HEAT TRANSFER
General Description on Heat Transfer Heat: Heat is a process quantity, as opposed to being a state quantity, and is to thermal energy as work is to mechanical energy. Heat flows between regions that are not in thermal equilibrium with each other; it spontaneously flows from areas of high temperature to areas of low temperature. All objects (matter) have a certain amount of internal energy, a state quantity that is related to the random motion of their atoms or molecules. When two bodies of different temperature come into thermal contact, they will exchange internal energy until the temperature is equalized; that is, until they reach thermal equilibrium. The amount of energy transferred is the amount of heat exchanged. It is a common misconception to confuse heat with internal energy: heat is related to the change in internal energy and the work performed by the system. The term heat is used to describe the flow of energy, while the term internal energy is used to describe the energy itself. In common usage the term heat denotes the warmth, or hotness, of surrounding objects and is used to mean that an object has a high temperature. The concept that warm objects "contain heat" is not uncommon, but hot is nearly always used as a relative term (an object is hot compared with its surroundings or those of the person using the term) so that high temperature is directly associated with high heat transfer. The amount of heat that has to be transferred to or from an object when its temperature varies by one degree is called heat capacity. Heat capacity is specific to each and every object or substance. When referred to a quantity unit (such as mass or moles), the heat exchanged per degree is termed specific heat and depends primarily on the composition and physical state (phase) of an object. Fuels generate predictable amounts of heat when burned; this heat is known as heating value and is expressed per unit of quantity. Upon changing from one phase to another, pure substances can exchange heat without their temperature suffering any change. The amount of heat exchanged during a phase change is known as latent heat and depends primarily on the substance and the initial and final phase. Heat Transfer Mechanism
From the fundamental law of heat transfer, it is known that heat tends to move from a high temperature region to a low temperature region. This heat transfer may occur by the mechanisms conduction and radiation. In engineering, the term convective heat transfer is used to describe the combined effects of conduction and fluid flow and is regarded as a third mechanism of heat transfer. Conduction Conduction is the most significant means of heat transfer in a solid. On a microscopic scale, conduction occurs as hot, rapidly moving or vibrating atoms and molecules interact with neighboring atoms and molecules, transferring some of their energy (heat) to these neighboring atoms. In insulators the heat flux is carried almost entirely by phonon vibrations. The "electron fluid" of a conductive metallic solid conducts nearly all of the heat flux through the solid. Phonon flux is still present, but carries less than 1% of the energy. Electrons also conduct electric current through conductive solids, and the thermal and electrical conductivities of most metals have about the same ratio. A good electrical conductor, such as copper, usually also conducts heat well. The Peltier-Seebeck effect exhibits the propensity of electrons to conduct heat through an electrically conductive solid. Thermoelectricity is caused by the relationship between electrons, heat fluxes and electrical currents. When a temperature gradient exists in a body, there is an energy transfer from the high temperature region to the low temperature region. So the energy is transferred by conduction and that the heat transfer rate per unit area is proportional to the normal temperature gradient: q/A ~ δT/δx When the proportionality constant is inserted, q= -kA (δT/δx) Where q is the heat transfer rate and δT/δx is the temperature gradient in the direction of the heat flow. The positive constant k is called the thermal conductivity of the material, and the minus sign is inserted so that the second principal of thermodynamics will be satisfied. So conduction is a heat transfer process by which heat flows is occurred by the vibratory action of molecules without permanent changing of there relative position within a medium for higher to lower temperature region. In conduction heat flow the energy is transferred by direct molecular communication without appreciable displacement of the molecules. When the molecules in one region acquire a mean kinetic energy greater than that of molecules in the adjacent region, as manifested by a difference in temperature, the molecules possessing the greater energy will transmit part of there energy to the molecules in the lower temperature region. Convection
Convection is usually the dominant form of heat transfer in liquids and gases. This is a term used to characterize the combined effects of conduction and fluid flow. In convection, enthalpy transfer occurs by the movement of hot or cold portions of the fluid together with heat transfer by conduction. For example, when water is heated on a stove, hot water from the bottom of the pan rises, heating the water at the top of the pan. Two types of convection are commonly distinguished, free convection, in which gravity and buoyancy forces drive the fluid movement, and forced convection, where a fan, stirrer, or other means is used to move the fluid. Buoyant convection is because of the effects of gravity, and hence does not occur in microgravity environments. Radiation Radiation is the only form of heat transfer that can occur in the absence of any form of medium and as such is the only means of heat transfer through a vacuum. Thermal radiation is a direct result of the movements of atoms and molecules in a material. Since these atoms and molecules are composed of charged particles (protons and electrons), their movements result in the emission of electromagnetic radiation, which carries energy away from the surface. At the same time, the surface is constantly bombarded by radiation from the surroundings, resulting in the transfer of energy to the surface. Since the amount of emitted radiation increases with increasing temperature, a net transfer of energy from higher temperatures to lower temperatures results. Other heat transfer mechanisms •
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Latent heat: Transfer of heat through a physical change in the medium such as water-to-ice or water-to-steam involves significant energy and is exploited in many ways: steam engine, refrigerator, etc. Heat pipe: Using latent heat and capillary action to move heat, it can carry many times as much heat as a similar sized copper rod. Originally invented for use in satellites, they are starting to have applications in personal computers
Survey of Literature A useful engineering quantity to describe the thermal conduction at the interface is the contact conduction uc, which is defined as q = uc ∆Ti Veziroĝlu has analyzed a large number of experiments reported in the literature in order to develop a useful engineering correlation. The contact materials included iron, steel, aluminum, brass, bronze, gun metal, uranium, and magnox. The Interstitial fluids included air, argon, helium, water, glycerol, lubricating oil, and paraffin. The interstitial fluids included air, argon, helium, water, glycerol, lubricating oil and paraffin. The contact conductance’s ranged from 340 to 230,000 W/m 2-K, the contact pressures from 0.017 to 138 MPa, the mean contact temperatures from 27 to 316 oC, The thermal conductivities of the material from 22 to 216 W/m-K, the thermal conductivities of the interstitial fluids from 0.017 to 0.62 W/m-K, the Meyer hardness from
68.9 to 2,400 MPa and the mean surface roughness from 0.08 to 838 µm. The correlation developed by Veziroĝlu is shown graphically. The thermal contact conductance is included in the Nusselt number located on the ordinate, which also includes the effective gap thickness l and the equivalent conductivity of the interstitial fluid λf . On the abscissa is the ratio of the gap number B to the conductivity number K.
The parameter in the plot is the constriction number C. Calculation of the thermal contact conductance may prove difficult, even impossible, due to the difficulty in measuring the contact area, A (A product of surface characteristics, as explained earlier). Because of this, contact conductance/resistance is usually found experimentally, by using a standard apparatus. There have been a number of investigations of joint conductance, as noted by the annotated bibliographies of Hsieh and Davis, and Moore, Atkins, and Blum. Relatively few of these reported investigations, however, have dealt with joint conductance including thermal control materials. Further, no suitable general method has been developed for the prediction of the joint conductance of metallic junctions. The results of such experiments are usually published in Engineering literature, on magazines such as Journal of Heat Transfer, International Journal of Heat and Mass Transfer, etc. Unfortunately, a centralized database of contact conductance coefficients does not exist, a situation which sometimes causes companies to use outdated, irrelevant data, or not taking contact conductance as a consideration at all. CoCoE (Contact Conductance Estimator), a project founded to solve this problem and create a centralized database of contact conductance data and a computer program that uses it, was started in 2006. Backgrounds for Selecting the Present Project The study of thermal contact conductance is an important factor in a variety of numerous engineering applications, largely due to the fact that many physical systems contain a mechanical combination of two materials. Some of the fields where contact conductance is of importance are •
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Electronics o Electronic packaging o Heat sinks o Brackets Industry o Nuclear reactor cooling o Gas turbine cooling o Internal combustion engines
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Flight o o
Heat exchangers Hypersonic flight vehicles Thermal supervision for space vehicles
The previous attempt regarding this experiment was an experimental setup with a mild steel-brass specimen in lieu of which copper-mild steel is used at present. The attempt was taken by a group of brilliant students from BUET. In our case, a screw-loading system has been employed to create the pressure whereas spring scale was used before. After being acquainted with all previous attempts to determine the thermal contact conductance of different materials, an improved version of experimental setup for determining thermal contact conductance with higher accuracy is fabricated. Objectives of the Present Study The objective of this project is to study experimentally thermal contact conductance of different materials. The study of this contact conductance phenomenon implies to plot Temperature vs. distance curve at different pressures to yield the slop of the curve which is being the temperature gradient contained in the Fourier’s Law. Thermal contact conductance at different pressures is also obtained. After obtaining the thermal contact conductance for different pressures, a pressure vs. contact conductance curve is also to be plotted. While availing this project work, infeasibility of various digital equipments for the accuracy of setup is faced. If the pressure sensor were used in lieu of screw-loading system, the experiment would have been carried out with lots of accuracy and precision.
THERMAL CONTACT CONDUCTANCE Thermal Contact Conductance
Fig. 1: Heat flow between to solids in contact and the temperature distribution.
When two solid bodies come in contact, such as A and B in Figure 1, heat flows from the hotter body to the colder body. From experience, the temperature profile along the two bodies varies, approximately, as shown in the figure. A temperature drop is observed at the interface between the two surfaces in contact. This phenomenon is said to be a result of a thermal contact resistance existing between the contacting surfaces. Thermal contact resistance is defined as the ratio between this temperature drop and the average heat flow across the interface. According to Fourier's law, the heat flow between the bodies is found by the relation:
----------------------------------- (1) where q is the heat flow, k is the thermal conductivity, A is the cross sectional area and dT/dx is the temperature gradient in the direction of flow. From considerations of energy conservation, the heat flow between the two bodies in contact, bodies A and B, is found as:
--------------- (2) One may observe that the heat flow is directly related to the thermal conductivities of the bodies in contact kA and kB, the contact area A and the thermal contact resistance 1/hc, which, as previously noted, is the inverse of the thermal conductance coefficient hc. The thermal contact resistance may not be applied for the sandwich kind of materials since they are manufactured by rolling under high temperatures so that the decrease in thermal conductivity is negligible. Factors Influencing Thermal Contact Conductance
Thermal contact conductance is a complicated phenomenon, influenced by many factors. Experience shows that the most important ones are as follows: Contact pressure The contact pressure is the factor of most influence on contact conductance. As contact pressure grows, contact conductance grows (And consequentially, contact resistance becomes smaller). This is attributed to the fact that the contact surface between the bodies grows as the contact pressure grows. Since the contact pressure is the most important factor, most studies, correlations and mathematical models for measurement of contact conductance are done as a function of this factor. Surface cleanliness The presence of dust particles, acids, etc., can also influence the contact conductance. Interstitial materials No truly smooth surfaces really exist, and surface imperfections are visible under a microscope. As a result, when two bodies are pressed together, contact is only performed in a finite number of points, separated by rather large gaps, as can be shown in Fig. 2. Since that actual contact area is reduced, another resistance for heat flow exists. The gasses/fluids filling these gaps may largely influence the total heat flow across the interface. Air is the most common interstitial material. The thermal conductivity of the interstitial material and its pressure are the two properties governing its influence on contact conductance. In the absence of interstitial materials, such as the bodies are in vacuum, the contact resistance will be much larger, since flow through the intimate contact points is dominant. Surface roughness, waviness and flatness One can characterise a surface that has undergone certain finish operations by three properties: Roughness, waviness and flatness. Among these, roughness is of most importance, and is usually indicated by an rms value, Ďƒ. Surface deformations When the two bodies come in contact, surface deformation may occur on both bodies. This deformation may either be plastic or elastic, depending on the material properties and the contact pressure. When a surface undergoes plastic deformation, contact resistance is lowered, since the deformation causes the actual contact area to increase. Modern Equipment for Measuring Thermal Contact Conductance For bulk materials (e.g. two metal rods stuck end-to-end) there are two primary paths for heat conduction between two interfaces at room temperature: one is solid-solid conduction through the contact points, and the other is conduction through an interstitial material
Measurements of contact interfaces have shown that TCCs measured in vacuum are significantly lower than those measured with an interstitial gas, usually air. This behavior is typically attributed to the additional conduction paths offered by the air. For micro machined devices, the roughness of interfaces is on the order of nanometers, several orders of magnitude less than for bulk materials. We have done extensive testing of heat transfer in micro machined devices. Our data shows suggests that trapped interstitial gas at nanometer roughness serves primarily to reduce the solid-solid contact area, overwhelming its traditional role in providing alternate conduction paths
Fig. 3. a) an optical micrograph(b) of a test structure used in this study to measure thermal contact conductance
Definitions of Some Related Terms To evaluate thermal contact conductance, there are some terms that will be necessary: Thermal Conductivity Thermal conductivity, k, is the intensive property of a material indicates its ability to conduct heat.
that
It is defined as the quantity of heat, Q, transmitted in time t through a thickness L, in a direction normal to a surface of area A, due to a temperature difference ΔT, under steady state conditions and when the heat transfer is dependent only on the temperature gradient. Thermal conductivity = heat flow rate × distance / (area × temperature difference)
Constriction number (C) C = (P/M) 1/2 Where P = Contact Pressure M = Meyer hardness of the softer surface Meyer hardness information appropriate for these calculations is discussed in detail by Cetinkale and Fishenden. They consider both the effects of the time of pressure application and average interface temperature on the appropriate value to use for M. As a first approximation, which neglects the time and temperature effects, the value listed in Table may be used. Material
M, MPa
Cast steel
3.52 X 103
Mild steel
1.64 X 103
Brass
1.18 X 103
Aluminum
1.04 X 103
Pure aluminum
0.32 X 103
Table1: Meyer Hardness for several materials
Gap Thickness (l) If l1 and l2 are the RMS roughness values in micrometers of the two surfaces, then: l = 3.56(l1+l2) if l1+l2 < 7 µm l = 0.46(l1+l2) if l1+l2 > 7 µm Interface Size Number (S) Interface size number (S) can be calculated from the square root of the cross-sectional area of each of the mating surfaces (A) divided by the effective gap thickness between them (l). S = √A/l Where A = Cross-sectional area of each of the mating surfaces l = the effective gap thickness between the surfaces. Gap number (B)
B can be calculated from the Constriction number (C) and the gap thickness (l) by the following relation: B = 0.335CY Where Y = 0.315S0.137 A = the total interfacial area (one side).
Conductivity number (K) K = ka (km+ kc) / 2kskc Here the conductivities λ1 and λ2 of the contact solids may be evaluated at the mean gap temperature Τm and ka is the equivalent conductivity of the air. The overall heat transfer coefficient In many instances, it is customary to express the heat flow rate in the cases of the plane wall and cylinder (single or multilayered) with convection at the boundaries in terms of an “overall conductance” or “overall heat transfer coefficient”. This overall heat transfer coefficient, symbolized by U, is simply defined as a quantity such that the rate of heat flow through a configuration is given by taking a product of U, the surface area (A) and the overall temperature difference (Δt)overall: q = U.A.(Δt)overall The dimensions of U are seen to be those of a conductance. If one utilizes the equivalent resistance concept of the electrical networks, the overall conductance U is simply related to the total resistance between the points at which the overall potential (heat) is applied: U = 1/ŖtotalA Fourier’s Law of Heat Conduction: When there exists a temperature gradient within a body, heat energy will flow from the region of high temperature to the region of low temperature. This phenomenon is known as conduction heat transfer, and is described by Fourier's Law (named after the French physicist Joseph Fourier),
This equation determines the heat flux vector q for a given temperature profile T and thermal conductivity k. The minus sign ensures that heat flows down the temperature gradient.
DESCRIPTION OF EXPERIMENTAL SETUP & PROCEDURE
Fig. 4: A photograph of the experimental setup
Experimental Setup EXPERIMENTAL APPARATUS The following apparatus are needed for this experiment:
Loading system o Spring mass type o 8M Bolt & Nut o Coil spring (spring material: Music Wire) Heating system o Cartridge heater Specifications – 220V, 300W, 9.5 mm dia. Rod Specimens o Copper (Upper Part) Size: dia. - 38.0 mm, height - 152.4 mm o Mild Steel (Lower Part) Size: dia. - 38.0 mm, height - 152.4 mm Glass Wool An O-ring to hold the combined Copper-Mild Steel rods A water container made of Galvanized Iron Copper Pipe Mild Steel plates: 7.6 mm thick Eight thermocouples One temperature read-out meter & selector switch Hoses
EXPERIMENTAL ASSEMBLY Figure shows the setup of the experiment. The cylindrical metal pieces are pressed together by a screw loading mechanism whereby a high seating pressure is applied to the interface. The cylindrical surface is insulated to ensure one dimensional heat flow. One metal is Copper and the other metal is Mild Steel. They are insulated circumferentially. The top end of the upper test piece (Copper) is heated by an electric cartridge heater. The bottom end of the lower test piece (Mild Steel) is cooled by water circulation. Type K (Chromel (Ni-Cr alloy) / Alumel (Ni-Al alloy)) thermocouples are embedded at different locations on each metal piece. A coil spring mass loading assembly has been used to apply and indicate the force applied on the system. In the coil spring-mass loading system, two separate hollow cylindrical chambers have been used to hold the spring in-between them. To indicate the magnitude of load being applied, a scale is graded on the hollow chambers. With the compression of the spring, the load is recorded from the grooved scale on the surface of the hollow chambers.
In the lower portion of the assembly, there is a water container made of Galvanized Iron in which the O-ring, holding the mild steel piece is welded. There are water inlet and outlet in this container. The plates are bolted to each other for the ease of assembly and maintenance and good reliability. ď&#x192;&#x2DC; EXPERIMENTAL PROCEDURE The experimental setup contains of two cylindrical metal specimens that are pressed together by a spring mass loading system and whose thermal contact conductance has to be determined. In the interface of the contact, a high seating pressure is applied. The specimens are copper and mild steel. Insulation is provided in the cylindrical surface of the metal specimens by means of glass wool to ensure one dimensional heat flow. They are insulated circumferentially. The top end of the upper test piece i.e. copper is heated by a cartridge heater whereas the bottom end of the lower test piece i.e. mild steel is cooled by the continuous flow of cooling water. Thermocouples are embedded at different locations on each rod. A spring mass loading system has been employed to apply and indicate the force applied on the system. The spring force, at first, is set at 200N. Then the electric heater is switched on along with the circulation of water. It must be continued for a while for temperature distribution or the system to attain steady state. This can be checked by plotting Temperature vs. Time curve for any of the thermocouples. However, when the temperature derivative with respect to time will be zero, the system is assumed to be at steady state. After the steady state being achieved, the readings of all the thermocouples are recorded and written in the data sheet. The above-mentioned procedure is repeated for the spring forces of ď&#x192;&#x2DC; DATA COLLECTION i. From circular steel chamber, the applied force, Fa is to be obtained. ii. Then P is calculated from P = Fa/A ,where A is the cross-sectional area of the rod, m2 iii. For each pressure, Distance vs. Steady state temperature is plotted and hereby the mean gap temperature Tm is also to be obtained. iv. Then S, C and B are calculated from their respective definitions. v. The values of ka, kb and kc at mean gap temperature Tm are found out from the table for conductivity values. vi. kf and K are calculated and then the value of B/K is calculated. vii. U vs. B/K is to be plotted as to find the value of U. viii. uc is to be found out from the formula uc = Ukf/l CALIBRATION OF THERMOCOUPLE
Numerous temperature readings were taken in the experiment using thermocouples. In this experiment, K- type chromel-alumel thermocouples were used. Chromel (90 % Nickel with 10 % Chromium) against alumel (95% Nickel with Al, Si and Mn comprising the remainder) can works under the temperature range -200oc to 0oc and 0oc to 200oc. Some desirable properties in thermocouple materials are as follows: • • • •
Capability of resisting oxidation and corrosion Development of relatively large emf A continuous increase of emf with temperature over its entire ranges Stability of emf with respect to temperature
As the experiments required temperature readings in positive temperature region, so the thermocouples were calibrated in that region. The fused ends of the thermocouple were placed over the tube or pipe at different positions. Six thermocouples were placed over the test section, one was placed over the inlet section and another one is placed over the outlet section. Corresponding temperature of the thermocouple were recorded with the help of digital temperature measurement device and a selector switch Temperature Measuring Means Thermocouple Thermocouples are pairs of dissimilar metal wires joined at least at one end, which generate a net thermoelectric voltage between the open pair according to the size of the temperature difference between the ends, the relative coefficient of the wire pair and the uniformity of the wire-pair relative coefficient.
Fig. 5: Different types of thermocouple wires
Types of thermocouple:
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A variety of thermocouples are available, suitable for different measuring applications (industrial, scientific, food temperature, medical research, etc.). In this experiment we used K- type thermocouple.
Type K (Chromel (Ni-Cr alloy) / Alumel (Ni-Al alloy):
It is known as the "general purpose" thermocouple. It is low cost and, owing to its popularity, it is available in a wide variety of probes. They are available in the −200 °C to +1200 °C range. The type K was specified at a time when metallurgy was nowhere near as advanced as today and consequently characteristics vary considerably between examples. There is another problem in that one of the consituent metals is magnetic (Nickel). The characteristic of the thermocouple undergoes a step change when a magnetic material reaches its Curie point. This occurs for this thermocouple at 354°C. Sensitivity is approximately 41 µV/°C.
Type E (Chromel / Constantan (Cu-Ni alloy):
Type E has a high output (68 µV/°C) which makes it well suited to low temperature (cryogenic) use. Another property is that it is non-magnetic.
Type J (Iron / Constantan) :
Limited range (−40 to +750 °C) makes type J less popular than type K. The main application is with old equipment that cannot accept modern thermocouples. J types cannot be used above 760 °C as an abrupt magnetic transformation causes permanent decalibration. Type J's have a sensitivity of ~52 µV/°C .
Type N (Nicrosil (Ni-Cr-Si alloy) / Nisil (Ni-Si alloy)) :
High stability and resistance to high temperature oxidation makes type N suitable for high temperature measurements without the cost of platinum (B, R, S) types. They can withstand temperatures above 1200 °C. Sensitivity is about 39 µV/°C at 900°C, slightly lower than a Type K. Designed to be an improved type K, it is becoming more popular. Thermocouple types B, R, and S are all noble metal thermocouples and exhibit similar characteristics. They are the most stable of all thermocouples, but due to their low sensitivity (approximately 10 µV/°C) they are usually only used for high temperature measurement (>300 °C).
Type B (Platinum-Rhodium/Pt-Rh):
It is also suited for high temperature measurements up to 1800 °C. Unusually type B thermocouples (due to the shape of their temperature-voltage curve) give the same output at 0 °C and 42 °C. This makes them useless below 50 °C.
Type R (Platinum /Platinum with 13% Rhodium):
It is suited for high temperature measurements up to 1600 °C. Low sensitivity (10 µV/°C) and high cost makes them unsuitable for general purpose use.
Type S (Platinum /Platinum with 10% Rhodium):
It is suited for high temperature measurements up to 1600 °C. Low sensitivity (10 µV/°C) and high cost makes them unsuitable for general purpose use. Due to its high stability type S is used as the standard of calibration for the melting point of gold (1064.43 °C).
Type T (Copper / Constantan):
It is suited for measurements in the −200 to 350 °C range. The positive conductor is made of copper, and the negative conductor is made of constantan. It is often used as a differential measurement since only copper wire touches the probes. As both conductors are non-magnetic Type T thermocouples are a popular choice for applications such as Electrical Generators which contain strong magnetic fields. Type T thermocouples have a sensitivity of ~43 µV/°C Thermocouples are usually selected to ensure that the measuring equipment does not limit the range of temperatures that can be measured. Note that thermocouples with low sensitivity (B, R, and S) have a correspondingly lower resolution. Temperature read-out meter
Fig. 6: Temperature read-out meter
Temperature instruments and temperature indicators are designed for temperature monitoring and analysis. These instruments either come equipped with an integral sensor, or require sensor input. In this experiment we used a circular pipe which has 3 sections. In the middle section (Test section) there is 8 points which contains thermocouple wires. By giving the heat through the variable wattmeter we find different temperature for different thermocouple wires point by rotating the selector switch. These different temperatures are shown in the temperature read-out meter. Selector
switch
Fig. 7: Selector switch
Selector Switches are handled individually and custom manufactured to your exact specifications, or you may choose from a wide offering of standard switches available from franchised distributors. Selector Switches provide thousands of variations of shorting and non-shorting circuitry including mixed shorting and non-shorting circuit combinations within the same pole. Design flexibility is further enhanced by intermixing on the same switch and can also include manufactured AC power switches and variable resistors sections. Selector switches truly offers a one-source supply for the complete switch package. DESIGN & FABRICATION DESIGN & FABRICATION Construction Part •
Selection of Metal Specimen: The metal specimens are selected on the basis of two criteria – one is temperature gradient and another one is thermal conductivity. As copper possesses a greater thermal conductivity when compared to mild steel and a lower temperature gradient, heat will flow uniformly through the cross-section easily. The cartridge heater is inserted in copper rod specimen due to which heat at a greater rate will dissipate through the copper rod and finally to the mild steel specimen. The size i.e. the diameter and height of the specimens were decided by iteration from the Fourier’s Law. On the basis of the result obtained from the linear interpolation, the diameter and height of the metal specimens were firmed.
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Material of Construction: Mild steel plates are selected as the material of construction. Each plate is 7.5 mm thick. In this experiment, higher load (750N) was applied due to which the materials of the construction must resist high load. If metal plates were of smaller thickness, it would not resist higher load exerted by the spring, as a result of which deformation of the structure may occur.
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Position & Selection of Thermocouples: The length of the combined copper-mild steel specimen is one feet. Six thermocouples are embedded in the specimen having the seperation of two inches in-between two consecutive thermocouples. The rest two thermocouples are used in water inlet and outlet to measure the temperatures of water. There are several types of thermocouples available suitable for different measuring applications (industrial, scientific, food temperature, medical research, etc.). In this experiment K- type thermocouple [Chromel (Ni-Cr alloy) / Alumel (Ni-Al alloy)] is selected.
Fabrication Part •
Heating System: The heater is a cartridge type heater. Its specification is 220V, 300W. It is 9.5 mm in diameter. For the aid of the insertion of the heater, drilling is done on the top of the copper rod. Through this hole, the heater is inserted. In this experiment, cartridge type heater is used in lieu of wire heating because heat is much more uniformly flowed throughout.
• The Critical Thickness of Insulation: Insulation is done in heat conducting equipments due to minimize the dissipation of heat by means of convection and radiation process. There is huge practical significance in insulating small pipes or electrical wires. In case of a pipe of a given size, as the thickness of the insulation around it is changed, it exhibits the variation of heat loss from the pipe. As insulation is added to the pipe, the outer exposed surface temperature will decrease, but at the same time the surface areas available for convective heat dissipation will increase. These two opposing effects produce some interesting optimization effects.
Fig. 8: Critical thickness of insulation For ease of analysis, some simplifying assumptions will be made. As noted in Fig. , let
the pipe radius be R and the insulation radius r, so that (r-R) represents the insulation thickness. For fixed values of the temperature of the fluid carried by the pipe and the ambient air at ta, the addition of insulation will alter the pipe surface temperature, T. However, the variation of T is generally so slight that one may take it to be constant. If one also assumes that the heat
transfer coefficient at the exposed insulation surface, h, is also constant, then the heat loss from the pipe is q/L = 2π (T- ta)/[{1/hr} + {ln (r/R)/k}] ………….(_) in which r is the only variable.
Differentiation of Eq. (_) with respect to r will show that the heat loss q/L, reaches a maximum when the insulation radius is equal to r = rc = k/h The symbol rc denotes the “critical radius” of the insulation. The fact that q/L attains a maximum at r = rc is the result of the above-mentioned opposing effects: increasing r increases the thermal resistance of the insulation layer but decreases the thermal resistance of the surface coefficient because of the increasing surface area. At r = rc,
the total resistance reaches a minimum. Thus, it appears possible to increase the heat loss from a pipe by the addition of insulation. This is illustrated in Fig. 8. As shown, the critical radius rc is a quantity fixed by the thermal properties involved. If the pipe size is such that R< rc, then the initial addition of insulation will increase the heat loss until r = rc after which it will begin to decrease. The bare pipe heat loss is again reached at some radius, shown as r* in Fig. 8(a). For a larger pipe, as suggested in Fig. 8(b) for which R > rc, any insulation added will decrease the heat loss. So, this phenomenon is of greater significance that predicts the opposing effects a geometry change may introduce in the thermal resistance and available conductive area of a given situation.
Fig. 9(a)
Fig. 9(b)
Fig. 9: Effect of Critical Thickness upon Heat Transfer
•
Selection of Loading System: The spring-mass loading system is selected. The spring used in this purpose is made of Music Wire that contains 60-70% Carbon content. Similar specifications are UNS G10850, AISI 1085, ASTM A228-51 and BS 5216 gr. 4 and 5. This is the best, toughest and most widely used of all spring materials for small
springs. It can withstand higher stresses under repeated loading than any other spring material. It is advisable to avoid its use above 120 o C or at subzero temperatures. The loading system also has a nut-bolt assembly. The coil spring stays inside two steel chambers those can move within each other with a load scale on its surface. As the bolt is moved downward through the nut, it creates pressure on the steel chamber compressing the spring and hereby the load is applied on the copper rod. The magnitude of the load being applied through the spring by moving the bolt down is indicated on a scale graduated on the upper steel chamber containing the half of the coil spring. The scaling is accomplished according to the deflection of the coil spring obtained from a compression tester in which the spring is calibrated. To withstand the high pressure exerted by the spring, an O-ring exists which is being welded to the water container and clamps the mild steel specimen. Mechanism: As mentioned earlier, loading system contains a coil spring. The main fact is how the spring force is acted upon the copper-mild steel specimen. The spring is designed and calibrated by a compression tester to exert the load of 750N. In this experiment, it is assumed to be the maximum load. Starting from 100N maintaining the sequence by 50N, the load of 750N is recorded by the tester. For each load, the deflection of the coil spring was recorded. From this deflection several grooves was machined on the surface of the upper steel chamber. The chambers move within each other. As a result of which the lower chamber exerts force on the copper rod. For the proper application of load, the axis of load application must be the same as that of the specimens. To avoid the application of load being eccentric, a ball indenter (ball from ball bearing) is machined to the lower surface of the bolt. Otherwise, it wouldnâ&#x20AC;&#x2122;t be a point contact. The advantage of point contact is that the load exerted by the spring will be applied directly and fully to the specimens. The setup located at the heat transfer lab of BUET used a beam-like structure having a lever mechanism of load application. In this particular case, there will be a moment of the beam to overcome which a part of the applied load will be used up. So, the load being exerted by the spring will not be fully or accurately applied upon the specimens in absence of direct contact. In addition, the structure will require extra support for its being rigid. Deflections of the coil spring obtained from the compression tester machine with which aid the spring mass loading system was fabricated is given below Load (N) Deflection (mm) 100 3.66 200 6.81 300 9.94 400 13.02 500 16.03 600 18.83 700 22.41 750 24.11 950 28.45
Fig. 10: Mechanism of Loading System
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Cooling System: Cooling was provided by means of water. The water container is made of galvanized iron (G.I.). It is basically a G.I. pipe. It has a thread on its one side and on the other side there is a hole whose diameter is equal to the diameter of the mild steel specimen with a bit clearance so that mild steel rod can move easily through the hole. There is a O-ring welded upper portion of the water container. There is a cover of G.I. pipe which is also made of Galvanized Iron and is attached to beneath of
the pipe to hold the incoming water from the supply line. The purpose of providing cover is for the aid of cleaning and maintenance of the container. While inserting the 6th thermocouple, it is of huge convenience. The O-ring supports the whole coppermild steel specimen. It must well designed and made of stronger material as to provide good clamping of the mild steel rod. Otherwise, the whole setup may lead to deconstruction. There is a water outlet opposite to the water inlet to maintain a uniform and almost constant flow. Both water inlet and outlet possess one thermocouple to record their respective temperature with the aid of the readout meter. To avoid the overflow of the cooling water, sealing was provided.
Fig. 11: Water container
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Inhibition of Rust & Corrosion: Painting is done in order to provide shield against rust & corrosion. It not only acts as coating but also improvise aesthetic quality of the object. It helps in beautification of the setup. Rust & corrosion can be effectively minimized by providing paint on the setup.
DATA & CALCULATION DATA & CALCULATION Experimental Tables
Temperature (oC) No. Of Obs .
Applied Force, Fs (N)
1
For Copper Rod
For mild Steel Rod
TC-1
TC-2
TC-3
TC-4
TC-5
TC-6
20
259
257
240
129
101
92
2
50
258
256
240
130
102
92
3
60
258
254
240
131
102
93
4
70
258
254
239
131
103
93
5
75
258
253
240
131
103
93
Table2: Recorded Temperatures from the Readout Meter
No. Of Obs.
1
2
3
4
5
Applied Force Fs (N)
20
50
60
70
75
Pressure, P (MPa)
0.173
0.433
0.519
0.605
0.649
184.5
185.0
185.5
185.0
185.0
Items Of Calculation
Average Gap Temperature, Tm (o C) Interface Size Number, S
5282
Constriction Number, C
0.013
0.021
0.023
0.024
0.025
Gap Number, B (×10-3)
4.01
6.53
7.17
7.48
7.81
0.035535
0.0355 6
0.0355 9
0.0355 6
0.0355 9
Kc at temp. Tm (W/m-K)
374.775
374.75
374.72 5
374.75
374.72 5
Ks at Temp. Tm (W/m-K)
47.95388
47.971 2
47.988 5
47.971 2
47.988 5
Kf (W/m-K)
0.035535
0.0355 6
0.0355 9
0.0355 6
0.0355 9
K(10-4)
0.41791
0.4181 3
0.4183 5
0.1813 4
0.1835 3
B/K
9595.228
15616. 9
17138. 6
17888. 9
18668. 4
U From Graph
103
2×103
2.6×103
2.7×103 2.8×103
uc (W/m2-K)(106)
5.79
11.54
15.01
Ka at temp. Tm (W/m-K)
15.58
16.1
Table3: Calculated Data Table
Graphs Temperature vs Distance Curve
Temperature ( celcius)
300 250 200 150
Temperature curve
100 50 0 0
2
4
6
8
10
12
14
Distance (inches)
Obs.: 1
Temperature vs Distance Curve
Temperature ( celcius)
300 250 200 150
Temperature curve
100 50 0 0
2
4
6
8
Distance (inches)
Obs.: 2
10
12
14
Temperature vs Distance Curve
Temperature ( celcius)
300 250 200 150
Temperature curve
100 50 0 0
2
4
6
8
10
12
14
Distance (inches)
Obs.: 3
Temperature vs Distance Curve
Temperature ( celcius)
300 250 200 150
Temperature curve
100 50 0 0
2
4
6
8
Distance (inches)
Obs.: 4
10
12
14
Temperature vs Distance Curve
Temperature ( celcius)
300 250 200 150
Temperature curve
100 50 0 0
2
4
6
8
10
12
14
Distance (inches)
Obs.:5
Sample Calculation Interface Size Number (S) S = √A/l Where A = Cross-sectional area of each of the mating surfaces = Cross-sectional area of Metal-Cross-sectional area of pin = (1.134×10-3 – 7.088×10-5) m2 = 1.06×10-3 m2 l = the effective gap thickness between the surfaces. = 0.46(l1+l2) Where, l1 and l2 are the RMS roughness values in micrometers of the surfaces (Copper & Mild steel), l1=3.4 µm.4, l2=10 µm. So, l= 0.46(3.4+10) µm = 6.164 µm Now, S = √ (1.06×10-3)/ (6.164×10-6) = 5282 Constriction number (C) C = (P/M) 1/2 Where P = Contact Pressure =Fs/A, where, A=X-sectional area of metal = (20×9.81)/1.134×10-3 = 0.173 MPa
two
M = Meyer hardness of the softer surface = 1.02×103 MPa So, C = (0.173/1.02×103)1/2 = 0.013 Gap number (B) B can be calculated from the Constriction number (C) and the gap thickness (l) by the following relation: Where Y = 0.315S = 0.315(5282)0.137 = 1.019 So, B= 0.335 × (0.013)1.019 = 4 × 10-3
B = 0.335CY
0.137
Equivalent Conductivity of air (kf) kf = ka+5.164×10-13(Tm)3 ;where ka=Thermal conductivity of air = 0.03553+5.164×10-13× (184.5)3 = 0.03553 W/m-k (For Thermal Conductivity values see APPNENDIX – A) Conductivity number (K) K= kf (kc+ks)/(2×kc×ks) Where kc = Thermal conductivity of Copper = 347.775 W/m-k ks = Thermal conductivity of Mild Steel = 47.95 W/m-k So, K= 0.03553(347.775+47.95)/(2×347.775) = 0.4179 W/m-k Contact conductance (uc) uc = Ukf/l
Where, U=Conductance number, From graph of U vs. B/K, U=103 ;(See APPENDIX – B) So, uc = 103×0.03553/6.164×10-6 = 5.79×106 W/m2-k
DISCUSSION DISCUSSION
From the graphical representation of the obtained data, it is observed that thermal conductance varies at a proportional rate with the overall heat transfer co-efficient of the material. In this experiment since copper and mild steel are the metal specimens, it has been observed that greater heat transfer rate is through the copper rod. Copper having a thermal conductivity of 385 W/m-K at room temperature experiences a greater heat transfer than the mild steel. For this reason, the heater is drilled into the upper copper rod portion. The insulation is accomplished by employing glass wool to the circumferential area of the setup. The advantage of glass wool is that it is of low cost and has a low thermal conductivity of 0.0038 W/m-K. Besides, its availability is well enough. Here, form the theoretical aspect, the temperature vs. distance curve is linear for copper portion. But in case of our practical experience, it is not fully linear. It may be due to material defects, improper insulation, and improper contact characteristics values, etc. There is a drop of temperature is observed at the thermal contact between the two specimens. After the contact, it is almost linear for mild steel portion. It was not fully possible to provide a perfect cooling system. The water container of the cooling system was specially designed. If it were screw-threaded to the upper supporting metal plate, leakage problem arouse due to the defects would have been prevented. The diameters of the specimens, here, are large. If smaller diameters were taken, then heat would be uniformly distributed through the specimens that would help in attaining the steady state easily. From the Fourier’s law, the temperature gradient we have considered here was 60. If a smaller value than this were taken, the distance between the thermocouples was decreased along the heat transfer rate. Instead of all the drawbacks, the temperature distribution obtained is pretty much identical with the theoretical case. Recommendations for the Future Work For the future study and analysis, the following recommendations may be considered: •
Experiment may be performed with the combination of different metals other than copper and mild steel with the variation in their dimensions i.e. in their diameters and heights.
•
Experiment may be performed a wide range of thermal conductivities.
•
Experiment may be performed for a wide range of pressures by the loading system constructed. By changing the material of the coil spring and changing the diameters of the spring, a large range of load may be exhibited while doing the experiment.
•
Experiment may be performed employing pressure sensor in the surface contacts in order to attain highly accurate and precise results.
APPENDIX - A Table A1: Thermophysical Properties Of Selected Metallic Solids
Table A2: Thermophysical Properties Of Selected Metallic Solids (Contd.)
Table A3: Thermophysical Properties Of Selected Metallic Solids (Contd.)
APPENDIX - B
Fig B1: B/K vs. U Curve