Homework help:Heat transfer coefficient of flow over a flat plate

In summary, the average heat transfer coefficient for the plate is h=12.7W/m2K. This was calculated using the Reynold's Analogy approach, considering the relationship between Stanton number, Nusselt number and drag coefficient. The values of density, specific heat, dynamic viscosity and thermal conductivity of air at a temperature of 300K were used in the calculations. The average heat transfer coefficient was found to be 12.73W/m2K, which is reasonably close to the given value of 12.7W/m2K.
  • #1
Peridot
4
0
A 2-m x 3-m flat plate is suspended in a room, and is subjected to air flow parallel to its surfaces along its 3-m-long side. The free stream temperature and velocity of the air are 20oC and 7m/s. the total drag force acting on the plate is measured to be 0.86N. Determine the average heat transfer coefficient for the plate. Answer:h=12.7W/m2K
Properties of air at 300K(from my textbook
ρ=1.1763
c=1.007e03
μ=1.862e-05
v=1.5e-05
Pr=0.717
k=2.614e-02

Attempt at a solution
ReL=UL/v=7*3/1.5e-05=1.5e06 >5e05
xcr=(Recrv)/U=1.07

Nux,Laminar=0.332Pr1/3Rex1/2
Nux,Turbulent=(0.0296Re0.8Pr)/(1+2.11Rex-0.1(Pr-1))

Avg heat coeff
=(1/L){0xcrhx, Laminardx + xcr3hx, Turbulentdx}
= (1/L){0xcrNux, Laminar(k/x)dx + xcr3Nux, Turbulent(k/x)dx}
= ...
=14.39


I did approximate 1+2.11Rex-0.1(Pr-1) to be equal to 1 in my working because I didn't know how to integrate it. Is that acceptable? And I don't know how to use the drag force provided in this question. :x

I've been pondering over this question for a few days and I still can't get the answer please help check if my approach is correct. Thank you.
 
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  • #2
Hint: The problem states the force on the plate. That implies they want you to approach it from a Reynold's Analogy standpoint.
 
  • #3
Thanks, I'll give it a shot again.
 
  • #4
LawrenceC said:
Hint: The problem states the force on the plate. That implies they want you to approach it from a Reynold's Analogy standpoint.

Okay thanks for the hint once again. I tried again using Reynold's Analogy.

qx/(ρcu(T-Tw))=τwx/(ρu2)hx/c=τwx/(u)

τwx = (hxu)/(c)

AτwxdA = 0.86

A(hxu)/(c)dA = 0.86

(u/c)∫AhxdA = 0.86

(u/c)∫AhxdA = 0.86

AhxdA = (0.86c)/u

avg h
= (1/A)∫AhxdA
= (1/A) (0.86c)/u

Is this approach correct now? I subbed in the values of A=12, c = 1.007e03 and u=7 but the answer I got is 10.3 instead of the given 12.7.
I think the difference might be attributed to the value of c.

Thanks in advance
 
  • #5
I started off with the basic relationship:

St*Pr^2/3 = Cf/2

I don't see the Prndtl number anywhere in your computations.
 
  • #6
LawrenceC said:
I started off with the basic relationship:

St*Pr^2/3 = Cf/2

I don't see the Prndtl number anywhere in your computations.

Oops, I misread my notes, the formula I used earlier was only for Pr=1 >.<

I did as you told me and I got the answer.(at least reasonably close to it) ^^ Thanks a lot!(Sorry if I annoyed you with a lot of stupid mistakes and questions)
Here is my working if anyone is interested.

Stx = Nux/(RexPr) = hx/cpU

StxPr2/3= Cfx/2=тwx/(pU2)

(hx/cpU)Pr2/3= тwx(pU2)

hx = (c/U)(Pr-2/3wx

AhxdA = (c/U)(Pr-2/3AтwxdA

Avg heat coeff
=(1/A)∫AhxdA
=(1/A)(c/U)(Pr-2/3AтwxdA

sub A=12, c=1.007e03, U=7, Pr=0.717, ∫AтwxdA = 0.86

Avg heat coeff=12.86
 

1. What is the heat transfer coefficient?

The heat transfer coefficient is a measure of the rate at which heat is transferred from one material or substance to another. It is denoted by the symbol h and has units of watts per square meter-kelvin (W/m2-K).

2. How is the heat transfer coefficient calculated?

The heat transfer coefficient can be calculated using the equation h = q/(A * ΔT), where q is the heat flow rate, A is the surface area, and ΔT is the temperature difference between the two materials.

3. What factors affect the heat transfer coefficient?

The heat transfer coefficient can be affected by various factors such as the properties of the materials, the surface roughness, the velocity of the fluid, and the temperature difference between the materials.

4. How is the heat transfer coefficient of flow over a flat plate determined?

The heat transfer coefficient of flow over a flat plate can be determined experimentally by measuring the temperature difference between the surface of the plate and the fluid, and using this information to calculate the heat transfer coefficient using the appropriate equations.

5. Why is the heat transfer coefficient important in heat transfer analysis?

The heat transfer coefficient is an important parameter in heat transfer analysis because it helps us understand how heat is transferred between materials and how different factors can affect this transfer. It is also used in the design and optimization of heat transfer systems and processes.

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