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

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