Convection MCQ Quiz - Objective Question with Answer for Convection - Download Free PDF

Explanation:

Newton's Formula for Convective Heat Transfer:

• Newton's formula for convective heat transfer describes the rate of heat transfer from a fluid to a metallic wall or from a metallic wall to a fluid via convection. The formula is expressed as:

Q = ha(t_s - t_f)

Where:

• Q: Heat transfer by convection in Joules per second (J/s) or Watts (W).
• h: Heat transfer or film coefficient in J/m²°C·s or W/m²°C.
• a: Surface area through which heat is transferred in square meters (m²).
• t_s: Temperature of the surface or wall in degrees Celsius (°C).
• t_f: Temperature of the fluid in degrees Celsius (°C).

Working Principle:

Heat transfer by convection occurs when a fluid (liquid or gas) comes into contact with a solid surface (e.g., a metallic wall). The temperature difference between the fluid (tf) and the solid surface (ts) drives the heat transfer process. Newton's law of cooling provides a mathematical relationship for this process, indicating that the rate of heat transfer is proportional to:

• The temperature difference (ts - tf).
• The surface area (a) exposed to heat transfer.
• The convective heat transfer coefficient (h), which depends on the properties of the fluid and the nature of the surface.

The formula Q = ha(ts - tf) accurately describes this phenomenon and is widely used in engineering calculations for convective heat transfer analysis.

Explanation:

Forced Convection

Definition: Forced convection is a mode of heat transfer in which fluid motion is generated by an external source like a pump, fan, or a mixer. This movement enhances the heat transfer rate between a solid surface and the fluid or between different fluid layers. Unlike natural convection, where the fluid motion is driven by buoyancy forces due to density variations caused by temperature differences, forced convection relies on external mechanisms to create the fluid flow.

Working Principle: In forced convection, an external device such as a fan or pump moves the fluid over a surface, thereby increasing the heat transfer rate. The motion of the fluid disrupts the thermal boundary layer, which is the layer of fluid in the immediate vicinity of the heat transfer surface where the temperature gradient is significant. By reducing the thickness of this boundary layer, forced convection enhances the heat transfer coefficient, resulting in more efficient heat transfer.

Example: The correct example of forced convection from the given options is "Air blown over a car radiator by a fan" (Option 4). In this case, the fan forces air to flow over the radiator's surface, thereby increasing the heat transfer from the hot coolant within the radiator to the air. This forced movement of air significantly improves the cooling efficiency of the radiator.

Advantages:

• Higher heat transfer rates compared to natural convection due to increased fluid velocity.
• Better control over the heat transfer process since the fluid flow can be regulated by adjusting the speed of the external device (fan, pump, etc.).

Disadvantages:

• Requires additional energy input to operate the external devices such as fans or pumps.
• More complex system design and higher initial costs compared to natural convection systems.

Applications: Forced convection is widely used in various engineering applications where efficient heat transfer is crucial, such as in automotive cooling systems, air conditioning units, heat exchangers, and electronic device cooling.

Analysis of Other Options:

Option 1: Heat transfer through a stationary fluid layer

This option describes conduction rather than convection. In conduction, heat transfer occurs through a stationary medium (solid or fluid) by the transfer of energy from one molecule to another without any bulk movement of the medium itself.

Option 2: Thermal energy transmitted by electromagnetic waves

This option describes radiation, not convection. Radiation is a mode of heat transfer where thermal energy is transmitted in the form of electromagnetic waves (e.g., infrared radiation) and does not require a medium for transmission.

Option 3: Warm air naturally rising from a hot surface

This option describes natural convection. In natural convection, the fluid motion is caused by buoyancy forces that arise from density differences due to temperature gradients. Warm air rises naturally from a hot surface as it becomes less dense compared to the cooler surrounding air.

Option 5: [Blank]

No information is provided for option 5, so it cannot be evaluated.

Explanation:

The relationship between the thermal boundary layer and the hydrodynamic boundary layer is given by Prandtl number 

Prandtl Number: It is defined as the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{\nu }{\alpha } = \frac{{momentum\;diffusivity}}{{Thermal\;diffusivty}} = \frac{{\frac{\mu }{\rho }}}{{\frac{k}{{{c_p}\rho }}}} = \frac{{\mu {c_p}}}{k}\)

The relationship between the two is given by the equation

\(\frac{{{\delta }}}{\delta_t } = P_r^{ \frac{1}{3}}\)

δ = the thickness of the hydrodynamic boundary layer; the region of flow where the velocity is less than 99% of the far-field velocity.

δT = the thickness of the thermal boundary layer; the region of flow where the local temperature nearly reaches the value (99%) of the bulk flow temperature

• If Pr > 1 the momentum or hydrodynamic boundary layer will increase more compared to the thermal boundary layer. 
• If Pr < 1 the thermal boundary layer will increase more compared to the momentum or hydrodynamic boundary layer.
• If Pr = 1 The the thermal boundary layer and momentum or hydrodynamic boundary layer will increase at the same rate.

If the velocity and thermal boundary layers coincide then Pr = 1. ​

Explanation:

Non-Dimensional Numbers:

• Non-dimensional numbers are crucial in fluid dynamics and heat transfer as they allow the analysis of complex systems by reducing the number of variables. In free convection, these numbers help determine the transition between laminar and turbulent flow regimes and provide insights into the behavior of the system under different conditions.

Rayleigh Number:

• The Rayleigh number (Ra) is a dimensionless number that plays a critical role in the study of free convection. It is used to predict the transition from laminar to turbulent flow in fluid systems driven by buoyancy forces. The Rayleigh number combines the effects of thermal diffusivity, kinematic viscosity, and buoyancy, and is expressed as:

Ra = Gr × Pr

Where:

• Gr is the Grashof number, which represents the ratio of buoyancy forces to viscous forces.
• Pr is the Prandtl number, which relates momentum diffusivity to thermal diffusivity.

The Rayleigh number signifies the dominance of buoyancy forces compared to viscous and thermal effects. In free convection, the critical Rayleigh number (typically Ra_crit ≈ 10⁶) indicates the onset of turbulence. When Ra is below this threshold, the flow remains laminar. Above this value, the flow transitions to turbulence, characterized by chaotic and irregular motion.

Additional InformationPeclet Number

• The Peclet number (Pe) is a dimensionless parameter that relates the rate of advection of thermal energy to the rate of thermal diffusion. It is expressed as:

Pe = Re × Pr

Where:

• Re is the Reynolds number, representing the ratio of inertial forces to viscous forces.
• Pr is the Prandtl number.

Grashof Number

• The Grashof number (Gr) is a critical parameter in free convection, representing the ratio of buoyancy forces to viscous forces. It is given by:

Gr = (g × β × ΔT × L³) / ν²

Where:

• g is the acceleration due to gravity.
• β is the coefficient of thermal expansion.
• ΔT is the temperature difference.
• L is the characteristic length.
• ν is the kinematic viscosity.

Reynolds Number

• The Reynolds number (Re) is a widely used dimensionless parameter that predicts the transition from laminar to turbulent flow in forced convection. It is defined as:

Re = (ρ × V × L) / μ

Where:

• ρ is the fluid density.
• V is the velocity of the fluid.
• L is the characteristic length.
• μ is the dynamic viscosity

Explanation:

Free Convection

• Free convection is a type of heat transfer that occurs naturally due to the movement of fluid (liquid or gas) caused by differences in temperature and density.
• In free convection, the fluid motion is induced by buoyancy forces that arise from temperature gradients within the fluid.
• Unlike forced convection, where external means like fans or pumps are used to move the fluid, free convection relies solely on natural buoyancy effects.
• In free convection, when a fluid is heated, it becomes less dense and rises, while cooler, denser fluid descends to take its place.
• This movement creates a continuous circulation pattern, allowing heat to be transferred from one region to another.
• The process continues until thermal equilibrium is reached, with the fluid transporting heat from hotter areas to cooler areas.

Advantages:

• No external power source is required for fluid movement, making it energy-efficient.
• Simple and cost-effective, as it relies on natural processes.

Disadvantages:

• Slower and less efficient compared to forced convection, as the fluid movement is driven by natural buoyancy forces.
• Limited to specific applications where natural convection currents are sufficient for heat transfer.

Applications:

• Free convection is commonly observed in various natural and industrial processes, such as atmospheric circulation, ocean currents, heating and cooling of buildings, and heat transfer in electronic devices.

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.

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

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.

Prandtl Number: It is the ratio of momentum diffusivity (ν) and thermal diffusivity (α). 

Pr = ν / α 

ν = Momentum diffusivity (Kinematic Viscosity) = μ / ρ ,α = Thermal diffusivity = k / ρc_p, μ = Dynamic viscosity, ρ = Density of fluid

c_p = Specific heat at constant pressure

Important Non-dimensional numbers:

• Biot number  → Ratio of internal thermal resistance to boundary layer thermal resistance
• Grashof number  → Ratio of buoyancy to viscous force
• Prandtl number  → Ratio of momentum to thermal diffusivities
• Reynolds number  → Ratio of inertia force to viscous force

Explanation:

For Turbulent flow in natural convection, the Nusselt number (Nu) is given by:

Nu = C [Gr, Pr]1/3

The Grashoff number (Gr) is given by

\(\left( {Gr} \right) = \frac{{g \beta \left( {{\rm{\Delta }}T} \right)L_e^3}}{{{\nu ^2}}}\)

i.e. Gr ∝ L3

where L = characteristic length.

For various setups, the characteristic length changes and some are given below:

For vertical plate = L (length of the plate)

For Vertical cylinder = L (length of the cylinder)

For Horizontal cylinder = D (diameter of the cylinder)

For square plate - 0.25 a (a is side of the square plate)

Now;

Nu = C [Gr, Pr]1/3

\(\frac{{hD}}{k} = C{\left[ {\frac{{g \beta \left( {{\rm{\Delta }}T} \right){D^3}}}{{{\nu ^2}}}} \right]^{\frac{1}{3}}}{\left( {Pr} \right)^{1/3}}\)

\(\therefore \frac{{hD}}{k} \propto {D}\)

i.e. h is independent of characteristic length or diameter of the cylinder.

The correct answer is 212^o F.

Key Points

• Under normal conditions, the boiling point of water is 100°C that is equal to 212°F.
• The boiling point of a liquid is the temperature at which the vapour pressure of a liquid equals the standard sea-level atmospheric pressure.

• Relation between degree Celsius and Fahrenheit  can be expressed as:

  \(\frac{{F - 32}}{9} = \frac{C}{5} \)

  \(\therefore F=\frac{9}{5}C+32=\frac{9}{5}\times 100{}^\circ ~C+32\)

  \(F=180+32\Rightarrow F=212~{}^\circ ~F\)

• 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.

 ​Additional Information

Concept:

Always remember standard results mentioned below;

Part – I For constant surface heat flux (q_s = constant);

Hydrodynamically and thermally fully developed laminar flow through a circular pipe of constant cross section

Nu_q = 4.36      …1)

Part – II For constant wall temperature (T_w = constant)

For this case

Nu_T = 3.66     …2)

Calculation:

Comparing 1) and 2)

Nu_q > Nu_T ⇒ Option A is correct.

Key Points

Go through both derivations (i.e. q_s = constant and T = constant) and remember graphs of both cases.

Explanation:

If fluid flows on a surface having a different temperature than the surface, the thermal boundary layer is developed similar to the velocity boundary layer.

For the flow of viscous fluid over a flat plate, if the fluid temperature is the same as the plate temperature, the thermal boundary layer is not formed at all.

Concept:

The relation between hydrodynamic boundary layer thickness (δ) and thermal boundary layer thickness (δT) is given as

\(\frac{\delta }{{{\delta _T}\;}} = {\left( {Pr} \right)^{1/3}}\)

The relation between Nusselt number and Prandtl number for laminar flow over a flat plate is

Nu = F (Re, Pr)

For constant temperature, boundary condition

Nu = 0.332 (Re)1/2 (Pr)1/3

For constant heat flux boundary condition

Nu = 0.453 (Re)1/2 (Pr)1/3

Nu ∝ Re^1/2Pr^1/3

Calculation:

Given:

Nu₂ = 2Nu₁, Re₂ = 4Re₁

Nu ∝ Re1/2Pr1/3

\(Pr\propto \left(\frac{Nu}{{Re}^{1/2}}\right)^3\)

\(\frac{{Pr}_2}{{Pr}_1}= \left(\frac{Nu_2}{Nu_1}\right)^3\;\times \left(\frac{Re_1}{Re_2}\right)^{3/2}\)

\(\frac{{Pr}_2}{{Pr}_1}= \left(\frac{2Nu_1}{Nu_1}\right)^3\;\times \left(\frac{Re_1}{4Re_1}\right)^{3/2}\)

\(\frac{{Pr}_2}{{Pr}_1}= \left(\frac{2}{1}\right)^3\;\times \left(\frac{1}{4}\right)^{3/2}\)

\(\frac{{Pr}_2}{{Pr}_1}= \left(8\right)\;\times \left(\frac{1}{8}\right)\)

∴ Pr₂ = Pr₁

Hence the new value of the Prandtl number will be the same as before.