Heat Transfer Flashcards

Thermal diffusivity α is defined as which of the following combinations of material properties?

Answer: k/(ρcp)

Thermal diffusivity α = k/(ρcp) represents how quickly a material conducts heat relative to its ability to store it.

For a hollow cylinder with inner radius r₁, outer radius r₂, length L, and thermal conductivity k, the conductive thermal resistance is:

Answer: ln(r₂/r₁) / (2πkL)

Integrating Fourier's Law in cylindrical coordinates gives R_cyl = ln(r₂/r₁)/(2πkL).

The Log Mean Temperature Difference (LMTD) method is primarily used to analyze:

Answer: Heat exchanger performance

LMTD provides the effective mean driving temperature difference for heat exchangers where temperatures vary along the length.

In a counterflow heat exchanger compared to a parallel-flow arrangement with the same inlet conditions and UA product, which statement is correct?

Answer: Counterflow achieves higher LMTD and greater heat transfer

Counterflow maintains a more uniform temperature difference along its length, yielding a higher LMTD and therefore greater heat transfer capacity.

Fin efficiency (η_f) is defined as:

Answer: Actual fin heat transfer divided by maximum heat transfer if entire fin were at base temperature

Fin efficiency η_f = q_actual / q_max, where q_max = hA_f(T_b − T∞) assumes the entire fin surface is at the base temperature.

For radiation exchange between two large parallel plates with emissivities ε₁ and ε₂, the net heat flux is given by:

Answer: q" = σ(T₁⁴ − T₂⁴) / (1/ε₁ + 1/ε₂ − 1)

The radiation network for two large parallel plates gives q" = σ(T₁⁴−T₂⁴)/(1/ε₁ + 1/ε₂ − 1), accounting for surface resistances.

The Prandtl number (Pr) for a fluid is defined as the ratio of:

Answer: Momentum diffusivity to thermal diffusivity (ν/α)

Pr = ν/α = μcp/k; it characterizes the relative thickness of the velocity and thermal boundary layers.