Which of the following is the SI unit of thermal conductivity?
Answer: A
Thermal conductivity is expressed as W/(m·K) in SI units, equivalent to J/(s·m·K). This represents heat flow rate per unit area per unit temperature gradient.
Q.2Easy
In heat conduction through a composite wall, the overall heat transfer rate is determined by which principle?
Answer: A
The thermal resistance network (Ohm's law analogy) is used where total thermal resistance equals the sum of individual resistances in series for composite walls.
Q.3Easy
Which dimensionless number represents the ratio of buoyancy forces to viscous forces in natural convection?
Answer: A
Grashof number (Gr = gβΔT L³/ν²) represents the ratio of buoyancy to viscous forces. Ra = Gr × Pr combines both effects.
Q.4Easy
Which of the following best describes the behavior of thermal conductivity with temperature for most metals?
Answer: B
For most pure metals, thermal conductivity decreases with increasing temperature due to increased lattice vibrations causing phonon scattering.
Q.5Easy
The thermal diffusivity (α) has dimensions of which of the following?
Answer: A
Thermal diffusivity α = k/(ρ·C_p) has dimensions L²/t, representing how fast thermal disturbances propagate through a material.
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Q.6Easy
The Biot number (Bi) is defined as the ratio of which resistances in transient heat conduction?
Answer: B
Bi = hL_c/k, representing the ratio of internal conduction resistance to external convection resistance at the surface.
Q.7Easy
The Fourier number (Fo = αt/L²) in unsteady-state conduction represents the ratio of:
Answer: A
Fo represents the relative importance of heat conducted (diffused) into the object compared to heat stored, dimensionless time.
Q.8Easy
The Stefan-Boltzmann constant (σ) has SI units of:
Answer: B
From Q = σAT⁴, σ has units W·m⁻²·K⁻⁴ (5.67 × 10⁻⁸ W·m⁻²·K⁻⁴).
Q.9Easy
The Rayleigh number (Ra) in natural convection is defined as Ra = Gr·Pr. When Ra < 10⁹ for vertical surfaces, the heat transfer is primarily:
Answer: B
For Ra < 10⁹, natural convection remains laminar; transition to turbulence occurs around Ra ≈ 10⁹.
Q.10Easy
The dimensionless Stanton number (St = h/(ρ·v·c_p)) in heat transfer represents:
Answer: A
St represents the fraction of heat that can be transferred relative to the sensible heat available in flowing fluid per unit area per unit time.
Q.11Easy
In a parallel flow heat exchanger, hot fluid enters at 80°C and exits at 50°C while cold fluid enters at 20°C and exits at 40°C. Calculate the Log Mean Temperature Difference (LMTD).
Which of the following dimensionless numbers is used to predict the transition from laminar to turbulent flow in forced convection?
Answer: B
Reynolds number determines the flow regime in forced convection. Re < 2300 indicates laminar flow, Re > 4000 indicates turbulent flow. Grashof and Rayleigh are used for natural convection, while Fourier number is for transient conduction.
Q.13Easy
In the context of thermal radiation, the Stefan-Boltzmann constant has a value of:
Answer: A
The Stefan-Boltzmann constant σ = 5.67 × 10⁻⁸ W/m²·K⁴ is used in radiation heat transfer calculations (Q = σAε(T⁴)). Other options are physical constants used in different domains.
Q.14Easy
A horizontal cylindrical pipe carries hot water at 80°C through ambient air at 20°C. The convective heat transfer coefficient is 25 W/m²·K and pipe diameter is 50 mm. Calculate heat loss per unit length if the pipe is not insulated.
Which of the following materials would be most suitable for a heat sink application requiring high thermal conductivity and low cost?
Answer: B
Aluminum alloys offer an excellent balance of thermal conductivity (160 W/m·K, sufficient for most applications), cost-effectiveness, light weight, corrosion resistance, and ease of machining. While copper has higher conductivity, aluminum's cost-benefit ratio is superior for heat sink applications.
Q.16Easy
In a shell-and-tube heat exchanger, what is the primary advantage of using baffles?
Answer: A
Baffles in shell-and-tube heat exchangers create turbulence by forcing the fluid to flow in a cross-flow pattern, significantly increasing the convective heat transfer coefficient on the shell side, which enhances overall heat transfer effectiveness.
Q.17Easy
The Nusselt number (Nu) relationship for laminar flow in a circular pipe is given by Nu = 3.66. What does this value represent?
Answer: B
The value of 3.66 is the fully developed Nusselt number for laminar flow in circular pipes under constant wall temperature (T_s constant) boundary condition, representing the thermal development region.
Q.18Easy
In radiation heat transfer, the Stefan-Boltzmann constant σ has a value of 5.67 × 10⁻⁸ W/(m²·K⁴). A black body at 500 K radiates heat. If the temperature is doubled to 1000 K, by what factor does the radiated heat increase?
Answer: D
According to Stefan-Boltzmann law, Q = σAT⁴. When T increases from 500 K to 1000 K, the factor becomes (5001000)⁴ = 2⁴ = 16 times. Radiation is highly temperature-dependent due to the fourth-power relationship.
Q.19Easy
A flat-plate solar collector has a black absorber plate maintained at 80°C. The ambient temperature is 20°C and the heat loss coefficient (overall U value including radiation and convection) is 8 W/(m²·K). For a collector area of 4 m², what is the heat loss rate to the surroundings?
Answer: C
Q_loss = U × A × ΔT = 8 × 4 × (80-20) = 8 × 4 × 60 = 1920 W. The overall U value already accounts for both convective and radiative losses.
Q.20Easy
What is the SI unit of thermal conductivity?
Answer: D
Thermal conductivity is expressed as W/(m·K) in SI units, which is equivalent to J/(s·m·K) since 1 W = 1 J/s.
