3 1. HEAT TRANSFER

3‐1. HEAT TRANSFER3 1. HEAT TRANSFER

by Aj.Sanchai Ramphueiphad ,Program in Air Conditioning & RefrigerationDepartment of Mechanical Engineering

www.arc.rmuti.ac.th;Email:[email protected] 1


Q

Heat Transfer per unit mass

(kJ/kg)m

Qq =

t2

∫⋅

Heat Transfer rate is denoted Q

(kJ)dtQQt1

∫=


(kJ)Q Δ=⋅

tQ


12ttt

( )Q

−=Δ

Q



Historical Background on Heatg



Energy transfer by WorkWork done per unit mass of system,w

W(kJ/kg)

m

Ww =

k d i i i ll dWork done per unit time is called power

kWorkJ/sW.•

kWorkJ/s,W

Path function have inexact differential designated b the s mbol δdesignated by the symbol δ

Exact differential designated by the symbol dsymbol d



The volume change during a process between states 1 and 2 is

VVVdV Δ=−=∫2

12

between states 1 and 2 is

∫1

12

Total work done during process 1‐2

)( WnotWW Δ=∫2

112δ



Electrical Work

VNWe =N คือปริมาณไฟฟาที่ผานจุดหนึ่งๆ โดยมีกระแส 1 แอมป แรงเคลือ่น 1 โวลตใน 1 นาที

(W).

VIWe = powerelectricaltheisWe

.

โดยทั่วไปแรงเคลื่อน และกระแสไฟฟาแปรผันตามเวลา

)(kJdtVIWe ∫=2

1

VและI คงที่

)(kJtVIWe Δ=



MECHANICAL FROMS OF WORK

)(kJFsW =

F is not constant

kJFdW ∫2

)(kJFdsW ∫=1



Moving Boundary Work

F is not constant

งานทีไ่ดจากการเคลือ่นที่ของขอบเขต

PdVPAdsFdsWb ===δ

F is not constant

(kJ)∫=2

PdVWb ( )∫1

b

The total area A under the processThe total area A under the process curve 1‐2 is obtained by adding these differential area

(kJ)∫∫ ===22

PdVdAAAera

these differential area

9

11

Moving Boundary Work

(kJ)∫=2

1

dVPW ib

Pi=Pressure is inner face of the pistonW = represent the amount of energy

1

Wb = represent the amount of energy transferred from the system during an expansion process p p

crankatmfrictionb WWWW ++=

dxFAPF crankatmfriction∫ ++=2

1

)(1



EXAMPLE 3‐5 A rigid tank contains air at 500 kPa and 150 °C . As aresult of heat transfer to the surroundings, the temperature andpressure inside the tank drop to 65 °C and 400 kPa, respectively.Determine the boundary work done during this processDetermine the boundary work done during this process.

Analysis: The boundary work can be determined fromAnalysis: The boundary work can be determined from eq. 3‐11 to be

2

12

0)(dv(kJ),02

1

=== ∫ PdVWb

EXAMPLE 3‐6 A frictionless piston‐cylinder device contains 4.5kg of water vapor at 0.4 MPa and 200 °C. Heat is nowg ptransferred to the steam unit the temperature reaches 250°C. If the piston is not attached to the shaft and its mass ispconstant, determine to work done by the steam during thisprocess.p

)()( 1212

2

0

2

VVmPWorVVPdVPdVPW oboib −=−=== ∫∫

13

11

kJkgmkPakgWb 62.109]/)5342.05951.0)[(400)(5.4( 3 =−=

EXAMPLE 3‐6: Isothermal Compression of an ideal gasA piston‐cylinder device initially contains 0.4 m3 of air at 100p y ykPa and 80 °C. The air is now compressed to 0.1 m3 in such away that the temperature inside the cylinder remainsy p yconstant. Determine the work done during this process.

14

EAMPLE 3‐7

15

Polytropic ProcessCPV n =

16

3 1. HEAT TRANSFER

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