< 9. Transport phenomena 2 Problems >
< Transport phenomena 2 by JD >
P.297 Problem 1) A 0.2m wide plate, 0.8m long, is placed on the bottom of a shallow tank. The plate is heated
and maintained at a constant surface temperature of 60℃. Liquid water 12cm deep flows over the flat plate with
bulk volumetric flow rate of 2.4 × 10 𝑚 /𝑠𝑒𝑐. The bulk liquid water temperature may be assumed to remain
constant at 20℃ as it flows along the length of the plate.
0.2m
a) What are the values of 𝑹𝒆𝑳 and 𝑷𝒓 for this convective heat transfer process?
Is the flow laminar or turbulent at the end of the plate?
𝑅𝑒 =
𝜌𝑈𝐿 992.2 × 0.1 × 0.8
=
= 120,632
𝜇
658 × 10
Laminar flow (𝑅𝑒 <200,000)
𝑃𝑟 =
𝜇𝐶
658 × 10 × 4175
=
= 4.14
𝑘
0.663
< Transport phenomena 2 by JD >
P.297 Problem 1) A 0.2m wide plate, 0.8m long, is placed on the bottom of a shallow tank. The plate is heated
and maintained at a constant surface temperature of 60℃. Liquid water 12cm deep flows over the flat plate with
bulk volumetric flow rate of 2.4 × 10 𝑚 /𝑠𝑒𝑐. The bulk liquid water temperature may be assumed to remain
constant at 20℃ as it flows along the length of the plate.
0.2m
b) What is the local heat flux at a distance 0.5 m from the leading edge of the plate?
Use the Blasius solution based Nusselt number equation.
𝑘
/
ℎ = 0.332 𝑅𝑒 𝑃𝑟 /
𝑥
0.663
992.2 × 0.1 × 0.5
= 0.332 ×
×
0.5
658 × 10
𝑄
=ℎ 𝑇 −𝑇
𝐴
/
× 4.14
/
= 194.1
= 194.1 × 40 = 7764𝑊/𝑚
< Transport phenomena 2 by JD >
P.297 Problem 1) A 0.2m wide plate, 0.8m long, is placed on the bottom of a shallow tank. The plate is heated
and maintained at a constant surface temperature of 60℃. Liquid water 12cm deep flows over the flat plate with
bulk volumetric flow rate of 2.4 × 10 𝑚 /𝑠𝑒𝑐. The bulk liquid water temperature may be assumed to remain
constant at 20℃ as it flows along the length of the plate.
0.2m
c) What is the total heat flux rate from the surface?
ℎ𝐿
/
= 0.664𝑅𝑒 𝑃𝑟 /
𝑘
992.2 × 0.1 × 0.8
= 0.664 ×
658 × 10
𝑁𝑢 =
ℎ = 370.3 ×
.
.
𝑄 = ℎ𝐴 𝑇 − 𝑇
/
× 4.14
/
= 370.3
= 307
= 307 × 0.16 × 40 = 1965𝑊/𝑚
< Transport phenomena 2 by JD >
Problem 2) From an experiment of fluid flow over a heated flat plate, it has been shown that the temperature
profile within the TBL is given as below. (Here, flow velocity is assumed to depend only on y coordinate)
𝑣
𝑇 = 400℃
𝑦
𝑇 = 300℃
𝑇−𝑇
𝑣
= 1 − (0.7 +
𝑦)
𝑇 −𝑇
𝜈
/
𝑥
Q. If 𝑇 = 400℃, 𝑇 = 300℃, 𝑘 = 0.037 𝑊/𝑚𝐾, and
= 1000/𝑚,
what is the heat flux and heat transfer coefficient on the surface?
< Transport phenomena 2 by JD >
Problem 2) From an experiment of fluid flow over a heated flat plate, it has been shown that the temperature
profile within the TBL is given as below. (Here, flow velocity is assumed to depend only on y coordinate)
𝑣
𝑇 = 400℃
𝑦
𝑘 = 0.037𝑊/𝑚𝐾
𝑇−𝑇
𝑣
= 1 − (0.7 +
𝑦)
𝑇 −𝑇
𝜈
𝑇 = 300℃
/
𝑥
𝜕𝑇
𝜕𝑦
=−
1
𝑇 −𝑇
7
𝑞 = −𝑘
𝜕𝑇
𝜕𝑦
𝑣
𝜈
0.7 +
=ℎ 𝑇 −𝑇
𝑣
𝑦
𝜈
=−
= 3947𝑊/𝑚
1
𝑇 −𝑇
7
𝑣
𝜈
0.7 +
𝑣
𝑦
𝜈
= −106,669𝐾/𝑚
ℎ = 39.5𝑊/𝑚 𝐾
< Transport phenomena 2 by JD >
Problem 2) From an experiment of fluid flow over a heated flat plate, it has been shown that the temperature
profile within the TBL is given as below. (Here, flow velocity is assumed to depend only on y coordinate)
𝑣
𝑇 = 400℃
𝑦
𝑇 = 300℃
𝑘 = 0.037𝑊/𝑚𝐾
𝑇−𝑇
𝑣
= 1 − (0.7 +
𝑦)
𝑇 −𝑇
𝜈
/
𝑥
Further discussion) What if, velocity is dependent both on 𝒙
and 𝒚 ??
Hint. Energy balance analysis with control volume integral (P.286~287)
< Transport phenomena 2 by JD >
Problem 3) Consider a human body as a cylinder with 40cm diameter and 1.8m height in still air. If the body
temperature is 2 ℃ lower than that of the air, how much of energy will be required to maintain body
temperature(37 ℃)? Generally, a human intakes about 8400KJ (2000kcal)/day. Compare it with calculated value.
1) Vertical cylinder problem 
(𝐺𝑟 =
2)
=
.
.
= 0.222 ≥
= 1.16 × 10 × 2 × 1.8
=
.
= 0.182
= 191.8)
< Churchill and Chu’s Experiments >
0.387 × 1.16 × 10 × 2 × 1.8 × 0.705
= 0.825 +
/
1 + 0.492/0.705 /
= 0.825 + 10.17
= 121  = ℎ = 121 × = 121 ×
.
.
= 1.82
/
= 121
< Transport phenomena 2 by JD >
Problem 3) Consider a human body as a cylinder with 40cm diameter and 1.8m height in still air. If the body
temperature is 2 ℃ lower than that of the air, how much of energy will be required to maintain body
temperature(37 ℃)? Generally, a human intakes about 8400KJ (2000kcal)/day. Compare it with calculated value.
3) 𝑄 = ℎ𝐴∆𝑇 = 1.82 × 0.4 × 𝜋 × 1.8 × 2 = 8.23𝑊
Total heat loss = 8.23𝑊 × 3600 × 24 = 711072
711072
= 0.084
8400 × 1000
About 8% of energy is used to maintain body temperature, even in the very hot weather
< Transport phenomena 2 by JD >
Problem 4)
Problem 4)
Problem 4)
𝑨
ODE to be solved
Boundary conditions
Problem 5) JD left a cup of coffee for two weeks in his office. Initially, height of coffee was 7cm.
Estimate the height of coffee after two weeks.
Temperature is 293K and diffusion coefficient (D) of coffee (water) is 𝐷 = 2.5 × 10 𝑚 /𝑠𝑒𝑐
and pressure is 2.34 × 10 𝑃𝑎.
z
1) Pseudo steady state assumption & Mass balance
𝑆𝑁
8cm
− 𝑆𝑁
𝑁
= 𝑦 (𝑁
=0
𝑁
+ 𝑁 ) − cD
𝑑𝑦
= constant
𝑑z
7cm
𝑁
=
= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑁
cD
1−y
ln(
)
z -z
1−y
=0
Problem 5) JD left a cup of coffee for two weeks in his office. Initially, height of coffee was 7cm.
Estimate the height of coffee after two weeks.
Temperature is 293K and diffusion coefficient (D) of coffee (water) is 𝐷 = 2.5 × 10 𝑚 /𝑠𝑒𝑐
and pressure is 2.34 × 10 𝑃𝑎.
z
𝑦 =
𝑁 A=
𝜌d(z − z )
A
Mdt
𝑁
8cm
=
𝑦 =0
cD
1−y
𝜌d(z − z )
ln(
)=
z -z
1−y
Mdt
7cm
C=
*
z − z d(z − z ) =
cMD 1 − y
ln(
)dt
𝜌
1−y
< Open position >
Complex fluid and Soft matter physics lab
연구 분야: 1) Rheology (물질의 변형과 흐름 연구)
2) Soft matter (Colloid & Polymer) 3) Process modeling & analysis
지원 자격: 대학원 진학을 고려하는 창의적이고 적극적인 3,4학년 (Attitude is all!!)
모집 인원: 2명
Colloidal gel
Colloidal glass
진행 예정 연구: 1) Temperature-Responsive polymer의 유변물성 제어를 통한 물질 전달 조절
(Sun-screen 및 Drug & Cosmetics에의 응용)
2) Li-ion battery paste의 rheological property에 따른 공정 및 성능 분석
3) Liquid metal의 유변학적 특성 분석 및 응용
4) 식품에 사용되는 Hydrocolloids의 유변학 특성 분석
5) 이론적 접근 (모델링 및 입자 시뮬레이션)을 이용한 Colloid suspension의 유변학 거동 분석
6) 수치해석을 이용한 유동 분석
7) 기타 본인이 하고 싶은 연구 제안 얼마든지 환영!!
< Open position >
Complex fluid and Soft matter physics lab
근무 조건: 출퇴근 자유, 주1회 개인 미팅, 주1회 연구실 미팅 (Paper & Research presentation)
연구 및 학업에만 집중할 수 있는 인건비, 자유로운 & 학문적인 분위기 (과제 부담 X)
시작 시기: 2021.1월 혹은 3월 ~
이런 분에게 추천
- 물리화학, 공학수학, 전달현상 1&2 에 흥미를 느낀다 (화학 보다는 물리 & 수학이지!)
Colloidal gel
Colloidal glass
- 실험을 많이 하는게 싫다 & 몸에 안 좋은 화학약품을 쓰고 싶지 않다
- 컴퓨터 시뮬레이션이나 이론이 좋다 (나는 전생에 선비였다)
- 궁금한 건 못 참아! 알 때까지 고민한다!
- 어려운 문제를 해결하는 것에서 재미를 느낀다
- 남들 다하는 에너지, 바이오는 식상해!!
- ENTJ 랑 잘 맞겠는데?
지원 방법: jdpark@sookmyung.ac.kr 로 간단한 자기소개 & 지원동기 적어서 보내주세요~
(12월 28일 월요일까지), 지원전에 궁금한점이 있거나 상담을 원해도 연락주세요~