Heat Transfer: Aerospace Application 2025

(a) Conduction heat transfer occurs mainly due to:

1. Bulk fluid motion
2. Molecular interactions
3. Electromagnetic waves
4. Surface radiation

(b) Cryogenic cooling in aerospace is primarily used for:

1. Passenger cabin temperature control
2. Rocket propellant storage and cooling electronic systems
3. Wing de-icing
4. Reducing aerodynamic drag

(c) In hypersonic flight, the major thermal challenge arises from:

1. Natural convection
2. Cloud moisture
3. Strong shock-induced aerodynamic heating
4. Cockpit electronics

(d) Fourier's law relates heat flux to:

1. Temperature
2. Thermal conductivity and temperature gradient
3. Density and viscosity
4. Pressure difference

(e) The steady-state 1D heat diffusion equation in a plane wall without internal generation reduces to:

1. $dT/dx = \text{constant}$
2. $d^2T/dx^2 = 0$
3. $dT/dt = 0$
4. $k \cdot dT/dx = 0$

(f) Thermal conductivity represents:

1. A material's ability to store heat
2. Resistance to heat flow
3. Ability to conduct heat
4. Heat generation rate

(g) The Effectiveness-NTU method is particularly useful when:

1. Outlet temperatures are known
2. Inlet temperatures are unknown
3. Flow is always laminar
4. LMTD is zero

(h) The LMTD method requires knowledge of:

1. No flow arrangement
2. Both inlet and outlet temperatures
3. Only mass flow rate
4. No heat capacity information

(i) A perfect blackbody is defined as a surface that:

1. Reflects all incident radiation
2. Transmits all radiation
3. Absorbs all incident radiation
4. Emits no radiation

(j) Stefan-Boltzmann law states that total emitted radiation varies as:

1. $T$
2. $T^2$
3. $T^3$
4. $T^4$

(a) Write the Fourier rate equation for heat transfer by conduction. Give the units.

(b) A composite furnace wall is to be constructed with two layers of materials ($K_1 = 2.5\text{ W/m}\cdot^\circ\text{C}$ and $K_2 = 0.25\text{ W/m}\cdot^\circ\text{C}$). The convective heat transfer coefficient at the inside and outside surfaces is expected to be $250\text{ W/m}^2\cdot^\circ\text{C}$ and $50\text{ W/m}^2\cdot^\circ\text{C}$ respectively. The temperature of gases and air are $1000\text{ K}$ and $300\text{ K}$. If the interface temperature is $650\text{ K}$, Calculate (i) the thickness of the two materials when the total thickness does not exceed $65\text{ cm}$ and (ii) the rate of heat flow. Neglect radiation.

(a) Compare aerodynamic heating in subsonic, supersonic, and hypersonic regimes in terms of: (i) stagnation temperature rise, (ii) heat flux scaling, (iii) boundary layer behaviour.

(b) Explain ablative cooling mechanism with a sketch showing char, pyrolysis, and virgin material zones. List two ablative materials used in re-entry capsules.

(a) Derive the temperature distribution and heat transfer rate for steady-state conduction through a hollow cylindrical shell, as used in rocket nozzle cooling jackets.

(b) A spherical satellite sensor housing has inner radius $5\text{ cm}$ and outer radius $7\text{ cm}$. The inner surface is at $350\text{ K}$ and outer surface at $300\text{ K}$. The thermal conductivity is $15\text{ W/mK}$.

Determine: (a) Temperature distribution (b) Heat transfer rate.

(a) With neat sketches, explain the use of Heisler charts to solve transient conduction problems in plane walls and cylinders. Provide a sample aerospace application e.g., cooling of engine liners.

(b) Derive Newton's law of cooling and discuss the physical significance of Nusselt, Reynolds, Prandtl, Grashof's, and Rayleigh numbers in aerospace heat-transfer problems.

(a) Explain the concept of blackbody radiation and derive Planck's law for spectral emissive power of a blackbody.

(b) A blackbody cavity in a satellite instrument is maintained at $500\text{ K}$. (a) Using Stefan-Boltzmann law, calculate the total radiated power per unit area (in $\text{W/m}^2$). (b) Using Wien's law, find the wavelength of peak emission. (c) If the cavity opening is $4\text{ cm}^2$, estimate the total power radiated from the opening. (Given: $\sigma = 5.67 \times 10^{-8}\text{ W/m}^2\text{K}^4$)

(a) State and explain Kirchhoff's law of thermal radiation. How does it relate absorptivity, emissivity, and temperature for real surfaces?

(b) Define a heat exchanger. Discuss the applications of heat exchangers as intercoolers, recuperators, and precoolers in propulsion systems.

(a) A parallel flow heat exchanger in an aircraft ECS has:
Hot fluid: $T_{h1} = 180^\circ\text{C}$, $T_{h2} = 100^\circ\text{C}$, $C_h = 800\text{ W/K}$
Cold fluid: $T_{c1} = 30^\circ\text{C}$, $C_c = 1000\text{ W/K}$
(a) Calculate LMTD.
(b) If the same duty is to be achieved in counter flow, what will be the new LMTD?

(b) Explain the difference between parallel-flow and counter-flow heat exchangers. Derive the expression for the temperature variation along the flow direction in both cases.

(a) Explain the concept of additive manufactured heat exchangers. Discuss their design advantages, manufacturing challenges, and performance benefits in aerospace thermal management compared to conventional heat exchangers.

(b) Explain how advanced thermal management technologies, such as additive manufacturing, nanofluids, and PCMs - can be integrated into a reliable spacecraft or aircraft thermal control system.