Heat Transfer MCQ Quiz - Objective Question with Answer for Heat Transfer - Download Free PDF

Explanation:

Forced Convection

• Forced convection is a mechanism of heat transfer in which a fluid (such as air, water, or any other liquid or gas) is forced to flow over a surface or through a channel by an external device, such as a fan, pump, or blower. The external device generates motion in the fluid, facilitating the transfer of heat between the surface and the fluid. Forced convection is widely employed in various industrial and engineering applications due to its efficiency in transferring heat over large surfaces or volumes.
• In forced convection, the rate of heat transfer is significantly higher compared to natural convection. This is because the external force increases the velocity of the fluid, reducing the thermal boundary layer thickness and enhancing the heat transfer coefficient.
• In forced convection, an external device (such as a fan, pump, or blower) is used to induce motion in the fluid, enhancing the heat transfer process. The external force overcomes the resistance of the fluid, ensuring a controlled and efficient heat transfer mechanism. This distinguishes forced convection from natural convection, where the fluid motion is driven by natural buoyancy forces. The heat transfer in forced convection follows Newton's law of cooling, which states:

Q = h × A × ΔT

Where:

• Q = Rate of heat transfer (W)
• h = Convective heat transfer coefficient (W/m²·K)
• A = Surface area of heat transfer (m²)
• ΔT = Temperature difference between the surface and the fluid (K)

Examples of Forced Convection:

• Air Conditioning Systems: Fans are used to circulate air, improving the transfer of heat between the air and the cooling/heating coils.
• Car Radiators: A pump circulates coolant through the engine and radiator, while a fan helps dissipate heat from the radiator to the surrounding air.
• Heat Exchangers: Pumps and blowers are employed to move fluids through the heat exchanger, enhancing the transfer of heat between the fluids.
• Electronics Cooling: Fans are used to cool electronic components by forcing air over heat sinks or circuit boards.

Explanation:

The Stefan-Boltzmann Law

• The Stefan-Boltzmann law is a fundamental principle in thermal radiation, stating that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. Mathematically, the Stefan-Boltzmann law is expressed as:

E = σ × T⁴

Where:

• E: Total energy radiated per unit surface area (W/m²)
• σ: Stefan-Boltzmann constant (5.67 × 10^-8 W/m²K⁴)
• T: Absolute temperature of the black body (K)

The Stefan-Boltzmann law is derived from Planck's Law, which describes the spectral distribution of electromagnetic radiation emitted by a black body in thermal equilibrium. By integrating Planck's law over all wavelengths, the Stefan-Boltzmann law can be obtained. This integration process effectively sums up the contributions of radiation from all wavelengths, yielding the total emissive power of the black body.

Planck's law:

• Planck's law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T.
• Planck’s law for the energy Eλ radiated per unit volume by a cavity of a blackbody in the wavelength interval λ to λ + Δλ can be written in terms of Planck’s constant (h), the speed of light (c = λ × v), the Boltzmann constant (k), and the absolute temperature (T):

Energy per unit volume per unit wavelength:

\({E_\lambda } = \frac{{8\pi hc}}{{{\lambda ^5}}} \times \frac{1}{{{e^{\frac{{hc}}{{kT\lambda }} - 1}}}}\)

Energy per unit volume per unit frequency:

\({E_\nu } = \frac{{8\pi h}}{{{c^3}}} \times \frac{{{\nu ^3}}}{{{e^{\frac{{hv}}{{kT}} - 1}}}}\)

So Planck’s distribution function:

\(E\left( {\omega ,T} \right) = \frac{1}{{{e^{\frac{{h\omega }}{\tau }}} - 1}}\)

Using planck’s law, when we plot Ebλ with λ, we get the curve as shown below.

As temperature increases, the peak of the curve shift towards a lower wavelength.

Explanation:

Thermal Radiation and Its Mechanism

• Thermal radiation is a mode of heat transfer that occurs through the emission of electromagnetic waves, primarily in the infrared spectrum, but it can also include visible light and other wavelengths. This form of energy transfer does not require a medium, meaning it can occur in a vacuum. The energy is emitted by all bodies that have a temperature above absolute zero, due to the thermal vibrations of their molecules and atoms. The amount and nature of the radiation depend on the temperature and the surface properties of the body.

Radiation as a heat transfer mechanism is governed by Stefan-Boltzmann’s law, which states:

Q = σ × A × T⁴

Where:

• Q = Heat transfer via radiation (W)
• σ = Stefan-Boltzmann constant (5.67 × 10⁻⁸ W/m²K⁴)
• A = Surface area of the body (m²)
• T = Absolute temperature of the body (K)

Thermal radiation is characterized by the following:

• Electromagnetic Waves: It is the primary mechanism by which thermal radiation occurs. These waves can travel through a vacuum, making radiation the dominant form of heat transfer in outer space.
• Emissivity: The ability of a material to emit energy as thermal radiation is determined by its emissivity, which ranges from 0 (perfect reflector) to 1 (perfect emitter or blackbody).
• Temperature Dependence: The intensity and wavelength distribution of the emitted radiation depend on the temperature of the object.

Explanation:

Emissivity Factor for Energy Emitted by a Grey Body

• Emissivity is a measure of the efficiency of a surface in emitting thermal radiation compared to a perfect black body. A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence, and emits the maximum amount of energy at any given temperature. A grey body, however, emits less energy than a black body at the same temperature.

Mathematically, the emissivity factor (ε) is defined as the ratio of the energy emitted by a grey body per unit area per unit time (E) to the energy emitted by a perfect black body per unit area per unit time (E_B) at the same temperature:

\( \varepsilon = \frac{E}{E_B} \)

• \( E \) = Emitted energy by grey body (W/m²)
• \( E_B \) = Emitted energy by black body (W/m²)

Key Points:

• For a perfect black body, emissivity is equal to 1 because it emits the maximum possible energy at any given temperature.
• For real-world objects (grey bodies), emissivity is less than 1, as they emit less energy compared to a black body.
• Emissivity is a dimensionless quantity and typically ranges between 0 and 1.

Physical Significance:

The emissivity factor is crucial in determining the thermal radiation properties of materials. It plays a significant role in applications such as:

• Thermal engineering, where heat transfer calculations involve radiation.
• Designing heat exchangers and radiative cooling systems.
• Understanding and modeling the behavior of materials in high-temperature environments.
• Developing thermal imaging systems and sensors.

Concept:

The rate of heat transfer in a heat exchanger is calculated using enthalpy change when there is no change in kinetic or potential energy. Enthalpy for air is given by:

\( h = C_p \cdot T \)

Calculation:

• Initial temperature: \( T_1 = 15^\circ C = 288~K \)
• Final temperature after heat exchanger: \( T_2 = 800^\circ C = 1073~K \)
• Specific heat: \( C_p = 1.005~kJ/kg·K \)
• Mass flow rate: \( \dot{m} = 2~kg/s \)

Heat added in exchanger:

\( \dot{Q} = \dot{m} \times C_p \times (T_2 - T_1) \)

\( \dot{Q} = 2 \times 1.005 \times (1073 - 288) = 2 \times 1.005 \times 785 = 1580~kJ/s \)

The correct answer is 212° F.

• At 1 atmosphere of pressure (sea level), water boils at 100° C (212° F).
• When a liquid is heated, it eventually reaches a temperature at which the vapor pressure is large enough that bubbles form inside the body of the liquid. This temperature is called the boiling point.
  • Once the liquid starts to boil, the temperature remains constant until all of the liquid has been converted to a gas.

Important Points

• The boiling point of water depends on the atmospheric pressure, which changes according to elevation.
  • Water boils at a lower temperature as you gain altitude (e.g., going higher on a mountain).
  • Water boils at a higher temperature if you increase atmospheric pressure (coming back down to sea level or going below it).
• The boiling point of water also depends on the purity of the water.
  • Water that contains impurities (such as salted water) boils at a higher temperature than pure water. This phenomenon is called boiling point elevation.
  • It is one of the colligative properties of matter.

Key Points

• Liquids have a characteristic temperature at which they turn into solids, known as their freezing point.
  • Water freezes at 32° F or 0° C or 273.15 Kelvin.
• Pure, crystalline solids have a characteristic melting point, the temperature at which the solid melts to become a liquid.
• In theory, the melting point of a solid should be the same as the freezing point of the liquid.

Explanation:

In case of the counter-flow heat exchanger when the heat capacities of both the fluids are the same.

i.e. ṁ_hc_h = ṁ_cc_c

Q = ṁ_hc_h(T_h1 – T_h2) = ṁ_cc_c(T_c2 – T_c1)

⇒ (T_h1 – T_h2) = (T_c2 – T_c1)

⇒ (T_h1 – T_c2) = (T_h2 – T_c1)

⇒ ΔT₁ = ΔT₂

For parallel flow heat exchanger,  ΔT1 will always be greater than ΔT2.

Explanation:

Gases transfer heat by the collision of molecules.

As the temperature increases, the kinetic energy of molecules of gases also increases and eventually collision between molecules also increases which increases the thermal conductivity of gases.

∴ As temperature increases the thermal conductivity of gases increases.

For liquid and solids, generally as the temperature increases, the thermal conductivity decreases.

Concept:

Prandtl number Pr is defined as the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{{\mu {C_p}}}{K} = \frac{{\left( {\frac{\mu }{\rho }} \right)}}{{\left( {\frac{K}{{\rho {C_p}}}} \right)}}\)

\(Pr = \frac{\nu }{\alpha } = \frac{{momentum\;diffusivity}}{{thermal\;diffusivity}}\)

In another way, we can define Prandtl number as, the ratio of the rate that viscous forces penetrate the material to the rate that thermal energy penetrates the material.

\(\frac{δ }{{{δ _T}}} = {\left( {Pr} \right)^{1/3}}\;\)where, δ is hydrodynamic boundary layer thickness and δ_T is thermal boundary layer thickness.

Calculation:

Given:

Pr = 0.7 

from, \(\frac{δ }{{{δ _T}}} = {\left( {Pr} \right)^{1/3}}\;\)=  \({0.7^{\frac{1}{3}}} = 0.88 < 1\)

thus, δ < δ_T .

When              P_r < 1               δ_T > δ 

                        P_r  > 1               δT < δ 

Explanation:

Prandtl member is the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{\nu }{\alpha } = \frac{\mu }{{\frac{{\rho k}}{{\rho {C_p}}}}} = \frac{{\mu {C_p}}}{k}\)

Typical ranges of Prandtl member is listed below

Thermal conductivity of different metals in liquid state is given below

Sodium (Na) – 140 W/m-K

Potassium (K) – 100 W/m-K

Lithium (Li) – 85 W/m-K

Tin (Sn) – 64 W/m-K

Lead (Pb) – 36 W/m-K

Mercury ( Hg) – 8 W/m-K

So out of given options Sodium has highest thermal conductivity.

Concept:

Explanation:

• As we know the radiation travels with the speed of light, thus the rate of heat transfer is maximum in radiation in form of electromagnetic radiations

Explanation:

Insulation

• It is defined as a process of preventing the flow of heat from the body by applying insulator materials to the surface which controls the rate of heat transfer.
• The insulating ability of an insulator depends on various factors:
  • thickness of insulator
  • material of insulator
  • surrounding conditions
  • temperature difference  
• Generally, air packets are present in porous insulating materials.
• Since water which is a more conductive material is replacing air which is a less conductive material, so the overall insulating ability of the insulator will decrease. Most insulators are porous in nature.
• If it has been about Non-porous insulators then the insulating ability will remain unaffected.

Explanation:

• There are three methods of heat transfer between the two systems. They are conduction, convection, and radiation.
• Conduction is a method of heat transfer in solids and heat transfer takes place without the movement of particles.
• Convection is a method of heat transfer in fluids (gases and liquids) and heat transfer takes place due to the movement of particles.
• Radiation is a method of heat transfer where heat is transferred from one place to another without affecting the medium of heat transfer.

Now let's see what happens in a steam boiler:

• A steam boiler is designed to absorb the maximum amount of heat released from the process of combustion.
• Heat transfer within the steam boiler is accomplished by three methods: radiation, convection, and conduction. The heating surface in the furnace area receives heat primarily by radiation.
• The remaining heating surface in the steam boiler receives heat by convection from the hot flue gases. Heat received by the heating surface travels through the metal by conduction
• Heat is then transferred from the metal to the water by convection.

Explanation:

Net radiation heat exchange between two bodies is given by:

Q̇ = AF × σ × (T₁⁴ - T₂⁴)

where F, A, σ are shape factor, Area and Stefan-Boltzmann constant respectively

Now explanding  (T14 - T24)

Q̇ = AF × σ × ((T1)²)² - (T2)²)²)

Q̇ = AF × σ × (T12 - T22) × (T12 + T22)

Q̇ = AF × σ × (T₁ - T₂)(T₁ + T₂) ×  (T12 + T22)

\(\dot Q =\frac{T_1-T_2}{\frac{1}{\sigma \times AF \times(T_1+T_2)\times(T_1^2+T_2^2)}}\)

Comparing with the electrical analogy \(i=\frac VR\)

We will get thermal resistance as \(\frac{1}{{FA\sigma \left( {{T_1} + {T_2}} \right)\left( {T_1^2 + T_2^2} \right)}}\)