Highest voted questions in Fluid Mechanics and Thermal Sciences / GO Mechanical

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GATE2016-3-40
The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses and assume the water level in the tank to remain constant. The net horizontal force experienced by the wall is ___________ $kN$. Density of water is $1000 \: kg/m^3$. Acceleration due to gravity $g=10 \: m/s^2$.

The water jet exiting from a stationary tank through a circular opening of diameter $300 \: mm$ impinges on a rigid wall as shown in the figure. Neglect all minor losses ...

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GATE2016-3-41
For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vectors in the $x-y$ Cartesian coordinate system. Identify the CORRECT statements from below. The flow is incompressible. The flow is ... $(2)$ and $(3)$ $(1)$ and $(3)$ $(1)$ and $(2)$ $(3)$ and $(4)$

For a two-dimensional flow, the velocity field is $\overrightarrow{u}=\dfrac{x}{x^2+y^2}\hat{i}+\dfrac{y}{x^2+y^2}\hat{j}$ where$\hat{i}$ and $\hat{j}$ are the basis vec...

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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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GATE2016-3-43
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 heat transfer coefficient is $250 \: W/m^2-K$. The density, specific heat and thermal ... $k=43 \: W/m-K$, respectively. The time required for the rod to reach $300^ \circ C$ is ________ seconds.

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 heat ...

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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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GATE2016-3-19
The blade and fluid velocities for an axial turbine are as shown in the figure. The magnitude of absolute velocity at entry is $300$ $m/s$ at an angle of $65^\circ$ to the axial direction, while the magnitude of the absolute velocity at exit is ... downward direction. Given that the axial (horizontal) velocity is the same at entry and exit, the specific work (in $kJ/kg$) is__________

The blade and fluid velocities for an axial turbine are as shown in the figure.The magnitude of absolute velocity at entry is $300$ $m/s$ at an angle of $65^\circ$ to the...

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GATE2016-3-13
A channel of width $450$ $mm$ branches into two sub-channels having width $300$ $mm$ and $200$ $mm$ as shown in figure. If the volumetric flow rate (taking unit depth) of an incompressible flow through the main channel is $0.9$ $m^3/s$ and the velocity ... velocity in the sub-channel of width $300$ $mm$ is _____________ $m/s$. Assume both inlet and outlet to be at the same elevation.

A channel of width $450$ $mm$ branches into two sub-channels having width $300$ $mm$ and $200$ $mm$ as shown in figure. If the volumetric flow rate (taking unit depth) of...

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GATE2016-3-14
For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves $x^2y^2 = \text{constant}$ $xy^2 = \text{constant}$ $2xy − y^2 \text{constant}$ $xy = \text{constant}$

For a certain two-dimensional incompressible flow, velocity field is given by $2xy\hat{i}-y^2\hat{j}$ . The streamlines for this flow are given by the family of curves$...

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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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GATE2016-3-16
Grashof number signifies the ratio of inertia force to viscous force buoyancy force to viscous force buoyancy force to inertia force inertia force to surface tension force

Grashof number signifies the ratio ofinertia force to viscous forcebuoyancy force to viscous forcebuoyancy force to inertia forceinertia force to surface tension force

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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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GATE2016-2-52
The surface irregularities of electrodes used in an electrochemical machining (ECM) process are $3 \: μm$ and $6 \: μm$ as shown in the figure. If the work-piece is of pure iron and $12V \: DC$ ... $F_e^{+2}$ and the Faraday constant to be $96500$ Coulomb.

The surface irregularities of electrodes used in an electrochemical machining (ECM) process are $3 \: μm$ and $6 \: μm$ as shown in the figure. If the work-piece is of ...

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GATE2016-2-53
For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$ $H=(R+r)+(D+r)$ $H=(R+r)+\sqrt{D^2-R^2}$ $H=(R+r)+\sqrt{2D(R+r)-D^2}$

For the situation shown in the figure below the expression for $H$ in terms of $r$, $R$ and $D$ is $H=D+\sqrt{r^2+R^2}$$H=(R+r)+(D+r)$$H=(R+r)+\sqrt{D^2-R^2}$$H=(R+r)+\sq...

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GATE2016-2-39
The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $45$ percent of its volume is in oil while the rest is in water. The density of the body is _________ $kg/m^3$. The specific gravity of oil is $0.7$ and density of water is $1000$ $kg/m^3$. Acceleration due to gravity $g$ = $10$ $m/s^2$.

The large vessel shown in the figure contains oil and water. A body is submerged at the interface of oil and water such that $45$ percent of its volume is in oil while th...

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GATE2016-2-40
Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary bottom plate at a speed of $3\: m/s$. The flow between the plates is solely due to the motion of the top plate. The ... $N/m^2$. Viscosity of the fluid $μ = 0.44 \:kg/m-s$ and density $\rho = 888 \: kg/m^3$.

Consider fluid flow between two infinite horizontal plates which are parallel (the gap between them being $50 \: mm$). The top plate is sliding parallel to the stationary...

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GATE2016-2-41
Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ at the bottom of an open tank as shown in the figure. The head of the plug has the shape of a semi-cylinder of radius $R$. The tank is filled with a liquid of density $\rho$ up to the tip ... $2\rho R^2gL(1+\dfrac{\pi }{4}) \\$ $\pi R^2\rho gL \\$ $\dfrac{\pi }{2}\rho R^2gL$

Consider a frictionless, massless and leak-proof plug blocking a rectangular hole of dimensions $2R \times L$ at the bottom of an open tank as shown in the figure. The he...

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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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GATE2016-2-43
Two cylindrical shafts $A$ and $B$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperature at all times after they are introduced into the furnace. The temperature variation in the axial ... required (in hours) for the centerline of the shaft B to attain the temperature of $400^ \circ C$ is _______ .

Two cylindrical shafts $A$ and $B$ at the same initial temperature are simultaneously placed in a furnace. The surfaces of the shafts remain at the furnace gas temperatur...

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GATE2016-2-44
A piston-cylinder device initially contains $0.4 \: m^3$ of air (to be treated as an ideal gas) at $100 \: kPa$ and $80^ \circ C$. The air is now isothermally compressed to $0.1 \: m^3$. The work done during this process is ________ $kJ$.

A piston-cylinder device initially contains $0.4 \: m^3$ of air (to be treated as an ideal gas) at $100 \: kPa$ and $80^ \circ C$. The air is now isothermally compressed ...

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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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GATE2016-2-46
A refrigerator uses $R-134a$ as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between $0.14 \: MPa$ and $0.8 \: MPa$.if the mass flow rate of refrigerant is $0.05 \: kg/s$,the rate of heat rejection to the environment is_______$kW$ ... $\text{At } P=0.8 \: MPa, \: h=93.42 \: kJ/kg, \: \text{ (saturated liquid) }$

A refrigerator uses $R-134a$ as its refrigerant and operates on an ideal vapour-compression refrigeration cycle between $0.14 \: MPa$ and $0.8 \: MPa$.if the mass flow ra...

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GATE2016-2-47
The partial pressure of the water vapour in a moist air sample of relative humidity $70\%$ is $1.6 \: kPa$,the total pressure being $101.35 \: kPa$ ... where $p_o=101.325 \: kPa$. The dry bulb temperature of the moist air sample (in $_{}^{\circ}\textrm{C}$) is

The partial pressure of the water vapour in a moist air sample of relative humidity $70\%$ is $1.6 \: kPa$,the total pressure being $101.35 \: kPa$.moist air may be treat...

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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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GATE2016-2-14
Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics is linear exponential quadratic cubic

Assuming constant temperature condition and air to be an ideal gas, the variation in atmospheric pressure with height calculated from fluid statics islinearexponentialqua...

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GATE2016-2-15
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 is $\dfrac{\ln(r_2/r_1)}{2\pi kL} \\$ $\dfrac{\ln(r_1/r_2)}{2\pi kL} \\$ $\dfrac{2\pi kL}{\ln(r_2/r_1)} \\$ $\dfrac{2\pi kL}{\ln(r_1/r_2)}$

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 is$\d...

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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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GATE2016-2-17
The internal energy of an ideal gas is a function of temperature and pressure volume and pressure entropy and pressure temperature only

The internal energy of an ideal gas is a function oftemperature and pressurevolume and pressureentropy and pressuretemperature only

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GATE2016-2-18
The heat removal rate from a refrigerated space and the power input to the compressor are $7.2$ $kW$ and $1.8$ $kW$, respectively. The coefficient of performance (COP) of the refrigerator is ______

The heat removal rate from a refrigerated space and the power input to the compressor are $7.2$ $kW$ and $1.8$ $kW$, respectively. The coefficient of performance (COP) of...

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GATE2016-2-19
Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycles, the pressure ratio is $6$ and the ratio of the specific heats of the working medium is $1.4$. The ratio of minimum to maximum ... $K$) in the regenerative cycle. The ratio of the thermal efficiency of the simple cycle to that of the regenerative cycle is _________

Consider a simple gas turbine (Brayton) cycle and a gas turbine cycle with perfect regeneration. In both the cycles, the pressure ratio is $6$ and the ratio of the specif...

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GATE2016-2-21
In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by $a, b, c$ and $d$. At which temperature will a sample get solutionized the fastest? $a$ $b$ $c$ $d$

In the phase diagram shown in the figure, four samples of the same composition are heated to temperatures marked by $a, b, c$ and $d$.At which temperature will a sample g...

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GATE2016-2-6
A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with the smooth wall and rebounds. The total change (final minus initial) in the momentum of the mass is $-2MV \cos\theta \hat{j}$ $2MV \sin\theta \hat{j}$ $2MV \cos\theta \hat{j}$ $-2MV \sin\theta \hat{j}$

A point mass having mass $M$ is moving with a velocity $V$ at an angle $\theta$ to the wall as shown in the figure. The mass undergoes a perfectly elastic collision with ...

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GATE2016-2-13
The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is $\mid \Psi _1+\Psi _2\mid$ $\Psi _1\Psi _2$ $\Psi _1/\Psi _2$ $\mid\Psi _1-\Psi _2\mid$

The volumetric flow rate (per unit depth) between two streamlines having stream functions $\Psi _1$ and $\Psi _2$ is$\mid \Psi _1+\Psi _2\mid$$\Psi _1\Psi _2$$\Psi _1/\Ps...

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GATE2016-1-44
A fluid (Prandtl number, $P_r=1$) at $500\:K$ flows over a flat plate of $1.5\:m$ length, maintained at $300\: K$. The velocity of the fluid is $10 \: m/s$. Assuming kinematic viscosity,$v=30\times 10^{-6}$ $m^2/s$, the thermal boundary layer thickness (in $mm$) at $0.5 \:m$ from the leading edge is __________

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

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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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GATE2016-1-46
An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $1$) and at the end (subscript $2$) of the process with usual notation are: $p_1 = 100 \: kPa$, $V_1 = 0.2 \: m^3$ ... $R=0.275\:kJ/kg-K$. The magnitude of the work required for the process (in $kJ$) is ________

An ideal gas undergoes a reversible process in which the pressure varies linearly with volume. The conditions at the start (subscript $1$) and at the end (subscript $2$) ...

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GATE2016-1-47
In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at $3 \: MPa$ and $350^ \circ C$. The condenser pressure is $75$ $kPa$. The thermal efficiency of the cycle is ________ percent. Given data: For saturated liquid, at $P=75 \:kPa$ ... $T=350^\circ C$ (superheated steam), $h=3115.3 \: kJ/kg$, $s=6.7428 \: kJ/kg-K$

In a steam power plant operating on an ideal Rankine cycle, superheated steam enters the turbine at$3 \: MPa$ and $350^ \circ C$. The condenser pressure is $75$ $kPa$. Th...

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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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GATE2016-1-40
Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity, $v_w=0.89\times 10^{-6}\:m^2/s$) is flowing through a model pipe of diameter $20 \:mm$. For satisfying the dynamic similarity, the velocity of water (in $m/s$) is __________

Oil (kinematic viscosity, $v_{\text{oil}}=1.0\times 10^{-5} \:m^2/s$) flows through a pipe of $0.5$ $m$ diameter with a velocity of $10$ $m/s$. Water (kinematic viscosity...

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GATE2016-1-41
A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b$ is uniform, while that at a downstream location $c-d$ ... rate, $\dot{m}_{bd}$ leaving through the horizontal section $b-d$ to that entering through the vertical section $a-b$ is ___________

A steady laminar boundary layer is formed over a flat plate as shown in the figure. The free stream velocity of the fluid is $U_o$. The velocity profile at the inlet $a-b...

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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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