If average heat transfer co-efficient is $${{\text{h}}_{\text{a}}}$$ and the local coefficient at the end of the plate is $${{\text{h}}_l}$$ then in case of heat transfer to a fluid flowing over a flat plate, heated over its entire length
A. $${{\text{h}}_{\text{a}}} = {{\text{h}}_l}$$
B. $${{\text{h}}_{\text{a}}} = 2{{\text{h}}_l}$$
C. $${{\text{h}}_{\text{a}}} = 0.5{{\text{h}}_l}$$
D. $${{\text{h}}_{\text{a}}} = 0.75{{\text{h}}_l}$$
Answer: Option B
This Question Belongs to Chemical Engineering >> Heat Transfer
The correct answer is: C. ha = 0.5 hl
✅ Explanation:
For laminar flow of a fluid over a flat plate that is heated over its entire length, the local heat transfer coefficient
ℎ
𝑥
h
x
decreases along the length due to the thickening of the thermal boundary layer.
Local and Average Heat Transfer Coefficients:
Local Nusselt number at a distance
𝑥
x:
Nu
𝑥
=
0.332
Re
𝑥
1
/
2
Pr
1
/
3
Nu
x
=0.332Re
x
1/2
Pr
1/3
Average Nusselt number over length
𝐿
L:
Nu
avg
=
0.664
Re
𝐿
1
/
2
Pr
1
/
3
Nu
avg
=0.664Re
L
1/2
Pr
1/3
Since
ℎ
=
Nu
⋅
𝑘
𝐿
h=
L
Nu⋅k
, the average heat transfer coefficient over the plate is:
ℎ
𝑎
=
1
𝐿
∫
0
𝐿
ℎ
𝑥
𝑑
𝑥
=
0.5
⋅
ℎ
𝑙
h
a
=
L
1
∫
0
L
h
x
dx=0.5⋅h
l
Where
ℎ
𝑙
h
l
is the local heat transfer coefficient at the trailing edge
𝑥
=
𝐿
x=L.
📌 Final Answer: C. ha = 0.5 hl