# Recent questions and answers in Heat Transfer

The spectral distribution of radiation from a black body at $T_1=3000 \: K$ has a maximum at wavelength $\lambda_{\text{max}}$. The body cools down to a temperature $T_2$. If the wavelength corresponding to the maximum of the spectral distribution at $T_2$ is $1.2$ times of the original wavelength $\lambda_{\text{max}}$, then the temperature $T_2$ is _________ $K$ (round off to nearest integer)
Match the following ... $P-1,\:Q-1,\:R-3\:,S-2$ $P-3,\:Q-3,\:R-1\:,S-3$ $P-4,\:Q-3,\:R-2\:,S-1$
In a concentric tube counter-flow heat exchanger, hot oil enters at $102^{\circ}C$ and leaves at $65^{\circ}C$. Cold water enters at $25^{\circ}C$ and leaves at $42^{\circ}C$. The log mean temperature difference $(LMTD)$ is ________ $^{\circ}C$ (round off to one decimal place).
A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ in $4.35$ ... the convective heat transfer coefficient $(in\:W/m^{2}.K)$ between the metal bead and the fluid stream is $283.3$ $299.8$ $149.9$ $449.7$
A plane slab of thickness $L$ and thermal conductivity $k$ is heated heated with a fluid on one side $(P)$, and the other side $(Q)$ is maintained at a constant temperature, $T_Q$ of $25^{\circ}C$, as shown in the figure, the fluid is at $45^{\circ}C$ and ... $T_P$ (in $^{\circ}$C) of the side which is exposed to the fluid is _____ (correct to two decimal places)
Sphere $1$ with a diameter of $0.1$ m is completely enclosed by another sphere $2$ of diameter $0.4$m. The view factor $F_{12}$ is $0.0625$ $0.25$ $0.5$ $1.0$
One-dimensional steady state heat conduction takes places through a solid whose cross-sectional area varies linearly in the direction of heat transfer. Assume there is no heat generation in the solid and the thermal conductivity of the material is constant and independent of temperature. The temperature distribution in the solid is Linear Quadratic Logarithmic Exponential
A thin vertical flat plate of height $L$, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The temperatures of the plate and the surroundings by natural convection. The temperatures of the plate and the surroundings ... first plate is $h_1$ and that for the second plate is $h_2$, the value of the ratio $h_1/h_2$ is ____________
Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids are $C_h=2000 \: W/K$ and $C_c =1200 \: W/K$, respectively. If the outlet temperature of ... is $45^{\circ} C$, the log mean temperature difference (LMTD) of the heat exchanger is __________ $K$ (round off to two decimal places).
A slender rod of length $L$, diameter $d$ $(L > >d)$ and thermal conductivity $k_1$ is joined with another rod of identical dimensions, but of thermal conductivity $k_2$, to form a composite cylindrical rod of length $2L$. The heat transfer in radial direction and contact resistance are ... the composite rod is $k_1+k_2 \\$ $\sqrt{k_1k_2} \\$ $\dfrac{k_1k_2}{k_1+k_2} \\$ $\dfrac{2k_1k_2}{k_1+k_2}$
A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\circ}C$ and the bulk modulus is $200$ GPa. If the cube is constrained all around and heated uniformly to $42^{\circ}C$, then the magnitude of volumetric (mean) stress (in MPa) included due to heating is _______
Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat generation with an average value equal to $10000 \: Wm^{-3}$, while the left and right slabs have no internal ... $T_1$ is measured to be $100^{\circ} C$, the right extreme face temperature $T_2$ is ______$^{\circ} C$.
Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 cm^2$. The specific heat of air $C_p$ is $1008$ J/kg.K. The exit temperature of the air is $516$ K $532$ K $484$ K $468$ K
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Air enters an adiabatic nozzle at $300$ kPa, $500$ K with a velocity of $10$ m/s. It leaves the nozzle at $100$ kPa with a velocity of $180$ m/s. The inlet area is $80 \: cm^2$. The specific heat of air $C_p$ is $1008$ J/kg.K. The exit area of the nozzle in $cm^4$ is $90.1$ $56.3$ $4.4$ $12.9$
A solid steel cube constrained on all six faces is heated so that the temperature rises uniformly by $\Delta T$. If the thermal coefficient of the material is $\alpha$, Young's modulus is $E$ and the Poisson's ratio is $\upsilon$ ... $-\dfrac{\alpha (\Delta T) E}{3 (1-2 \upsilon)}$
Water $(C_p=4.18 \: kJ/kg.K)$ at $80^{\circ} C$ enters a counterflow heat exchanger with a mass flow rate of $0.5 \: kg/s$. Air ($C_p=1 \: kJ/kg.K$) enters at $30^{\circ} C$ with a mass flow rate of $2.09 \: kg/s$. If the effectiveness of heat exchanger is $0.8$, the LMTD (in $^{\circ} C$) is $40$ $20$ $10$ $5$
Which one of the following configurations has the highest fin effectiveness? Thin, closely spaced fins Thin, widely spaced fins Thick, widely spaced fins Thick, closely spaced fins
During $\textit{normalizing}$ process of steel, the specimen is heated between the upper and lower critical temperature and cooled in still air above the upper critical temperature and cooled in furnace above the upper critical temperature and cooled in still air between the upper and lower critical temperature and cooled in furnace
The radiative heat transfer rate per unit area $(W/m2)$ between two plane parallel grey surfaces (emissivity $0.9$) maintained at $400 \: K$ and $300 \: K$ is (Stefan Bottzman constant $\sigma=5.67 \times 10^{-6} W/m^2K^4$) $1020$ $464$ $812$ $567$
The relation ${p^{V}}^{\gamma}$= constant, where $\gamma$ is the ratio of the specific heats of ideal gad=s, is applicable o Any adiabatic process Only reversible adiabatic process Only irreversible adiabatic process Only isothermal process
Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\circ}C$ and exists at $22^{\circ}C$. The total surface area of the tubes is $50 \: m^2$, ... transfer coefficient is $2000 \: W/m^2 \: K$. The heat transfer (in $MW$) to the condenser is _________ (correct to two decimal places).
A $0.2 \:m$ thick infinite black plate having a thermal conductivity of $3.96 \: W/m-K$ is exposed to two infinite black surfaces at $300 \: K$ and $400 \: K$ as shown in the figure. At steady state, the surface temperature of the plate facing the cold ... Assuming $1-D$ heat conduction, the magnitude of the heat flux through the place (in $W/m^2$) is ___________ (correct to two decimal places)
The peak wavelength of radiation emitted by a black body at a temperature of $2000 \: K$ is $1.45 \: \mu m$. If the peak wavelength of emitted radiation changes to $2.90 \: \mu m$, then the temperature (in $K$) of the black body is $500$ $1000$ $4000$ $8000$
Which one of the following statements is correct for a superheated vapour? Its pressure is less than the saturation pressure at a given temperature Its temperature is less than the saturation temperature at a given pressure Its volume is less than the volume of the saturated vapour at a given temperature Its enthalpy is less than the enthalpy of the saturated vapour at a given pressure
Two optically flat plates of glass are kept at a small angle $\theta$ as shown in the figure. Monochromatic light is incident vertically. If the wavelength of light used to get a fringe spacing of $1$ $mm$ is $450$ $nm$, the wavelength of light (in $nm$) to get a fringe spacing of $1.5$ $mm$ is _________
In a counter-flow heat exchanger, water is heated at the rate of $1.5 \: kg/s$ from $40^{\circ}$ C to $80^{\circ} \: C$ by an oil entering at $120^{\circ}$ C and leaving at $60 ^{\circ}$ C. The specific heats of water and oil are $4.2 \: kJ/kg.K$ ... heat transfer coefficient is $400 W/m^{2}.K$. The required heat transfer surface area (in $m^{2}$) is $0.104$ $0.022$ $10.4$ $21.84$
A metal ball of diameter $60$ mm is initially at $220^{\circ}$ C. The ball is suddenly cooled by an air jet of $20^{\circ}$ C. The heat transfer coefficient is $200 W/m^{2}.K$. The specific heat, thermal conductivity and density of the metal ball are $400$ J/kg.K, ... $^{\circ} C$) after $90$ seconds will be approximately $141$ $163$ $189$ $210$
The emissive power of a blackbody is $P$. If its absolute temperature is doubled, the emissive power becomes $2 P$ $4 P$ $8 P$ $16 P$
The heat loss from a fin is $6$ W. The effectiveness and efficiency of the fin are $3$ and $0.75$, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is _______.
A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature $\Delta T=100^{\circ}C$. If the coefficient of thermal expansion and Young's modulus of elasticity of steel are $11 \times 10^{-6}/^{\circ} C$ and $200$ GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is _______
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 is $25 W/m.K$. Under steady state conditions, the temperature difference between the centre and the surface of the rod is ______ $^{\circ} C$.
Two black surfaces, AB and BC, of lengths $5$ m and $6$ m, respectively, are oriented as shown. Both surfaces extend infinitely into the third dimension. Given that view factor $F_{12}=0.5, T_{1}=800 K, T_{2}=600 K, T_{\text{surrounding}}=300 K$ and Stefan-Boltzmann ... $2$ to the surrounding environment is _______ kW.
A heat pump absorbs $10$kW of heat from outside environment at $250$ K while absorbing $15$ kW of work. It delivers the heat to a room that must be kept warm at $300$ K. The Coefficient of Performance (COP) of the heat pump is ________.
The molar specific heat at constant volume of an ideal gas is equal to $2.5$ times the universal gas constant ($8.314$ J/mol.K). When the temperature increases by $100$K, the change in molar specific enthalpy is __________ J/mol.
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 Temperature Difference (LMTD) is ________ $^{\circ}$ C.
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 conductivity of steel ... $k=43 \: W/m-K$, respectively. The time required for the rod to reach $300^ \circ C$ is ________ seconds.
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 __________
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 and the ... $C_{\text{max}} \triangle T_{\text{max}}$ $C_{\text{max}} \triangle T_{\text{min}}$
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
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 __________