Heat Transfer Flashcards

For the lumped capacitance method, the temperature response of a body cooling in a fluid follows which mathematical form?

Answer: Exponential decay with time constant τ = ρVcp/(hAs)

The lumped capacitance solution is (T−T∞)/(Ti−T∞) = exp(−t/τ), an exponential decay with time constant τ = ρVcp/(hAs).

A blackbody at 1000 K emits thermal radiation at what power per unit area? (σ = 5.67 × 10⁻⁸ W/m²·K⁴)

Answer: 56,700 W/m²

E_b = σT⁴ = 5.67×10⁻⁸ × (1000)⁴ = 5.67×10⁻⁸ × 10¹² = 56,700 W/m².

In the NTU-effectiveness (ε-NTU) method for heat exchanger analysis, effectiveness ε is defined as:

Answer: Actual heat transfer rate divided by maximum possible heat transfer rate

Effectiveness ε = q_actual/q_max, where q_max = Cmin(Th,i − Tc,i) is the thermodynamic maximum.

For fully developed laminar flow inside a circular tube with a constant heat flux boundary condition, the Nusselt number is approximately:

Answer: 4.36

Nu = 4.36 for fully developed laminar flow in a circular tube with uniform (constant) heat flux; Nu = 3.66 applies for constant wall temperature.

Which dimensionless number characterizes the ratio of buoyancy forces to viscous forces and is the key parameter in natural convection analysis?

Answer: Grashof number (Gr = gβΔTL³/ν²)

The Grashof number Gr = gβΔTL³/ν² represents the ratio of buoyancy to viscous forces driving natural convection.

For a semi-infinite solid initially at uniform temperature Ti, suddenly exposed to a new surface temperature Ts at t = 0, the temperature distribution T(x,t) involves which mathematical function?

Answer: Complementary error function erfc(x/2√(αt))

The solution is (T−Ts)/(Ti−Ts) = erf(x/2√(αt)), so T involves the complementary error function erfc when expressed relative to Ts.

The radiation view factor F₁₂ is defined as the fraction of:

Answer: Radiation leaving surface 1 that is intercepted by surface 2

F₁₂ is the fraction of diffuse radiation leaving surface 1 (in all directions) that is intercepted by surface 2.