Forced Convection MCQ Quiz in मल्याळम - Objective Question with Answer for Forced Convection - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

Heat loss through the convection is given by

Q_loss = h × A × (∆T)

Nusselt number \(Nu = \frac{{h{l_c}}}{k}\)

Where l­_c is the characteristic length, in case of heater it is equal to the diameter of the sphere

Calculation:

Given, Nu = 31.4, k = 0.026 W/mK, D = 12 mm ⇒ r = 6 × 10-3 m , Surface temperature T_s = 27°C and atmospheric temperature T_∞ = 77°C

\(Nu = \frac{{h{l_c}}}{k}\)

⇒ \(h = \frac{{Nu\times{k}}}{l_c}\)

\(h = \frac{{31.4 \times 0.026}}{{0.012}} = 68.03\;W/{m^2}K\;\)

Surface area of sphere A = 4 × π × r² = 4 × 3.14 × (6 × 10^-3)²

Q_loss = 68.03 × 4 × 3.14 × (6 × 10^-3)² × (77 – 27) = 1.54 J/s

Explanation:

Nusselt number

It is the ratio of heat flow rate by convection process to the heat flow rate by the conduction process or it can be defined as the ratio of conductive thermal resistance to the surface convective resistance.

\(Nu = \frac{{{Q_{conv}}}}{{{Q_{cond}}}} =\frac{R_{conduction}}{R_{Convection}}= \frac{{hA{\rm{\Delta }}T}}{{\frac{{kA{\rm{\Delta }}T}}{L}}} = \frac{{hL}}{k}\)

Calculation:

Given:

Nu = 716, k = 0.02685 W/mK, L = 35 cm

\(716 =\frac{h \times 0.35}{0.02685}\)

h = 54.92 W/m²K

Explanation:

The variation of local heat transfer coefficient hx with the distance x for free convection from a vertical heated plate is given as, hx = Cx-1/4

where C is constant.

The average heat transfer coefficient havg is given as,

\({h_{avg}} = \frac{1}{x}\mathop \smallint \limits_0^x {h_x}dx = \frac{1}{x}\mathop \smallint \limits_0^x C{x^{ - 1/4}}dx\)

\({h_{avg}} = \frac{C}{x}\mathop \smallint \limits_0^x {x^{ - 1/4}}dx = \frac{C}{x}\left[ {\frac{{{x^{ - \frac{1}{4} + 1}}}}{{ - \frac{1}{4} + 1}}} \right]_0^x = \frac{4}{3}\frac{C}{x}\;{x^{3/4}} = \frac{4}{3}\;C{x^{ - 1/4}}\;\)

\({h_{avg}} = \frac{4}{3}\;{h_x}\)

\(\frac{h_{avg}}{h_x}=\frac43\)

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.

Concept:

Nusselt number

It is the ratio of heat flow rate by convection process to the heat flow rate by the conduction process or it can be defined as the ratio of conductive thermal resistance to the surface convective resistance.

\(Nu = \frac{{{Q_{conv}}}}{{{Q_{cond}}}} =\frac{R_{conduction}}{R_{Convection}}= \frac{{hA{\rm{\Delta }}T}}{{\frac{{kA{\rm{\Delta }}T}}{L}}} = \frac{{hL}}{k}\)

The average value of Nusselt number is given as, 0.664 Re0.5 Pr0.3

The Nusselt number is in

here Nu = Nusselt's Number

Re = Reynold's Number, Pr = Prandtl Number, Gr = Grashoff Number 

Other important dimensionless numbers are:

• 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:

Forced Convection

Definition: Forced convection is a mechanism or type of heat transfer in which fluid motion is generated by an external source (like a pump, fan, suction device, etc.). This differs from natural convection, where the fluid motion is caused by buoyancy forces that result from density variations due to temperature gradients in the fluid.

Working Principle: In forced convection, the external device (such as a fan or pump) actively moves the fluid, enhancing the heat transfer process. The movement of the fluid increases the rate at which heat is transferred from a surface to the fluid or from the fluid to a surface, depending on the temperature difference.

Advantages:

• Increased heat transfer rate compared to natural convection.
• Better control over the heat transfer process due to the ability to regulate the speed and direction of the fluid flow.
• Enhanced cooling or heating efficiency in various applications, such as electronic devices, industrial processes, and HVAC systems.

Disadvantages:

• Requires an external power source to operate the fan, pump, or other devices.
• Can be more complex and expensive to implement compared to natural convection systems.

Applications: Forced convection is widely used in many applications, including cooling of electronic components, HVAC systems, automotive cooling systems, and industrial heat exchangers.

Concept:

Laminar forced convection in a flat plate:

\(Nu_x=0.332(Re_x)^{\frac{1}{2}}(Pr)^{\frac{1}{3}}\)

\(\bar{Nu}=0.664(Re)^{\frac{1}{2}}(Pr)^{\frac{1}{3}}\)

∴ Nu ∝ (Re)1/2

∴ h ∝ (U∞)1/2

As \(Re=\frac{\rho U_{∞}D}{\mu}=\frac{U_∞ D}{\nu}\) and \(Nu=\frac{hD}{k}\)

As the R_e  is the function of velocity and N_u is the function of Thermal conductivity, Hence forced convection depends on the Velocity and conductivity of the fluid.

• Free convection heat transfer coefficient depends on gravity 
• Heat transfer coefficients depend on the conductivity of the fluid.
• the conductivity of material has nothing to do with heat transfer coefficients
• as velocity of fluid increases heat transfer coefficient increases.

Concept:

Nusselt number

It is the ratio of heat flow rate by convection process to the heat flow rate by the conduction process or it can be defined as the ratio of conductive thermal resistance to the surface convective resistance.

\(Nu = \frac{{{Q_{conv}}}}{{{Q_{cond}}}} =\frac{R_{conduction}}{R_{Convection}}= \frac{{hA{\rm{\Delta }}T}}{{\frac{{kA{\rm{\Delta }}T}}{L}}} = \frac{{hL}}{k}\)

The average value of Nusselt number is given as, 0.664 Re0.5 Pr0.3

The Nusselt number is in

here Nu = Nusselt's Number

Re = Reynold's Number, Pr = Prandtl Number, Gr = Grashoff Number 

Other important dimensionless numbers are:

• 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:

Rayleigh Number:

• The Rayleigh number is a dimensionless number in fluid dynamics and heat transfer that is important in predicting the onset of convection.
• It characterizes the flow regime in a fluid and is particularly useful in free convection scenarios.
• The Rayleigh number combines the effects of thermal expansion, viscosity, thermal diffusivity, and the temperature gradient driving the convection.
• The Rayleigh number (Ra) is given by the product of the Grashof number (Gr) and the Prandtl number (Pr).

Mathematically, it is expressed as:

Ra = Gr × Pr

Where:

• Gr is the Grashof number, which represents the ratio of buoyancy to viscous forces in the fluid.
• Pr is the Prandtl number, which represents the ratio of momentum diffusivity (viscosity) to thermal diffusivity.

Working Principle: In a free convection scenario, fluid motion is induced by the buoyancy forces that result from density variations due to temperature gradients within the fluid. The Rayleigh number helps determine whether the fluid flow will remain laminar or transition to turbulence. A higher Rayleigh number indicates a greater likelihood of turbulent flow.

Importance: The Rayleigh number is critical for engineers and scientists to predict and analyze the thermal behavior of fluids in various applications such as heating and cooling systems, natural convection in the atmosphere, and geological processes.

Convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface.

The ratio of molecular mass transport resistance to the convective mass transport resistance of the fluid is known as the Sherwood number (Sh).It is analogous to the Nusselt number (Nu) in heat transfer.

\(Sh = \frac{{molecular\;mass\;transport\;resistance}}{{convective\;mass\;tranport\;resistance}} = \frac{{{k_c}L}}{D}\)

Where, L is the characteristic length and kc is the convective mass-transfer coefficient.

Concentration-driven natural convection flows are based on the densities of different species in a mixture being different.

In natural convection mass transfer, the analogy between the Nusselt and Sherwood numbers is given as

Sh = (Sc, Gr)

i.e. Sherwood number is a function of Grashof number (Gr) and Schimdt Number (Sc).

The Grashof number in this case should be determined directly from

\(Gr = \frac{{g\left( {\frac{{{\rm{\Delta }}\rho }}{\rho }} \right)L_c^3}}{{{\nu ^2}}}\)

Where ρ is density and Δρ is the change in density Lc is the characteristic length and ν is the kinematic viscosity

In forced convection mass transfer, the analogy between the Nusselt and Sherwood numbers is given as

Sh = (Re, Sc)

In forced convection heat transfer, the analogy between the Nusselt and Reynold numbers is given as, Nu = f(Re, Pr)

Hence Statment 3 and 4 are correct.