Design and Optimization of Thermal Systems Episode 1 Part 7 pptx

Consequently, it is very important to understand the various types of models that may be developed; the basic procedures that may be used to obtain a satisfactory model; validation of th

several new ideas and materials What are the important means of communicating these designs and to which groups within or outside the company do you need to make presentations?

(a) A very efficient room air-conditioning system

(b) A new radiator design for an automobile

(c) A substantially improved and efficient household refrigerator.2.24 For the thermal systems in the preceding problem, outline the main design steps employed by you and your design group to reach optimal solutions

2.25 You have just joined the design and development group at Panasonic, Inc The first task you are given is to work on the design of a thermal system to anneal TV glass screens Each screen is made of semi-trans-parent glass and weighs 10 kg You need to heat it from a room temper-ature of 25°C to 1100°C, maintain it at this temperature for 15 minutes, and then cool slowly to 500°C, after which it may be cooled more rap-idly to room temperature The allowable rate of temperature change

with time, ∂T/∂t, is given for heating, slow cooling, and fast cooling

processes Any energy source may be used and high production rates and uniform annealing are desired

(a) Give the sketch of a possible conceptual design for the system and

of the expected temperature cycle Briefly give reasons for your choice

(b) List the requirements and constraints in the problem

(c) Give the location and type of sensors you would use to control the system and ensure safe operation Briefly justify your choices (d) Outline a simple mathematical model to simulate the process.2.26 You are asked to design the cleaning and filtration system for a

round swimming pool of diameter D and depth H The system must

be designed to run the entire volume of water contained in the pool through the system in 5 hours, after which a given level of purity must

be achieved

(a) Give the formulation of the design problem

(b) Provide a sketch of a possible conceptual design

(c) Suggest the location of two sensors for purity measurements.2.27 As an engineer at General Motors Co., you are asked to design an engine cooling system The system should be capable of removing 15 kW of energy from the engine of the car at a speed of 80 km/h and ambient temperature of 35°C The system consists of the radiator, fan, and flow arrangement The dimensions of the engine are given The distance between the engine of the car and the radiator must not exceed 2.0 m and the dimensions of the radiator must not exceed 0.5 m r 0.5 m r0.1 m

(a) Give the formulation of the design problem No explanations are needed.

(b) Give a possible conceptual design

(c) If you are allowed two sensors for safety and control, what sensors would you use and where would you locate these?

2.28 As an engineer employed by a company involved in designing and

manufacturing food processing equipment, you are asked to design a baking oven for heating food items at the rate of 2 pieces per second Each piece is rectangular, approximately 0.06 kg in weight, and less than 4 cm wide, 6 cm long, and 1 cm high The length of the oven must not exceed 2.0 m and the height as well as the width must not exceed 0.5 m

(a) Sketch a possible conceptual design for the system Very briefly give reasons for your selection

(b) List the design variables and constraints in the problem

(c) Which materials will you use for the outer casing, inner lining, and heating unit of the oven? Briefly justify your answers

Thermal Systems

3.1 INTRODUCTION

3.1.1 I MPORTANCE OF M ODELING IN D ESIGN

Modeling is one of the most crucial elements in the design and optimization of thermal systems Practical processes and systems are generally very complicated and must be simplified through idealizations and approximations to make a prob-lem amenable to a solution The process of simplifying a given problem so that

it may be represented in terms of a system of equations, for analysis, or a

physi-cal arrangement, for experimentation, is termed modeling By the use of

mod-els, relevant quantitative inputs are obtained for the design and optimization of processes, components, and systems However, despite its importance, and even though analysis is taught in many engineering courses, very little attention is given to modeling

Modeling is needed for understanding and predicting the behavior and teristics of thermal systems Once a model is obtained, it is subjected to a variety of operating conditions and design variations If the model is a good representation of the actual system under consideration, the outputs obtained from the model char-acterize the behavior of the given system This information is used in the design process as well as in the evaluation of a particular design to determine if it satis-fies the given requirements and constraints Modeling also helps in obtaining and comparing alternative designs by predicting the performance of each design, ulti-mately leading to an optimal design Thus, the design and optimization processes are closely coupled with the modeling effort, and the success of the final design

charac-is very strongly influenced by the accuracy and validity of the model employed Consequently, it is very important to understand the various types of models that may be developed; the basic procedures that may be used to obtain a satisfactory model; validation of the model obtained; and its representation in terms of equa-tions, governing parameters, and relevant data on material properties

3.1.2 B ASIC F EATURES OF M ODELING

The model may be descriptive or predictive We are all very familiar with

mod-els that are used to describe and explain various physical phenomena A working model of an engineering system, such as a robot, an internal combustion engine,

a heat exchanger, or a water pump, is often used to explain how the device works Frequently, the model may be made of clear plastic or may have a cutaway section to

show the internal mechanisms Such models are known as descriptive and are

fre-quently used in classrooms to explain basic mechanisms and underlying principles.Predictive models are of particular interest to our present topic of engineering design because these can be used to predict the performance of a given system The equation governing the cooling of a hot metal sphere immersed in an exten-sive cold-water environment represents a predictive model because it allows us

to obtain the temperature variation with time and determine the dependence of the cooling curve on physical variables such as initial temperature of the sphere, water temperature, and material properties Similarly, a graph of the number of items sold versus its cost, such as that shown in Figure 1.6, represents a predictive model because it allows one to predict the volume of sales if the price is reduced

or increased Models such as the control mass and control volume formulations in thermodynamics, representation of a projectile as a point to study its trajectory, and enclosure models for radiation heat transfer are quite common in engineer-ing analysis for understanding the basic principles and for deriving the governing equations A few such models are sketched in Figure 3.1

Modeling is particularly important in thermal systems and processes because

of the generally complex nature of the transport, resulting from variations with space and time, nonlinear mechanisms, complicated boundary conditions, cou-pled transport processes, complicated geometries, and variable material proper-ties As a result, thermal systems are often governed by sets of time-dependent,

FIGURE 3.1 A few models used commonly in engineering: (a) Control volume, (b) control

mass, (c) graphical representation, and (d) enclosure configuration for thermal radiation analysis.

multidimensional, nonlinear partial differential equations with complicated mains and boundary conditions Finding a solution to the full three-dimensional, time-dependent problem is usually an extremely involved process In addition, the interpretation of the results obtained and their application to the design pro-cess are usually complicated by the large number of variables involved Even

do-if experiments are carried out to obtain the relevant input data for design, the expense incurred in each experiment makes it imperative to develop a model to guide the experimentation and to focus on the dominant parameters Therefore, it

is necessary to neglect relatively unimportant aspects, combine the effects of ferent variables in the problem, employ idealizations to simplify the analysis, and reduce the number of parameters that govern the process or system This effort also generalizes the problem so that the results obtained from one analytical or experimental study can be extended to other similar systems and circumstances

dif-Physical insight is the main basis for the simplification of a given system to

obtain a satisfactory model Such insight is largely a result of experience in ing with a variety of thermal systems Estimates of the underlying mechanisms and different effects that arise in a given system may also be used to simplify and idealize Knowledge of other similar processes and of the appropriate approxima-tions employed for these also helps in modeling Overall, modeling is an innovative process based on experience, knowledge, and originality Exact, quantitative rules cannot be easily laid down for developing a suitable model for an arbitrary sys-tem However, various techniques such as scale analysis, dimensional analysis, and similitude can be and are employed to aid the modeling process These methods are based on a consideration of the important variables in the problem and are pre-sented in detail later in this chapter However, modeling remains one of the most difficult and elusive, though extremely important, aspects in engineering design

deal-In many practical systems, it is not possible to simplify the problem enough

to obtain a sufficiently accurate analytical or numerical solution In such cases, experimental data are obtained, with help from dimensional analysis to deter-mine the important dimensionless parameters Experiments are also crucial to the validation of the mathematical or numerical model and for establishing the accuracy of the results obtained Material properties are usually available as dis-crete data at various values of the independent variable, e.g., density and thermal conductivity of a material measured at different temperatures For all such cases,

curve fitting is frequently employed to obtain appropriate correlating equations

to characterize the data These equations can then serve as inputs to the model of the system, as well as to the design process Curve fitting can also be used to rep-resent numerical results in a compact and convenient form, thus facilitating their use Figure 3.2 shows a few examples of curve fitting as applicable to thermal processes, indicating best and exact fits to the given data In the former case, the curve does not pass through each data point but represents a close approximation

to the data, whereas in the latter case the curve passes through each point Curve fitting approaches the problem as a quantitative representation of available data Though physical insight is useful in selecting the form of the curve, the focus in this case is clearly on data processing and not on the physical problem

The validation of the model developed for a given system is another very

important consideration because it determines whether the model is a faithful representation of the actual physical system and indicates the level of accuracy that may be expected in the predictions obtained from the model Validation

is often based on the physical behavior of the model, application of the model

to existing systems and processes, and comparisons with experimental or numerical data In addition, as mentioned in Chapter 2, modeling and design are linked so that the feedback from system simulation and design is used to improve the model Models are initially developed for individual processes and components, followed by a coupling of these individual models to obtain the model for the entire system This final model usually consists of the gov-erning equations; correlating equations derived from experimental data; and curve-fit results from data on material properties, characteristics of relevant components, financial trends, environmental aspects, and other considerations relevant to the design

3.2 TYPES OF MODELS

There are several types of models that may be developed to represent a thermal system Each model has its own characteristics and is particularly appropriate for certain circumstances and applications The classification of models as descrip-tive or predictive was mentioned in the preceding section Our interest lies mainly

in predictive models that can be used to predict the behavior of a given system for

a variety of operating conditions and design parameters Thus, we will consider only predictive models here, and modeling will refer to the process of developing such models There are four main types of predictive models that are of interest

in the design and optimization of thermal systems These are:

Best fit

FIGURE 3.2 Examples of curve fitting in thermal processes.

is provided by conduction heat transfer through a multilayered wall, which may

be analyzed in terms of an analogous electric circuit with the thermal resistance represented by the electrical resistance and the heat flux represented by the elec-tric current, as shown in Figure 3.3(a) The temperature across the region is the potential represented by the electric voltage Then, Ohm’s law and Kirchhoff’s laws for electrical circuits may be employed to compute the total thermal resis-tance and the heat flux for a given temperature difference, as discussed in most heat transfer textbooks

Similarly, the analogy between heat and mass transfer is often used to apply the experimental and analytical results from one transport process to the other The density differences that arise in room fires due to temperature differences are often simulated experimentally by the use of pure and saline water, the latter being more dense and thus representative of a colder region The flows generated

in a fire can then be studied in an analogous salt-water/pure-water arrangement, which is often easier to fabricate, maintain, and control Figure 3.3(b) shows the analog modeling of a fire plume in an enclosure The flow is closely approxi-mated However, the jet is inverted as compared to an actual fire plume, which

is buoyant and rises; salt water is heavier than pure water and drops downward

A graph is itself an analog model because the coordinate distances represent the physical quantities plotted along the axes Flow charts used to represent computer codes and process flow diagrams for industrial plants are all analog models of the physical processes they represent; see Figure 3.3(c)

Clearly, the analog model may not have the same physical appearance as the system under consideration, but it must obey the same physical principles

Flow diagram 3

2 1

(c) (b)

(a)

Electrical circuit analog

Composite wall waterPure

Salt water jet

FIGURE 3.3 Analog models (a) Conduction heat transfer in a composite wall; (b) analog

model of plume flow in a room fire; and (c) flow diagram for material flow in an industry.

However, even though analog models are useful in the understanding of cal phenomena and in representing information or material flow, they have only

physi-a limited use in engineering design This is mphysi-ainly becphysi-ause the physi-anphysi-alog models themselves have to be solved and may involve the same complications as the original problem For instance, an electrical analog model results in linear alge-braic equations that are usually solved numerically Therefore, it is generally better to develop the appropriate mathematical model for the thermal system rather than complicate the modeling by bringing in an analog model as well

3.2.2 M ATHEMATICAL M ODELS

A mathematical model is one that represents the performance and characteristics

of a given system in terms of mathematical equations These models are the most important ones in the design of thermal systems because they provide considerable versatility in obtaining quantitative results that are needed as inputs for design Math-ematical models form the basis for numerical modeling and simulation, so that the system may be investigated without actually fabricating a prototype In addition, the simplifications and approximations that lead to a mathematical model also indicate the dominant variables in a problem This helps in developing efficient experimental models, if needed The formulation and procedure for optimization are also often based on the characteristics of the governing equations For example, the sets of equa-tions that govern the characteristics of a metal casting system or the performance of

a heat exchanger, shown respectively in Figure 1.3 and Figure 1.5, would, therefore, constitute the mathematical models for these two systems A solution to the equa-tions for a heat exchanger would give, for instance, the dependence of the total heat transfer rate on the inlet temperatures of the two fluids and on the dimensions of the system Similarly, the dependence of the solidification time in casting on the initial temperature and cooling conditions is obtained from a solution of the corresponding governing equations Such results form the basis for design and optimization

As mentioned earlier, the model may be based on physical insight or on curve fitting of experimental or numerical data These two approaches lead to two types

of models that are often termed as theoretical and empirical, respectively Heat

transfer correlations for convective transport from heated bodies of different shapes represent empirical models that are frequently employed in the design

of thermal systems The basic objective of mathematical modeling is to obtain mathematical equations that represent the behavior and characteristics of a given component, subsystem, process, or system Mathematical modeling is discussed

in detail in the next section, focusing on the use of physical principles such as servation laws to derive the governing equations Curve fitting of data to obtain mathematical representations of experimental or numerical results, thus yielding empirical models, is discussed later

con-3.2.3 P HYSICAL M ODELS

A physical model is one that resembles the actual system and is generally used to obtain experimental results on the behavior of the system An example of this is a

scaled down model of a car or a heated body, which is positioned in a wind tunnel

to study the drag force acting on the body or the heat transfer from it, as shown

in Figure 3.4 Similarly, water channels are used to investigate the forces acting

on ships and submarines In heat transfer, a considerable amount of experimental data on heat transfer rates from heated bodies of different shapes and dimensions,

in different fluids, and under various thermal conditions have been obtained by using such scale models In fact, physical modeling is very commonly used in areas such as fluid mechanics and heat transfer and is of particular importance in thermal systems The physical model may be a scaled down version of the actual system, as mentioned previously, a full-scale experimental model, or a prototype that is essentially the first complete system to be checked in detail before going into production The development of a physical model is based on a consideration

of the important parameters and mechanisms Thus, the efforts directed at ematical modeling are generally employed to facilitate physical modeling This type of model and the basic aspects that arise are discussed in Section 3.4

conditions and design parameters Only very simple cases can usually be solved by analytical procedures; numerical techniques are needed for most practical systems Numerical modeling refers to the restructuring and discretization of the governing equations in order to solve them on a computer The relevant equations may be algebraic equations, ordinary or partial differential equations, integral equations,

or combinations of these, depending upon the nature of the process or system under consideration

Numerical modeling involves selecting the appropriate method for the tion, for instance, the finite difference or the finite element method; discretizing the mathematical equations to put them in a form suitable for digital computa-tion; choosing appropriate numerical parameters, such as grid size, time step, etc.; and developing the numerical code and obtaining the numerical solution; see, for instance, Gerald and Wheatby (1994), Recktenwald (2000), and Matthews and Fink (2004) Additional inputs on material properties, heat transfer coefficients, component characteristics, etc., are entered as part of the numerical model The validation of the numerical results is then carried out to ensure that the numerical scheme yields accurate results that closely approximate the behavior of the actual physical system The numerical scheme for the solution of the equations that gov-ern the flow and heat transfer in a solar energy storage system, for instance, rep-resents a numerical model of this system Since numerical modeling is closely linked with the simulation of the system, these two topics are presented together

solu-in the next chapter Figure 3.5(a) shows a sketch of a typical numerical model for

a hot-water storage system in the form of a flowchart Figure 3.5(b) shows the

(b) (a)

Material property data

Experimental data

Mathematical model

Numerical model

Analytical methods

FIGURE 3.5 Numerical modeling (a) A computer flowchart for a hot-water storage

sys-tem and (b) various inputs and components that constitute a typical numerical model for

a thermal system.

various components of the code, such as material properties, mathematical model, experimental data, and analytical methods, that are linked together through the main numerical scheme to obtain the solution.

3.2.5 I NTERACTION BETWEEN M ODELS

Even though the four main types of modeling of particular interest to design are presented as separate approaches, several of these frequently overlap in practi-cal problems For instance, the development of a physical scale model for a heat treatment furnace involves a consideration of the dominant transport mechanisms and important variables in the problem This information is generally obtained from the mathematical model of the system Similarly, experimental data from physical models may indicate some of the approximations or simplifications that may be used in developing a mathematical model Although numerical modeling

is based largely on the mathematical model, outputs from the physical or analog models may also be useful in developing the numerical scheme Mathematical modeling is generally the most significant consideration in the modeling of ther-mal systems and, therefore, most of the effort is directed at obtaining a satisfac-tory mathematical model If an analytical solution of the equations obtained is not convenient or possible, numerical modeling is employed Physical models are used if the numerical solution is not easy to obtain; they also provide validation data for the mathematical and numerical models

3.2.6 O THER C LASSIFICATIONS

There are several other classifications of modeling frequently used to ize the nature and type of the model Thus, the model may be classified as steady state or dynamic, deterministic or probabilistic, lumped or distributed, and dis-crete or continuous

character-A steady-state model is one whose properties and operating variables do not change with time If time-dependent aspects are included, the model is dynamic.

Thus, the initial, or start-up, phase of a furnace would require a dynamic model, but this would often be replaced by a steady-state model after the furnace has been operating for a long time and the transient effects have died down The development of control systems for thermal processes and devices generally

require dynamic models Deterministic models predict the behavior of the system with certainty, whereas probabilistic models involve uncertainties in the system

that may be considered as random or as represented by probability distributions Models for supply and demand are often probabilistic, while typical thermal sys-

tems are analyzed with deterministic models Lumped models use average values over a given volume, whereas distributed models provide information on spatial variation Discrete models focus on individual items, whereas continuous models

are concerned with the flow of material in a continuum In a heat treatment tem, for instance, a discrete model may be developed to study the transport and temperature variation associated with a given body, say a gear, undergoing heat