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Modeling of Combustion Processes – Theory and
Application
7,5
ECTS
Ladok code:A506TA
The exam is given to: KMREC
Date of exam: 180528 Time: 14.00-18.00
Means of assistance: Calculator, Dictionary, Mathematical tables
Total amount of points on exam: 50 points Requirements for grading:
Grade F: Less than 17 points Grade FX: Minimum 17 points Grade E: Minimum 20 points Grade D: Minimum 25 points Grade C: Minimum 30 points Grade B: Minimum 35 points Grade A: Minimum 40 points
Additional information:
Next re-exam date:
The marking period is, for the most part, 15 working days, plus up to 5 working days for administration: Otherwise it´s the following date:
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1. One of the most important dimensionless numbers within heat transfer is the Nusselt number.
a. Show how it is defined and explain all included parameters. (2p) b. Explain the usage of the Nusselt number. (2p)
2. A planar wooden wall with thickness of 10 cm is surrounded by air at -10°C on side 1 and +20°C on the other side (side 2). The heat transfer coefficients are 10 W/m2,K on side 1
and 5 W/m2,K on side 2. The conductivity of the wall is 0.12 W/m,K.
a. Calculate the surface temperatures and draw the temperature profile in the wall (4p) b. What will be the surface temperatures if a 2 cm plaster board layer (k=0.17
W/m,K) is added on side 2? (2p)
3. Consider a stationary reaction on a catalytic surface. Substance A and B exists in the external flow with equal concentrations (5 mol/m3) and reacts according to A+B 2 C.
The reaction is endothermic with a heat of reaction of +100 kJ/mol A. The developed velocity boundary layer is 1 cm, Pr=0.7 and the effective convective coefficient is 10 W/m2,K. The flow is entering at 300°C and the surface should not be below 280°C. In
the boundary layer the effective diffusivity of specie A and B is equal to 10-4 m2/s. The
reaction is a first order reaction with the pre-exponential factor equal to 1e7 and the
activation energy of 50 kJ/mol. Determine what is limiting the reaction. List the
assumptions. (10p)
4. In order to evaluate a reaction, a TGA is often used whereby the reaction rate can be determined.
a. Explain what the meaning is of non-isothermal and isoconversional evaluation of reaction kinetics. (3p)
b. In a particular evaluation, both the KAS method (which is a p(y)-isoconversional method) and the rate-isoconversional method (differential evaluation of the expression also denoted as Type A). The following data was derived:
Conversion Ea (KAS) [J/mol] Ea (Type A) [J/mol]
0.2 10281 10250 0.4 10370 10726 0.6 12683 12841 0.8 12982 13157
Which of the two models would be best to use? (2p)
c. Is the assumption for evaluating the reaction kinetics according to these non-isothermal and isoconversional methods used fulfilled? What is missing?
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5. In many situations there is a need for numerical solutions of the heat transfer models. This is valid even for rather simple systems with only conduction as soon as the studied area is complex. There is therefore a need for introduction of a nodal network and estimation of the terms in the model. Show how the Fourier law can be expressed in two dimensional nodal network with equal spacing in x and y direction and constant
conductivity. (5p)
6. Explain the meaning of the following equation and also explain all included terms.
(4p)
7. On each side of a horizontal plate with a thickness of 5 cm there are flows with different concentrations. Above the plate the flow is consisting of two materials; the bulk material (noted as B) and specie A (concentration 2 mol/m3) is above the plate and below the
plate are specie C with concentration of 5 mol/m3. Each side has a flow velocity of 1
m/s. To test the diffusion, a hole was drilled in the plate with a diameter of 2 cm. a. What is the net flux through the hole? List the assumptions. (5p) b. What is the net flux if the hole instead goes between two small containers (spheres with a diameter of 5 cm)? (2p)
8. It is often a problem to correctly measure the temperature inside a furnace with a thermocouple. The reason is the radiation.
a. Estimate the temperature error when the temperature in the gas phase
surrounding the thermocouple is 700°C and the walls are around 500°C and they will cover the whole visible area from the thermocouple. At these condition the convective coefficient is 50 W/m2,K and the conductivity of the thermocouple is
very low (can be neglected). (4p) b. What will be the temperature if the gas phase is increased to 850°C? (1p) c. One method to handle this problem is to surround the thermocouple with a
sphere constructed a coarse metallic net. Explain why this would improve the temperature measurements. (2p)
