# Heat Transfer Operations Questions and Answers – Agitated Vessels Heat Transfer Coefficients

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This set of Heat Transfer Operations Question Paper focuses on “Agitated Vessels Heat Transfer Coefficients”.

1. Why are agitated vessels usually used in batch manufacture?
a) Necessary to calculate the time to heat or cool a batch
b) Because batch processes occur in vessels
c) It avoids harmful reactions
d) It supports endothermic reactions

Explanation: Agitated vessels usually used in batch manufacture because we need to calculate the time to heat or cool a batch so that highly exothermic reactions can be carried out with proper care.

2. The rate of change of temperature in an agitated vessel can be represented as which one of the following?
a) $$\frac{\delta T}{\delta t} = \frac{UA}{MCp}(T-Ts)$$
b) $$\frac{\delta T}{\delta t} = \frac{UA}{MCp}(Ts-T)$$
c) $$\frac{\delta T}{\delta t} = \frac{MCp}{UA}(Ts-T)$$
d) $$\frac{\delta T}{\delta t} = \frac{MCp}{UA(Ts-T)}$$

Explanation: This is because Q = UA(Ts-T) = MCp $$\frac{\delta T}{\delta t}$$. Hence, $$\frac{\delta T}{\delta t} = \frac{UA}{MCp}$$(Ts-T).

3. What is the term X in the following equation?
$$\frac{\delta T}{\delta t}= \frac{UA}{MCp}(X-T)$$
a) Service side temperature
b) Process side temperature
c) Service side temperature difference
d) Process side temperature difference

Explanation: In the equation of temperature gradient with time, the two temperature terms are Ts and t, where Ts is the Service side constant temperature and T is the temperature at time t.

4. Which one of the following is correct expression for calculating time ‘t’ to reach temperature T ?
a) $$t=\frac{MCp(Ts-To)}{UA(Ts-T)}$$
b) $$t=\frac{MCp(Ts-T)}{UA(Ts-To)}$$
c) $$t=\frac{UA(Ts-To)}{MCp(Ts-T)}$$
d) $$t=\frac{MCp}{UA}log\frac{Ts-To}{Ts-T}$$

Explanation: This is because Q = UA(Ts-T) = MCp $$\frac{\delta T}{\delta t}$$. Hence, $$\frac{\delta T}{\delta t} = \frac{UA}{MCp}(Ts-T)$$, integrating both sides, ln(Ts – T)= UA/MCp(t) or $$t=\frac{MCp}{UA}log(\frac{Ts-To}{Ts-T})$$.

5. For agitated vessels, what is the correct expression for the Overall Heat Transfer Coefficient?
a) $$\frac{1}{U} = \frac{1}{hAb}+\frac{X}{K}+\frac{1}{hAc}$$
b) $$\frac{1}{U} = \frac{1}{hAb}+\frac{K}{X}+\frac{1}{hAc}$$
c) $$\frac{1}{U} = \frac{1}{hAb}+\frac{1}{K}+\frac{1}{hAc}$$
d) $$\frac{1}{U} = \frac{1}{hAb}+\frac{1}{KX}+\frac{1}{hAc}$$

Explanation: The overall heat transfer coefficient is the combination of convective and conductive one. The first being on the process side hAb, heat transfer coefficient h and transfer area Ab, similarly the wall with X/K with X as vessel wall thickness and K=conductivity, and finally service side hAc.

6. What is the term X in the following equation for overall heat transfer coefficient?
$$\frac{1}{U}= \frac{1}{hAb}+\frac{X}{K}+\frac{1}{hAc}$$
a) Thickness of jacket
b) Thickness of vessel wall
c) Thickness of vessel + jacket
d) Thickness of vessel – jacket

Explanation: We have the conductivity of the vessel wall only and not of the jacket, hence the given X is the thickness of the vessel and not the combined thickness.

7. What is the correct expression for calculating Nusselt number for a Jacketed Vessel?
a) Nu=$$\frac{0.03Re^{3/4}Pr}{1+1.74Re^{-1/8}(Pr⁡-1)}\frac{\theta^{0.14}}{\theta w}$$
b) Nu=$$\frac{0.03Re^{3/4}Pr}{1+Re^{-1/8}(Pr⁡-1)}\frac{\theta^{0.14}}{\theta w}$$
c) Nu=$$\frac{0.03Pr}{1+1.74Re^{-1/8}(Pr⁡-1)}\frac{\theta^{0.14}}{\theta w}$$
d) Nu=$$\frac{0.03Re^{3/4}}{1+1.74Re^{-1/8}(Pr⁡-1)}$$

Explanation: When we are calculating the Reynolds number for the jacket side, we cannot apply Sieder-Tate Equation as the heat is not transferred from all the side; hence the below formula is used.
Nu=$$\frac{0.03Re^{3/4}Pr}{1+1.74Re^{-1/8}(Pr⁡-1)}\frac{\theta^{0.14}}{\theta w}$$

8. What is the equivalent diameter of Jacketed vessel, if the diameter of the jacket is 40mm and that of vessel is 30mm?
a) 8mm
b) 8.16mm
c) 9mm
d) 10mm

Explanation: The equivalent thickness is the difference of the jacket thickness and the vessel thickness multiplied with the constant 0.816. That is De = 0.816(Dj – Dt) = 0.816(40-30) = 8.16mm.

9. What is the expression for Equivalent diameter?
Dj = jacket thickness and
Dt = the vessel thickness
a) 0.816Dj
b) 0.8(Dj – Dt)
c) 0.816(Dj – Dt)
d) 0.8Dt

Explanation: The equivalent thickness is the difference of the jacket thickness and the vessel thickness multiplied with the constant 0.816.

10. What is the correct expression for Reynolds number in service side for jacket type Agitated Vessels?
a) $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/4}$$
b) $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$
c) $$Nu=K(\frac{\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/4}$$
d) $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/4}$$

Explanation: The expression for the Nusselt number in terms of the vessel length and its density terms is represented as $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$;here ΔTm is the mean temperature difference between the service and the vessel wall.

11. For conventional unbaffled jacket, what is the term X in the expression for Reynolds number in service side for upward flow, heating and downward flow cooling?
$$Nu=X(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$
a) 0.15
b) 0.015
c) 0.128
d) 0.28

Explanation: The value of X the proportionality constant is K=0.15 for the formula $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$ when it is calculated for upward flow, heating and downward flow cooling.

12. For conventional unbaffled jacket, what is the term X in the expression for Reynolds number in service side for upward flow, cooling and downward flow heating?
$$Nu=X(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$
a) 0.15
b) 0.015
c) 0.128
d) 0.28

Explanation: The value of X the proportionality constant is K=0.128 for the formula $$Nu=K(\frac{z^3\rho^2\beta g \Delta Tm}{\mu^2})^{1/3}Pr^{1/3}$$ when it is calculated for upward flow, cooling and downward flow heating.

13. A condensing coefficient in a jacket should be ______ compared to the process side.
a) Extremely High
b) Extremely Low
c) Equal
d) Approximate equal

Explanation: The condensing coefficient in the jacket should be really large else there would be unnecessary heat losses on the service side or the jacketside.

14. For a half pipe coil, the equation for Reynolds number is usually the formula_______
a) Sieder Tate
b) Gnielinski correlation
c) Dittus-Boelter equation
d) Sieder

Explanation: As the half pipe coil is completely immersed in the vessel where the fluid is in contact with all the sides, hence we use Sieder-Tate equation.

15. A conventional jacket is usually fitted with baffles.
a) True
b) False