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Curl Up and Dye produces a line of hair dyes for professional
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Curl Up and Dye produces a line of hair dyes for professional hairdressers.


In 20XX, they had sales revenues of $500,000, a cost of goods sold of $300,000, equipment

of $100,000, amortization expenses of $50,000, an ending inventory of $40,000, and

income tax expenses of $50,000.


In 20XY, they had sales revenues of $400,000, a cost of goods sold of $281,250, equipment

of $100,000, amortization expenses of $50,000, an ending inventory of $35,000, and

income tax expenses of $25,000.


Competitors in the same industry have an inventory turnover of 40 days.


Calculate and interpret the company?s inventor


A common thermal energy generation process involves the conversion from electrical

 

to thermal energy in a current-carrying medium (Ohmic, or resistance, or Joule heating).

 

The rate at which energy is generated by passing a current I through a medium of electrical

 

resistance Re is

 

(3.42)

 

If this power generation (W) occurs uniformly throughout the medium of volume V, the

 

volumetric generation rate (W/m3

 

) is then

 

(3.43)

 

Energy generation may also occur as a result of the deceleration and absorption of neutrons in

 

the fuel element of a nuclear reactor or exothermic chemical reactions occurring within a

 

medium. Endothermic reactions would, of course, have the inverse effect (a thermal energy

 

sink) of converting thermal energy to chemical bonding energy. Finally, a conversion from

 

electromagnetic to thermal energy may occur due to the absorption of radiation within the

 

medium. The process occurs, for example, when gamma rays are absorbed in external nuclear

 

reactor components (cladding, thermal shields, pressure vessels, etc.) or when visible radiation is absorbed in a semitransparent medium. Remember not to confuse energy generation

 

with energy storage (Section 1.3.1).

 

3.5.1 The Plane Wall

 

Consider the plane wall of Figure 3.10a, in which there is uniform energy generation per

 

unit volume ( is constant) and the surfaces are maintained at Ts,1 and Ts,2. For constant

 

thermal conductivity k, the appropriate form of the heat equation, Equation 2.22, is

 

(3.44)

 

d2

 

T q?

 

0

 

q?

 

q?

 


 

E?g

 

V

 

I

 

2

 

Re

 

V

 

E?gI

 

2

 

Re

 

TABLE 3.3 One-dimensional, steady-state solutions to the heat

 

equation with no generation

 

Plane Wall Cylindrical Wall

 

a

 

Spherical Wall

 

a

 

Heat equation

 

Heat ?ux ( )

 

Heat rate (q)

 

a

 

The critical radius of insulation is rcr k/h for the cylinder and rcr 2k/h for the sphere.

 

(1/r1) (1/r2)

 

4k

 

ln (r2 /r1)

 

2Lk

 

L

 

kA

 

4k T

 

(1/r1) (1/r2)

 

2Lk T

 


 

ln (r2 /r1)

 

kA

 

T

 

L

 

kT

 

r

 

2

 

[(1/r1) (1/r2)]

 

kT

 

r ln (r2

 

/r1)

 

k

 

T

 

L

 

q

 

Ts,1 T

 


 

1 (r1/r)

 

1 (r1/r2

 

) Ts, 2 T

 

ln (r/r2)

 

ln (r1/r2)

 

Ts,1 T

 

x

 

L

 

1

 

r

 

2

 


 

d

 

dr

 


 

r

 

2

 


 

dT

 

dr 0

 

1

 

r

 


 

d

 

dr

 


 

r

 

dT

 

dr 0

 

d2

 

T

 

dx2

 

0

 

Temperature

 

distribution

 

Thermal

 

resistance (Rt,cond)v

 


 

 







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