**Applied Thermodynamics & Heat Transfer (Mec-A1) - Solutions**

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Your exam is fast approaching. You might be working a job and have a family that needs your time. The last thing you want to do is spend $1,000 on a course to re-learn this material.

If that sounds like you, our **Applied Thermodynamics & Heat Transfer (Mec-A1)**** **help is for you.

**About:** The **Applied Thermodynamics & Heat Transfer exam** is written nationally for aspiring mechanical engineers and a few other disciplines. The code for this exam is:

- Mechanical -
**16-Mec-A1**(or you may see it like YY-Mec-A1,07-Mec-A1, Mec-A1) - Engineering Physics - Phys-B6
- Marine Engineering - Mar-A1
- Naval Architectural - Nav-B1
- Mechatronics - Mex-A4

The exam tests candidate’s understanding of thermodynamics (laws & cycles) and heat transfer (applications and analysis).

**Format:** 3-hour long, open book exam. Out of the eight questions that are asked in the exam, only five need to be attempted; 2 from part A and 3 from part B, or vice versa.

**Dates written:** The exam is offered twice every year in the months of May and December.

**Approved aids:** Since the course is highly computational, any non-communicating calculator is permitted.

After reviewing several previous exams, a pattern in the questions emerges. Here is a summary of the different question types.

Mechanical-A1 Applied Thermodynamics and Heat Transfer contains two parts in question paper thermodynamics and heat transfer. In this article, I’m going to tell you what those are and then I’ll explain how to approach each type.

**Part A – Thermodynamics**

**Heat Exchanger****–**This question tests your knowledge of heat transfer through devices called exchangers. You may be asked to calculate temperature difference calculations, logarithmic mean temperature difference (LMTD) method, or overall heat transfer coefficient, etc. The heat loss by the hot fluid is completely gained by the cold fluid. You have to examine the minute area of contact between two surfaces thereby you can estimate exact heat transfer.

**Reciprocating Air Compressors****-**The reciprocating compressors use a piston cylinder mechanism to increase the pressure for the air delivery. These questions verify your knowledge levels in thermodynamics areas relating to pressure, volume and temperature. You may be asked to calculate the induced power required to drive the compressor. You can consider the mean effective pressure which is theoretical. You may neglect some frictional losses.

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**Reheat and Regenerative Cycle**– Reheat and regenerative are the thermodynamic process. These kinds of questions measure your ability on problem-solving of boiler furnace process, that means heating and cooling air or water. In reheat cycle, the process starts with steam. It is extracted in the turbine. When it becomes wet, it is reheated with the help of flue gases which are in the boiler. The main purpose is to increase the efficiency of the turbine. You need to calculate the mass flow rate of the steam when the turbine power is megawatts. You may also have to calculate pump power and finally verify with the efficiency of reheat.

**Gas Turbine Engine Cycle –**These questions test your knowledge on the gas turbine engine cycle as this runs with open Brayton cycle. So, you'll need to be familiar with the Brayton cycle process. You will be asked to calculate the power output of the turbine from the input, minimum temperature and power required to drive the electric generator. This kind of cycle is generally used for aircraft engines. You will be asked to calculate fraction output and efficiency of the turbine to drive the compressor, the mass flow rate and volumetric flow rate of air entering into the compressor. Temperature and pressure points at entry will be given in the problem.

**Vapour Compression Refrigeration System –**This is based on the refrigeration cycle. You need to be familiar with the whole refrigeration cycle and process of cooling, heating as well as refrigerant properties. In these questions, different refrigerants may use and those properties will be given under a special table supplied for you at the back of the exam. Generally, Freon 12 will be used as the refrigerant and properties need to be verified using the steam tables. You need to calculate the power required to the drive compressor, capacity of the refrigerator in tons and finally the coefficient of performance (COP).

**Thermodynamic Process -**This question relates to the basic thermodynamic process. You need to calculate the efficiency for each thermodynamic process that includes the gas constant and specific heat terminologies. Sometimes, you need to derive the efficiency expression for various thermodynamic processes and you may need to calculate pressure and temperature at different phases. These type of questions deal with general knowledge in calculating the thermodynamic relations between pressure, volume and temperature.

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**Supersaturated or Meta stable Flow through Nozzle –**Flow through nozzles problems always relates to turbine, boiler furnaces, compressors, etc. This type question examines your ability in calculating supersaturated or meta stable flow through the nozzle. You'll need to examine the pressure changes at each phase. You may be asked to calculate the temperature of steam and the pressure of steam at any stages based on the initial parameters. You are required to know how to calculate the velocity of steam at the end of the expansion, which will be

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**Compression Ignition Engine (Diesel Engine) –**These types of questions belong to heat engines which work under a compression ignition cycle called the diesel engine cycle. You need to calculate pressure temperature at each point in the cycle– this can be calculated from the given parameters in the question such as the air that enters the engine with P1 and T1. Those values will be given to you in the question. This kind of calculation checks your knowledge on the thermodynamic relations in the diesel cycle. You need to calculate the efficiency of the cycle that can be found by taking the work done and dividing it by the heat absorbed.

** **

**Rankine Cycle**- The Rankine cycle deals in depth of thermodynamics relation similar to the gas turbine cycle. You will be asked to map the entire process of the turbine cycle. You need to familiar with all the type of stages during the cycle. Typically, you need to calculate the efficiency of Rankine cycle process– you can neglect the pump work (optional) since pump work is a small portion of energy in equations. Later at the final stages of your calculations, you are required to calculate the thermal efficiency of the Rankine cycle. You need to draw a Temperature-Entropy diagram at each phase and are required to calculate the net-work done of the steam.

**Pressure Calculation in Cylinders -**The question tests your knowledge about calculating thermodynamic calculations using single or Multi cylinders formula. You will be asked to calculate pressure in cylinder B based on the existing cylinder pressure A. You need to use continuity equation and find the areas of two cylinders. You need to use the universal gas constant and the Adiabatic index equation. It is based on variable area process using continuity equation P1V1 = P2V2 (Based on Fluid motion) for multi cylinder.

You can find the Gas pressure at cylinder B. Using heat supply equation (Q)

You can get the equation in form of P2; Substitute the equation in continuity equation. So you can find the pressure.

**Steady and Unsteady State Heat Exchangers -**This question is typically numerical and tests your knowledge in the Fourier law of conductions. This question mainly checks your analysis skills in selecting a design. The temperature at each point of the body varies with the position but not with time. Each point of the body remains constant in course of time. You need to calculate the amount of heat released and need to finalize the possible thickness for the nozzle that can withstand temperatures as high as possible. Use the formulas:

The fourier law of conduction (Q)

**Work done by piston calculation in cylinders –**These questions consists of both Thermodynamic and Refrigeration formulas. You will be asked to calculate System Work Done by the compressor. Since the process is isothermal Process Heat Supplied is equal to work done. In order to get the solution, you will be asked about heat calculation Integrating between pressure and temperature or work done by pressure and volume.

__Part B- Heat Transfer__

__Part B- Heat Transfer__

**Combined Conduction and Convection Heat Transfer -**The combination of conduction and convection heat transfer checks your knowledge skills in heat flow between various mediums as it examines your capabilities in designing heat equipment. You need to familiar with heat transfer formulas. Sometimes you may expect a twist in the question if it includes refrigeration formulas. You may expect air condition problems where you need to calculate minimum thickness of the composite window that is needed to ensure that the temperature of the outside surface is some amount of degrees.

The hot fluid temprature (T_{i}) is separated by the layers of solids from a cold fluid at temp (T_{o}).

The steady state heat flow through the system.

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**Convection problem –**These type of question specifically tests your skills on convection heat transfer problems. As the conductivity of the most fluid is much slower than heat transfer from the moving fluid to the solid wall surface, it will take place in convection. You need to calculate the rate of heat transfer by using the below equation and temperature at the exit of the tube.

**Based on Kirchhoff’s law of radiation****–**Tests your ability in calculating heat by light rays called radiation this can be formulated by Kirchoff’s law. There are already given inputs such as rectangular plate dimensions, temperature, anodized aluminium with surface emissivity. You need to calculate the temperature of the surface of the power amplifier. Use the equation:

The heat transfer between two surfaces

**Double Pipe Heat Exchanger -**This question is based on heat exchanger formulas. You will be given the minimal inputs to design a heat exchanger pipes. A heat exchanger is used to transfer heat from a hot to a cold body or between two or more fluids. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contact. You need to calculate number of tubes required consistent with specific in length.

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**Conduction of Heat through a Slab –**These questions are heat transfer related. It tests your knowledge in heat conduction through a slab (square cross section). You will be asked to calculate heat gained by the water when it is moving in a duct and the temperature of the water leaving the duct. Similar to heat transfer calculation you can calculate the temperature at duct outlet. The heat flow through a small elemental thickness dx of a slab under steady state condition. This equation is known as Fourier law of conduction.

**Conduction of Heat through Hollow Cylinder -**The question is based on conduction of heat through hollow conical cylinder. You will be asked to calculate vapour production rate and show the difference between open to ambient and insulated surface. The heat flow through cylinder is considered along radial direction only. Therefore the Fourier equation for cylinder will be (Q)

Consider an elemental thickness dr at a radius r. the heat flow equation through the element dr under steady state condition will be

**Cross Flow - Heat Exchanger (Density changes)****–**Density change questions are numerical problem regarding cross flow heat exchanger. You will be asked to calculate the temperature of the water and air leaving the heat exchanger. Minimum inputs such as water inlet temperature and air flowing is given. The temperature of the hot and cold fluid changes along x as well as along y directions and further you need to calculate the air inlet temperature when outlet conditions are changed.

**Heat Transfer from Insulation Cylinder –**This question is a conduction and convection heat transfer problem. Insulation is used to reduce the heat flow. Heat flow will go on increasing as the thickness of insulation increases. In these kinds of problems, you need to calculate the thickness at which the heat flow becomes max– this is known to be the critical insulation thickness. In addition, you have to calculate the heat flow from the cylinder to the surrounding under steady state conditions (Q).

**Thermo Physical Properties -**The question examines your knowledge in thermo physical properties of materials. You'll need to be familiar with engineering materials and its properties. You need to verify the heating conditions of the material and oil. Thermo physical properties can be simply defined as material properties. You need to calculate the temperature of the wall. If the temperature of the wall is greater than the estimated degrees it will be treated as a failure. If it is below the expected degrees, then it is a safe design operation.

Zak Mouslim is a Mechanical Engineering Graduate of the University of Ottawa (uOttawa). Since 2015, he has worked as a Mechanical Designer for uOttawa. During this time, he applied mechanical engineering principles in various projects such as Design of Turbines, Supercritical Loop, Smart Flap, Three-Wheel Hybrid Vehicle, etc. Also, a paper was published, by the journal International Journal of Heat and Mass Transfer, to support further R&D of the SCWR (Supercritical Cooled-Water Reactor) core system. He was a TA to the following courses but not limited to: Engineering Mechanics for Engineers, Mechanical Engineering, Advanced Strength of Materials, Heat Transfer, Machine Design, Thermodynamics, Fluid Mechanics, FEA, Aerodynamics, CFD, Dynamics of Machinery.

The recommended textbooks for this exam are:

- Fundamentals of Engineering Thermodynamics by Michael J. Moran and Howard N. Shapiro, John Wiley and Sons Incorporated
- Heat and Mass Transfer by Yunus A. Çengel and Afshin J. Ghajar, McGraw Hill Publishing Company Moran, M.J., H.N. Shapiro, B.R. Munson and D.P. DeWitt,
- Introduction to Thermal Systems Engineering: Thermodynamics, Fluid Mechanics, and Heat Transfer. John Wiley and Sons.

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