Mechanical Engineering: Project Heat Transfer - Coursework Example

Problem ment The aim in this study is to establish how heat transfer takes place in the common water heater. The water heater tank can be viewed as an internal heat generator as it stores incoming cold water, that in turns get heated by two electrical heater coils. The tank is covered by an electric resistor. The resistance is achieved by having polystyrene foam and a thin layer of fibreglass on top and bottom, followed by a thin steel shell and end caps. In Figure 1 there is a heater, with a sectional view cut directly down the middle of the heating element input lines. The isometric view shows the three holes on the top for feeds and outlets. The leftmost hole is the inlet from well, the middle is steam release (if the water heater were to be too pressurized, steam is released through here after a meltdown heating). The right opening acts as an opening for hot water movement the housing pipe systems. Two large cut insulation sections and holes exist on the side, where electrical heater can be placed in side to heat the water. There is also a hole for discharge at the lower side. Material specifications known are given as: Material Thickness (in) Steel tank (AISI C1020 Hot Rolled) 0.078 Polystyrene Insulation 1.5 Steel shell (AISI 304 Sheet Metal) 0.022 Figure 1: Heater details The heater tank brand is given as “Rheemglas standard” Figure 2: Materials and dimensions Parts of an Electric Water Heater For the process of heating water we need three main components. They are: Dip Tube (Inlet tube): This serves as a point for cold water entry into the tank. Outlet Tube: This is a pint of hot water discharge from the tank. Heating element: This serves in heating cold water. There are other essential components in a water heater; Steel tank: This component holds the water. The construction is done with focus on holding of water pressure found in the tank. Temperature and Pressure relief valve: These play a significant role in precautionary measures. The valve in the heater helps the heater to withstand strenuous condition such as extreme pressure and temperature. The location differs but mostly is fitted on the top or side of the tank. Drain Valve: This section is used for cleaning and maintenance. Thermostat: This plays a regulation role of temperature inside the tank. Anticorrosion Anode Rod/ Sacrificial Anode Rod: This section prevents corrosion from taking place inside the tank. The section is constituted of magnesium that acts as anticorrosive agent. The rod is regularly changed to maintain its properties. In addition, an insulator part covers the outer area of the tank. Working principle of hot water system The common voltage for the operation is 220. Water is heated by a current that moves through electrical resistance-heating element. The element are two with one located at the central part of the tank and the other at the lower side. The elements lack synchronization in their operation. This means that the upper and bottom tank heat in an alternating manner. The upper part heat the water between 120-140 F and then the water is moved to the lower heating section through a control mechanism. This is not the case in all heaters as some have only one heating element. This has been shown to be effective during process of maintenance as it is easy to detect any failure of the element. The elements derive power from a thermostat. The thermostat has a switch that takes note of the water temperature. Any drop in temperature triggers the switch to close for movement of current. Alternatively, it opens as the temperature reaches its maximum. Thermostat also has a place for setting the maximum possible temperature of the water. This temperature ranges between 130-140 degrees F. However, it may sometimes go as low as 120 degrees F. This helps in preservation of energy and scald regulation. The flow of the water in the tank takes place once the hot-water tap is opened. The entry of water takes place through the dip tube. The lowering of the temperature activates the thermostat together with the element at the base. This is followed by replacement of water at the top by the cold water. This leads to drop of temperature in the upper area and hence triggers the action of the element. There is no change that occurs once the tap is turned off. This is because the action of the heating element continues to occur until an upper limit is reached on the thermostats. The process is repeated as the hot water is used. Figure 3: 3D view of hot water system Assumptions Though the problem is 3 dimensional, the major part of heat transfer takes place through side wall and end wall, therefore problem can be treated as one dimensional. The heat transfer process is steady and conduction heat transfer take place within tank. The properties such as conductivity, heat transfer coefficient don`t vary with temperature. The outside air conditions is assumed as at room temperature (T=40 F). The conduction resistance is dominated by insulations. The radiation effect is insignificant. The top and bottom fibre glass are insignificant. Analysis 1D heat transfer through water and tank and convection heat transfer can approximate the problem from tank to air. The typical hot water system is shown in figure 3 below (Ref: 1) The heat transfer process is schematically shown in figure below with all heat transmission interactions. Here, L is length of cylinder D: Nominal diameter of cylinder Ts,1 : Inside temperature of water (120 F) T∞: Room temperature (40 F) Q: Heat generation by electric heater r1: inner radius of tank δ: thickness of insulation r2: outer radius of tank Heat conduction through cylinder The heat transfer process is estimated as one dimensional, as per Fourier’s law of heat conduction through cylinder layer is given by assumption as thermal conductivity is constant. Fouriers Law express conductive heat transfer as q = k A dT / s But as we have different layers in series so we will simplify it into Heat conducted through several walls in good thermal contact can be expressed as q = (T1 - Tn) / ((s1/k1A) + (s2/k2A) + ... + (sn/knA)) By Simplifying and putting boundary condition we get qk=qc+qr ; that equals q=∆T/[Rc+Rk,1+Rk,2+Rk,3]; where R is conduction resistance given by Rk =(L/k*A) and Rc=(1/h). Material Properties The thermal material properties of different materials used for hot water heater is taken from Mark`s handbook (ref: 2), the details are as: Steel tank (AISI C1020 Hot Rolled) Thermal conductivity: 27 btu /(h.ft.0F) Steel shell (AISI 304 Sheet Metal) Thermal conductivity: 9.4 btu /(h.ft.0F) Polystyrene Insulation Thermal conductivity: 0.019 btu /(h.ft.0F) Fiberglass Thermal conductivity: 0.23 btu /(h.ft.0F) Air Heat transfer coefficient: 0.352 btu /(h.ft.0F) Calculations Heat loss through side wall & end wall using resistance method: di = 15.67in do = 18.87in tsteel= 0.078 in tnsulation = 1.5 in tsteel shell = 0.022 in h = 0.352 Btu/h ft oF kinsulation = 0.019 Btu/h ft oF ksteel shell = 9.4 Btu/h ft oF kend wall = 27 Btu/h ft oF L =57.723 in Ts = 120oF T = 40oF As = 31.60in2 Ainsu. = 558.16in2 As.s = 7.98in2 q = ∆T/[(1/h)+(L/ks*As)+(L/kinsu.*Ainsu.)+(L/ks.s*As.s)] q = (120-40)/[(0.078/27*31.60)+(1.5/0.019*558.16)+(0.022/27*7.98)] q = 564.82 btu/hr Now we will find heat transfer through heat diffusion equation which is given by q = kA(D T)/(D x) Q is the heat we are solving for, k is the thermal conductivity = 27 Btu/(h * ft * oF) A is the area of the wall = 0.21944ft² D T is the temperature difference = 120 oF - 40 oF = 80 oF D x is the thickness of the wall = 0.078 inch =0.0065ft Q = 27 [Btu/(h * ft * oF)]*( 0.219)*(80 oF) / (0.0065ft) = 72775.38 Btu / h It is the heat required without insulation. Conclusion The experiment is about studying heat transfer in water-heater tank storage. This experiment analyzed using steady state heat transfer. In one hand, the maximum heat transfer is 564.82 btu/hr, which is transferred through the hot water. While on the other hand, the heat transferred without insulation is 72775.38 Btu / h, which is very large value, we can see that the insulation plays an important part in working of heater. There is conduction heat transfer through water and in the tank there is convection heat transfer from tank to air. The heat transfer is dependent in large extent on complexities and variability in heat transfer process. As it can be seen from above calculations, the heat resistance are dependent on dimensions and therefore affects heat transfer by means of variability of dimensions. The relationship is inversely related is if thickness increases the heat transfer decreases and vice versa. If the thickness is increased by 5% the heat transfer decreases by about 5%. References 1) Electric water heater, 2) Marks Standard Handbook for Mechanical Engineer, 11th edition 3) Introduction to Thermodynamics and Heat Transfer 2nd Edition, Yunus A. Cengel, McGraw−Hill Primis ISBN: 0−390−86122−7, 2008 4) Conductive Heat Transfer Read More