... water and oil are $4178 J/kg.K$ and $2130 J/kg.K$, respectively. The effectiveness of this heat exchanger is _______

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 $100^\circ C$ and flo...

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