Thermal Engg Lab (ME-306) - Important Questions

Derive the expression for the coefficient of performance (COP) of a vapour compression refrigeration system from laboratory measurements. Given the measured refrigerant mass flow rate $\dot{m}$, measured enthalpies at inlet and outlet of the evaporator $h_{1}$ and $h_{4}$, and the input electrical power $P_{in}$, show that the COP can be written as $$COP = \left( \frac{\dot{m}\,\left[\,h_{1} - h_{4}\,\right]}{P_{in}} \right).$$ Explain how each quantity $\dot{m}$, $h_{1}$, $h_{4}$ and $P_{in}$ is obtained in the laboratory and discuss typical sources of experimental error that affect COP.

From experimental test data of a vapour compression refrigeration unit, locate the state points on the pressure–enthalpy (P–h) diagram and calculate the following: refrigerating effect per unit mass, compressor work per unit mass, mass flow rate of refrigerant for a given cooling load $Q_{L}$, and the volumetric efficiency of the compressor. Present formulas using measured pressures $P$ and enthalpies $h$ and show the calculation steps. For example, express compressor work per unit mass as $$w_{c} = \left( h_{2} - h_{1} \right)$$ and refrigerating effect as $$q_{L} = \left( h_{1} - h_{4} \right).$$

A shell-and-tube heat exchanger is tested in the laboratory. Using the Log Mean Temperature Difference (LMTD) method, derive the expression to determine the overall heat transfer coefficient $U$ from measured inlet and outlet temperatures and heat duty. Given hot fluid inlet and outlet temperatures $T_{h,i}$ and $T_{h,o}$ and cold fluid inlet and outlet temperatures $T_{c,i}$ and $T_{c,o}$, show that the mean temperature difference is $$\Delta T_{lm} = \left( \frac{\left( T_{h,i} - T_{c,o} \right) - \left( T_{h,o} - T_{c,i} \right)}{\ln\left( \frac{T_{h,i} - T_{c,o}}{T_{h,o} - T_{c,i}} \right) } \right)$$ and that $$U = \left( \frac{\dot{Q}}{A\,\Delta T_{lm}} \right),$$ where $\dot{Q}$ is the measured heat duty and $A$ is the heat transfer area. Explain measurement techniques for $\dot{Q}$ and temperatures in the lab.

Describe the laboratory procedure to calibrate a thermocouple and an RTD. Explain how to obtain the calibration curve and determine the sensitivity and linear regression parameters. If calibration data pairs are $\left\{ T_{i}, V_{i} \right\}$ for thermocouple voltage $V$ and temperature $T$, write the least squares fit for $V$ as a function of $T$ and show the expression for slope and intercept.

Perform an uncertainty analysis for the experimentally determined COP of a refrigeration unit. If COP is given by $$COP = \left( \frac{\dot{m}\,\left[\,h_{1} - h_{4}\,\right]}{P_{in}} \right),$$ derive the expression for the combined standard uncertainty $u_{COP}$ using propagation of uncertainty assuming independent measurements of $\dot{m}$, $h_{1}$, $h_{4}$ and $P_{in}$. Express $u_{COP}$ in terms of the partial derivatives of COP with respect to each measured quantity and their standard uncertainties $u_{\dot{m}}$, $u_{h_{1}}$, $u_{h_{4}}$, $u_{P_{in}}$.

In a laboratory test on a heat exchanger, derive the relation between effectiveness $\varepsilon$ and Number of Transfer Units (NTU) for a counterflow exchanger with heat capacity rates $C_{min}$ and $C_{max}$. Show the formula for $\varepsilon$ as a function of NTU and the capacity ratio $C_{r} = \left( \frac{C_{min}}{C_{max}} \right)$ and explain how $U$ can be obtained from measured data using the NTU method.

From laboratory measurements on a condenser of a refrigeration unit, calculate the degree of subcooling and explain its effect on system COP. Given condensing temperature $T_{cond}$, liquid line temperature $T_{liq}$ and saturation temperature corresponding to condenser pressure $T_{sat}$, define subcooling as $$\Delta T_{sub} = \left( T_{sat} - T_{liq} \right)$$ and discuss how a measured increase in $\Delta T_{sub}$ affects refrigeration capacity and compressor work in practical observations.

Describe the experimental procedure for determining the efficiency of a small laboratory boiler using flue gas analysis. Explain how to compute the percentage heat loss due to dry flue gases and the overall boiler efficiency. Present the key formulae and indicate which measured quantities (fuel flow rate, flue gas temperature, flue gas composition, stack gas mass flow) are required.

For a heat transfer laboratory experiment, explain how to compute and present the non-dimensional numbers Reynolds $Re$ and Prandtl $Pr$ for the test conditions. Given fluid velocity $V$, characteristic length $L$, kinematic viscosity $\nu$, specific heat $c_{p}$ and thermal conductivity $k$, write expressions for $$Re = \left( \frac{V\,L}{\nu} \right)$$ and $$Pr = \left( \frac{c_{p}\,\nu}{k} \right).$$ Describe how these values are used to select correlations for heat transfer coefficient estimation and outline the recommended structure for reporting experimental results and uncertainty in a lab report.