Design and Optimization of Thermal Systems Episode 1 Part 3 pptx

22 Design and Optimization of Thermal Systems

It is important to recognize that thermal systems arise in many diverse fields of

engineering, such as aerospace engineering, manufacturing, power generation, and

air conditioning. Consequently, a study of thermal systems usually brings in many

additional mechanisms and considerations, making the problem much more com￾plicated than what might be expected from a study of thermal sciences alone.

1.3.2 ANALYSIS

The analysis of thermal systems is often complicated because of the complex

nature of fluid flow and of heat and mass transfer mechanisms that govern these

systems. As a result, typical thermal systems have to be approximated, simpli￾fied, and idealized in order to make it possible to analyze them and thus obtain

the inputs needed for design. Following are some of the characteristics that are

commonly encountered in thermal systems and processes:

1. Time-dependent

2. Multidimensional

3. Nonlinear mechanisms

4. Complex geometries

5. Complicated boundary conditions

6. Coupled transport phenomena

7. Turbulent flow

8. Change in phase and material structure

9. Energy losses and irreversibility

10. Variable material properties

11. Influence of ambient conditions

12. Variety of energy sources

Because of the time-dependent, multidimensional nature of typical systems,

the governing equations are generally a set of partial differential equations, with

nonlinearity arising due to convection of momentum in the flow, variable proper￾ties, and radiative transport. However, approximations and idealizations are used to

simplify these equations, resulting in algebraic and ordinary differential equations

for many practical situations and relatively simpler partial differential equations for

others. These considerations are discussed in Chapter 3 as part of modeling of the

system. However, the equations for a few simple cases are given here to illustrate the

nature of the governing equations and the effect of some of these complexities.

The simplest problems are those that assume steady-state conditions, with or

without flow, while also assuming uniform conditions in each part of the system.

These problems lead to algebraic equations, which are often nonlinear for ther￾mal systems. This situation is commonly encountered in thermodynamic systems

such as refrigeration, air conditioning, and energy conversion systems. Then, the

governing set of algebraic equations may be written as

f1 (x1, x2, x3,￾z￾, xn)  0

f2 (x1, x2, x3,￾z￾, xn)

Introduction 23

f3 (x1, x2, x3,￾z￾, xn)  0 (1.4)



fn (x1, x2, x3,￾z￾, xn)  0

where the xi

are the unknowns and the functions fi

, for i  1, 2, 3,￾z￾, n, may be

linear or nonlinear. Such problems are generally referred to as steady, lumped

circumstances and have been most extensively treated in papers and books deal￾ing with system design, such as Hodge (1985), Stoecker (1989), and Janna (1993).

However, these approximations are applicable for only a few idealized thermal

systems. Additional complexities, mentioned earlier, generally demand analysis

that is more accurate and the solution of ordinary and partial differential equa￾tions. Nevertheless, because of the ease in analysis, steady lumped systems are

effective in illustrating the basic ideas of system simulation and design. There￾fore, these are used as examples throughout the book while bearing in mind that,

in actual practice, more elaborate analysis would generally be needed.

If the time-dependent behavior of the system is sought, for a study of the

dynamic characteristics of the system, the resulting governing equations are ordi￾nary differential equations in time, if the assumption of uniform conditions within

each part is still employed. Then the governing equations may be written as

dx

d F x x x x for i n i

i n T   ( , , , , ) ,,, , 123 123 (1.5)

where, again, the functions Fi

may be linear or nonlinear. The systems for which

these approximations can be made are known as dynamic, lumped systems. Such

a treatment is valuable in many cases because of the resulting simplicity. In many

thermodynamic systems, such as heat engines and cooling systems, the individual

components are approximated as lumped and the dynamic analysis is of interest

in the startup and shutdown of the systems, as well as in determining the effects

of changes in operating conditions like flow rate, pressure, and heat input.

If the conditions in the different parts of the system cannot be assumed to

be uniform, the problem is referred to as distributed. A time-dependent, two￾dimensional flow with the assumption of constant fluid properties, as in a duct or

over a heated body, is represented by the equations (Burmeister, 1993)

t

t

u

x

t

t  v

y

0 (1.6)

t

t

u

T

 u

t

t

u

x

 v

t

t

u

y  1

R

t

t

p

x

 N

t

t

¤

¦

¥

2

2

u

x

t

t

³

µ

´

2

2

u

y (1.7)

t

t

v

T

 u

t

t

v

x

 v

t

t

v

y  1

R

t

t

p

y

 N

t

t

¤

¦

¥

2

2

v

x

t

t

³

µ

´

2

2

v

y (1.8)

where the first equation gives the conservation of mass and the other two give the

momentum force balance in the x and y directions, respectively. Here, u, v ar