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# Rocket Propulsion – Thrust Chambers – Heat Transfer Analysis

1 - Question

If dT/dL denotes temperature gradient with respect to thickness L at the surface A, k denotes the thermal conductivity, then the heat transferred per unit area is given by __________

a) Q/A = -k dT/dL

b) Q/A = -(1/k) dT/dL

c) Q/A = k dT/dL

d) Q/A = (1/k) kdT/dL

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Answer: aExplanation: Q/A = -k dT/dL is the expression for heat transferred per unit area. This is called as Fourier’s law of heat transfer. By negative symbol in the equation, we can see that the direction of heat transfer is in the direction of negative gradient (larger temperature to smaller temperature) of temperature along the length of the material.

2 - Question

Steady state heat transfer through a liquid-cooled rocket chamber wall can be considered as ___________

a) series type with strong temperature gradient

b) parallel type with weak temperature gradient

c) series type with weak temperature gradient

d) parallel type with strong temperature gradient

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Answer: aExplanation: The heat transfer through the liquid-cooled rocket chamber can be considered as a steady state series type process with strong temperature gradients. This involves a large temperature gradient across the thin gaseous film touching the wall, a temperature drop across the wall and a third temperature drop in the presence of the moving cooling fluid.

3 - Question

The whole process of heat transfer through the chamber wall is a combination of ________ through the chamber wall and ________ through the flowing fluids.

a) conduction; convection

b) convection; radiation

c) radiation; conduction

d) conduction; conduction

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Answer: aExplanation: Heat transfer through the chamber walls includes both the conduction through the chamber wall as well as convection through the flowing fluids. This problem is basically one that is associated with the heat and mass transport associated with through a wall.

4 - Question

For absolute chamber gas temperature Tg, absolute liquid temperature Tl, overall film coefficient h, gas film coefficient hg and liquid film coefficient hl, determine the expression for heat transferred per unit area q.

a) q = h/(hg hl) x (Tg – Tl)

b) q = hg (Tg – Tl)

c) q = hghl/h x (Tg – Tl)

d) q = h (Tg – Tl)

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Answer: dExplanation: q = h(Tg – Tl) is the correct expression for heat transferred per unit area. This relation assumes that the heat flow is radial in direction.

5 - Question

For absolute chamber gas temperature Tg, absolute liquid temperature Tl, absolute wall temperature on the gas side of the wall Twg, overall film coefficient h, gas film coefficient hg and liquid film coefficient hl, determine the expression for heat transferred per unit area q.

a) q = hl (To – Twg)

b) q = h (To – Twg)

c) q = hg (To – Twg)

d) q = hg/h (Twg – To)

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Answer: cExplanation: q = hg (To – Twg) is the correct expression for heat transferred per unit area q. This is true for a regeneratively cooled thrust chamber. The strength of the material as well as its thermal properties are considered to be a function of temperature.

6 - Question

_____ largely determines the numerical heat transfer rate and __________ largely determines the value of wall temperatures.

a) Gas film coefficient; liquid film coefficient

b) Gas film coefficient; thermal conductivity

c) Thermal conductivity; liquid film coefficient

d) Liquid film coefficient; gas film coefficient

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Answer: aExplanation: Gas film coefficient largely helps in the determination of numerical value of heat transfer rate. Liquid film coefficient largely helps in determining the value of wall temperatures.

7 - Question

Which of the following might simplify the determination of film coefficient?

a) Combustion oscillations

b) Boundary layer behavior

c) Uniform velocity profile

d) Complex geometry

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Answer: cExplanation: Film coefficient calculation might be simplified for a uniform velocity profile. In reality, the determination of this coefficient is very difficult because of the presence of combustion oscillations, complex geometry, non-uniform velocity profile and presence of boundary layers.

8 - Question

The quantity hgD/k, where hg is the gas film coefficient, D is the diameter of the chamber and k denotes the gas conductivity is __________

a) Bartz number

b) Froude number

c) Nusselt number

d) Prandtl number

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Answer: cExplanation: hgD/k is called as the Nusselt number. This is a parameter which comes into picture while dealing with heat transfer problems between a solid body and a moving fluid.

9 - Question

The quantity μCp/k, where μ is the absolute gas viscosity, Cp is the specific heat of gas at constant pressure and k is the thermal conductivity is called as _________

a) Nusselt number

b) Bartz number

c) Prandtl number

d) Froude number

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Answer: cExplanation: μCp/k is the Prandtl number. It is the ratio of momentum diffusivity to thermal diffusivity.

10 - Question

Determine the Prandtl number for a liquid having thermal conductivity of 4.6 W/mK, Cp of 8 kJ/kgK. Assume the viscosity to be 1.25 Cp.

a) 1.59

b) 7.21

c) 5.91

d) 2.17

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Answer: dExplanation: 1 Cp = 10-3 Pa s Prandtl number Pr = μCp/K = 1.25 10-3 x 8 x 103 / 4.6 = 2.17.