Find Tank Wall Temp: Heat Conductivity & Loss Analysis

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SUMMARY

The discussion focuses on calculating the temperature on the outside wall of a tank holding water at 60 degrees Celsius, with an external temperature of 10 degrees Celsius. Key parameters include the thermal conductivity of steel (λ = 50 W/mK), heat transfer coefficient between water and tank (h1 = 2700 W/m²K), and between air and tank (h2 = 15 W/m²K). The user successfully calculated the overall heat transfer coefficient (U = 14.86 W/m²K) but encountered difficulties determining the area of the tank wall (A) to compute the heat flow (Q) and the wall temperature (Tw1). The correct approach involves equating heat flows and using the appropriate equations for thermal analysis.

PREREQUISITES
  • Understanding of heat transfer principles, including conduction and convection.
  • Familiarity with thermal conductivity (λ) and heat transfer coefficients (h).
  • Knowledge of the equations for calculating heat transfer (Q) and overall heat transfer coefficient (U).
  • Basic proficiency in algebra for manipulating equations related to thermal analysis.
NEXT STEPS
  • Research the derivation and application of the overall heat transfer coefficient (U) in thermal systems.
  • Learn how to calculate the surface area (A) of cylindrical tanks for heat transfer analysis.
  • Study the principles of steady-state heat conduction and the use of Fourier's law.
  • Explore the impact of insulation on heat loss in storage tanks and how to calculate it.
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Engineers, thermal analysts, and anyone involved in the design or analysis of thermal systems, particularly those working with storage tanks and heat transfer calculations.

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A tank holds water at 60 degrees C. The outside temp. is 10. The thickness of the walls is 12mm. My goal is to find the temp on the wall on the outside of the tank. I've got some values I don't know the english name for, but hopefully you'll understand by the units.
\lambda for steel is 50\frac{W}{mK}
h between water and tank is 2700\frac{W}{m^2K}
h between air and tank is 15\frac{W}{m^2K}

How do I go about it?? I also need to find the effect loss...
 
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How to go about it : The heat flowing per unit area from the water, Q, is equal to the heat received per unit area by the outside air (and is also equal to the heat conducted per unit area through the tank wall). Calculate each of these heat flows and equate them to each other.

I've already said too much... in the future, if you want help, you must show what you've tried and where you are stuck.
 
First I found the value which we in norwegian denote U [W/(m^2*K)]
U=\frac{1}{(1/h_1)+(\delta_1/\lambda_1)+(1/h_2)}
Putting in the values this gives me U=14,86 W/(m^2*K)
Then I want to use the equation
\dot{Q}=U \cdot A(T_1-T_2)
where A is the area of the tank wall, T1 and T2 are the temp. of the water and the air and Q is the energy that passes through the wall. The problem is that I don't have the area, I only have the thickness of the wall, 0,012m. If I did know A, then I could calculate Q, and use this equation
\dot{Q}=h_1 \cdot A(T_1-T_w_1)
to find T_w_1 which is the temp. at the outside of the tank wall.
The funny thing is that if I follow this procedure and use my value for thickness istead of area, the answer comes out right (!), though the unit of the answer isn't correct. By the way, the answer is 59,5 degrees C.
What am doing wrong? Is there some other equation I should be using?
 

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