Convective heat transfer coefficient

[Melvinamarie]

Not sure if I'm getting this right, my answer seems very small, can anyone advise?

Question- butanol at a temperature of 28^oC is pumped at a velocity of 14ms-1 through a 100mm diameter tube kept at a wall temp of 90^oC. The properties of butanol are below. Determine the convective heat transfer coefficient.
Data:
Specific heat capacity - 2.142kJkg^-1K^-1
ρ 950kgm^-1
Dynamic viscosity at 28^oC - 2.9x10^-3kgm^-1s^-1
Dynamic viscosity at 90^oC- 1.2x10^-3kgm^-1s^-1
Thermal conductivity - 2.4x10^-4kWm^-1K^-1

Attempt:
Re=pUd/μ
Pr=Cpμ/K
Nu=0.332Re^0.5Pr^0.33
hx=Nu(k/x)

Re=950*14*0.1x10^-3/2.9x10^-3 458.62x10-4
Pr=2.142x2.9x^-3/2.41x10^-4 2.588
Nu=0.332x(458.62x10-4)^0.5x(2.588)^0.33 0.0973
Hx=0.0973*2.41x10^-4/0.1 2.3352x10^-4kWm^-2K^-1
Answer: 0.2335 Wm^-2K^-1

 

[SteamKing]

Not sure if I'm getting this right, my answer seems very small, can anyone advise?

Question- butanol at a temperature of 28^oC is pumped at a velocity of 14ms-1 through a 100mm diameter tube kept at a wall temp of 90^oC. The properties of butanol are below. Determine the convective heat transfer coefficient.
Data:
Specific heat capacity - 2.142kJkg^-1K^-1
ρ 950kgm^-1
Dynamic viscosity at 28^oC - 2.9x10^-3kgm^-1s^-1
Dynamic viscosity at 90^oC- 1.2x10^-3kgm^-1s^-1
Thermal conductivity - 2.4x10^-4kWm^-1K^-1

Attempt:
Re=pUd/μ
Pr=Cpμ/K
Nu=0.332Re^0.5Pr^0.33
hx=Nu(k/x)

Re=950*14*0.1x10^-3/2.9x10^-3 458.62x10-4
Pr=2.142x2.9x^-3/2.41x10^-4 2.588
Nu=0.332x(458.62x10-4)^0.5x(2.588)^0.33 0.0973
Hx=0.0973*2.41x10^-4/0.1 2.3352x10^-4kWm^-2K^-1
Answer: 0.2335 Wm^-2K^-1

Your calculations are confusing. Use '=' to separate the calculation from the final result.

As to your calculation of the Reynolds number, apparently you are saying that d = 0.1*10^-3m, which is equal to 0.1 mm. A tube diameter of 100 mm = 0.1 m.
The calculation you have shown contains arithmetic mistakes (a Re < 1 is unusual)

 

[Melvinamarie]

Thank you SteamKing. I missed the diameter mistake. I have corrected this but still get a low result.

Re=950*14*0.1/2.9x10-3 =0.4586
Pr=2.142x2.9x10^-32.41x10-4 =2.588x10^-7
Nu=0.332*(0.4586)^0.5*(2.588x10^-7)^0.33 =0.00151
Hx=0.00151*(2.41x10-4/0.1) =3.6391x10^-6kWm^- 2K-1

 

[SteamKing]

Thank you SteamKing. I missed the diameter mistake. I have corrected this but still get a low result.

Re=950*14*0.1/2.9x10-3 =0.4586

You still have a basic arithmetic problem here. You're taking a relatively sizable number and dividing by a small number and getting a small number. Are you sure you know how scientific notation works?

BTW, this equation should be written: Re = 950*14*0.1 / (2.9x10^-3) = ?

Pr=2.142x2.9x10^-32.41x10-4 =2.588x10^-7

This equation should read: Pr = 2.142 * (2.9x10^-3) / (2.41x10^-4) = ?

Try not bunching your terms together. Use additional spaces and parentheses to make calculations clear.

You also missed out the division by K in your version, making your calculation of the Prandtl No. incorrect.

Use the 'Preview' Button to check how your work will appear before posting. I know I use it a lot.

Nu=0.332*(0.4586)^0.5*(2.588x10^-7)^0.33 =0.00151

You are using an incorrect Reynolds number and an incorrect Prandtl number to calculate the Nusselt number.

Hx=0.00151*(2.41x10-4/0.1) =3.6391x10^-6kWm^- 2K-1

We'll worry about the calculation of Hx after you have fixed the previous calculations.

 

[Melvinamarie]

Ok, reviewed scientific notation, and am now getting the below. Am I on track?

Re = 950*14*0.1 / (2.9x10-3) = 458621
Pr = 2.142 * (2.9x10-3) / (2.4x10-4) = 25.8825

Re now indicates turbulent flow so dittus-bottler correlation for nusselt number to be used:
Nu= 0.023 *(458621)^0.8 * (25.8825)^0.4 = 2858.206

 

[SteamKing]

Ok, reviewed scientific notation, and am now getting the below. Am I on track?

Re = 950*14*0.1 / (2.9x10-3) = 458621
Pr = 2.142 * (2.9x10-3) / (2.4x10-4) = 25.8825

Re now indicates turbulent flow so dittus-bottler correlation for nusselt number to be used:
Nu= 0.023 *(458621)^0.8 * (25.8825)^0.4 = 2858.206

These calculations look good.

 

[Melvinamarie]

Great, so I'm now calculating hx using hx=Nu(k/x).

Hx = 2858.206 * ((2.4x10^-4) / 0.1 ) = 6.8597kWm^-2K^-1

= 6,859.7Wm^-2K^-1

Does this look along the right lines? Thank you for all your help.

 

[SteamKing]

Great, so I'm now calculating hx using hx=Nu(k/x).

Hx = 2858.206 * ((2.4x10^-4) / 0.1 ) = 6.8597kWm^-2K^-1

= 6,859.7Wm^-2K^-1

Does this look along the right lines? Thank you for all your help.

This calculation looks OK.

 

[Melvinamarie]

Brilliant, thankyou