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Assessment for ENG2023

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A cylindrical vessel for producing steam contains water at $100^oC$ and is mounted on insulated walls above a heater in the Figure shown below. The diameters of the vessel and the heater are both $1.0m$ and the heater is kept at $1200^oC$. The heater has an emissivity of $0.7$ and the surface of the vessel has an emissivity of $0.5$.

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Calcuate the view factor $F_{11}$.

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Calculate the viewfactor $F_{12}$.

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Calculate the viewfactor $F_{13}$.

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Calculate the viewfactor $F_{21}$.

Calculate the viewfactor $F_{22}$.

Calculate the viewfactor $F_{23}$.

Calculate the viewfactor $F_{31}$.

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Calculate the viewfactor $F_{32}$.

Calculate the viewfactor $F_{33}$.

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The rate of radiative heat transfer in $kW$ to the water. Please only mention the magnitude in your answer.

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The temperature of the insulated walls. Please provide your answer in $K$.

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An electrical cable of diameter $5mm$ is designed to carry an electrical current such that the heating effect is $300 W$ per metre length. The cable is in an environment having a temperature of $30^oC$. The heat transfer coefficient between the cable and the environment is $30 W/m^2K$. A very thin coating of electrical insulation is applied to the cable, with a contact resistance equivalent to $0.03 m^2K/W$.

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What is the electrical insulation temperature in $^oC$?

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What is the cable surface temperature in $^oC$?

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What is the difference between cable temperature with insulation and without insulation in $^oC$?

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The condenser of a large steam power plant is a heat exchanger in which steam is condensed to liquid water. Assume the condenser to be a shell-and-tube heat exchanger consisting of a single shell and 30,000 tubes, each executing two passes. The tubes are of thin wall construction with a diameter of $25 mm$, and steam condenses on their outer surface with an associated convection coefficient of $11000 W/m^2K$. The heat transfer rate that must be effected by the exchanger is $2000 MW$, and this is accomplished by passing cooling water through the tubes at a rate of $30,000kg/s$.

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The water enters at $20^oC$, while the steam condenses at $50^oC$. What is the temperature (in $^oC$) of the cooling water emerging from the condenser?

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Calculate the log mean temperature difference in $^oC$.

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What is the required tube length in $m$ per pass?

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An energy efficient house is equipped with a ground source heat pump with claimed $COP = 4.0$ to continuously deliver $300W$ for water heating at $60^oC$ and $2700W$ for space heating at $30^oC$ when the ground source temperature is $5^oC$:

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Calculate the power required to drive the heat pump in $W$.

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Calculate the rate of heat extraction in $W$ from the ground source.

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Evaluate the value of Clausius integral in $W/K$

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Is this system physically plausible?

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Please note that you have not attempted this part of the assessment.

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You have 5 minutes remaining to complete the exam.

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ENG2023: Thermal Engineering

This is an open-book assessment. A data sheet is also provided in the exam, at the end of the question list.

Answer all the questions.

Unless otherwise stated in the Question the following values may be assumed:

Air behaves as an ideal gas with constant specific heat capacities:
$c_p= 1005 J/(kg.K)$, $c_v= 718 J/(kg.K)$ and $R= 287 J/(kg.K)$

Density of liquid water $\\rho= 1000 kg/m^3$
Gravitational field strength $g=9.81 N/kg$
The Stefan-Boltzmann constant $\\sigma=5.67 \\times 10^{-8} W/(m^2.K^4)$

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