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The primary objective of this experiment is to gain an understanding of transient heating and cooling in a tank containing an aqueous solution. Additionally, we aim to familiarize ourselves with the WL110 Software, which is used to log data and analyze it. The experiment involves calculating the rate of heat loss from the hot fluid in the heat jacket to the cooling water inside the tank. Lastly, we will identify and address any potential hazards associated with the experiment.
Heating a well-mixed batch of liquid in a tank is accomplished by passing hot water around the fluid.
This process facilitates heat transfer from high-energy particles to lower-energy particles. Consider a liquid with a mass (M) in kilograms, initially at a temperature (T0) in Kelvin, and a constant flow rate (T1) in liters per minute into the jacket. The equation for the heat energy (Q) required for heat transfer is given by:
Q = M * cp * (T - T0) (1)
Where:
The rate of change in energy can be calculated by differentiating Equation (1) with respect to time (t), resulting in:
dQ/dt = M * cp * dT/dt (2)
The rate of energy loss of the hot fluid in the fluid jacket can be expressed as:
dQ/dt = UA * (Th - T) (3)
Where:
Using Equations (2) and (3), the rate of energy gained by the fluid in the tank is equal to the rate of energy lost by the hot fluid in the jacket, resulting in the equation:
UA * (Th - T) = M * cp * dT/dt (4)
For convenience, we replace A with Am, the logarithmic mean heat transfer area, defined as:
Am = (A_out - A_in) / ln(A_out / A_in) (5)
We also introduce ∆Th,m to account for fluctuations, where ∆Th,m is the logarithmic mean temperature difference between the inlet and outlet temperatures:
∆Th,m = (∆Th,max - ∆Th,min) / ln(∆Th,max / ∆Th,min) (6)
Here, ∆Th,max and ∆Th,min represent the largest and smallest differences between the inlet and outlet flow temperatures, respectively.
If Th,in is not constant, an average must be taken between all the inlet flow temperatures to obtain a mean value.
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The mean outlet temperature of the fluid in the jacket, denoted as ¯T, is calculated as:
¯T_(h,out) = Th,in - ∆Th,m (7)
The logarithmic mean temperature of the fluid is then computed using:
T_(h,m) = (Th,in - ¯T_(h,out)) / ln(Th,in / ¯T_(h,out)) (8)
Substituting Am and Th,m into Equation (4), we arrive at the following expression:
(T_(h,m) - T(t)) / (T_(h,m) - T0) = exp[-(UA_m) / (M * cp) * t] = e^(-t / τ) (9)
Where:
Heat transfer plays a crucial role in various industries, including the food and pharmaceutical sectors, which involve processes containing enzymes. Maintaining constant temperatures is essential for enzymes to operate efficiently, as extreme temperatures can either slow down enzyme reactions or denature the enzymes themselves. Transient heat transfer is a valuable technique for ensuring a consistent temperature, thereby promoting a high rate of enzyme reaction by cooling or heating a fluid as needed.
In this experiment, water was used as both the fluid inside the tank and in the fluid jacket. The heat exchanger was constructed from stainless steel.
The following equipment and procedures were employed:
One of the hazards in this experiment was the use of hot water in the pipes, which could cause harm on contact. Proper precautions, such as applying cold water to burns to prevent scalds and blisters, were taken to ensure safety during the experiment.
To calculate the height (h) of the cylinder, we assumed that the volume of water was equal to the volume of the tank. The volume equation for a cylinder is given by:
V"tank" = π * r^2 * h (11)
We also calculated the volume of water using mass (M) and density (ρ):
V"water" = M / ρ (12)
With the mass of 1.1985 kg of water and a known density of 997 kg m-3, we calculated hin and hout for different tank diameters using Equation (11).
The surface area of a cylinder can be determined using the formula:
A = 2 * π * r * h + 2 * π * r^2 (13)
Utilizing Equation (5), we calculated Am using Ain and Aout from Equation (14):
Am = (0.163326 - 0.144281) / ln(0.144281 / 0.163326) (14)
We also calculated ∆Th,m using Equation (6) for the flow rate of 2.0 liters per minute:
∆Th,m = (∆Th,max - ∆Th,min) / ln(∆Th,max / ∆Th,min) (15)
| Flow rate (l/min) | Mass of Water used (kg) | Am (m2) | T0 (K) | Th, m (K) | Th, in (K) | ¯Th, out (K) | ∆Th, m (K) | τ (s) | U (W m-2 K-1) | R (K W-1) | R (%) |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 1.0 | 1.1985 | 0.153607 | 308.7168 | 342.5102 | 342.8952 | 340.8237 | 2.3494 | 1111.1111 | 75.421 | 0.001525 | 1.28 |
| 2.0 | 1.2004 | 0.155203 | 304.5693 | 343.5710 | 343.9762 | 342.2535 | 1.0755 | 344.8276 | 233.326 | 0.000857 | 4.02 |
Analysis of the results reveals that a higher flow rate of 2.0 liters per minute leads to the system reaching a steady state in less time, resulting in larger increases in temperature over time. This observation aligns with Equation (3), where the rate of heat transfer is directly proportional to the difference in temperature. Additionally, the first law of thermodynamics dictates that T2 should never exceed T1 in normal circumstances, which is evident in the data. The trend in the graphs corresponds to the theoretical expectations.
The agitator's role in the experiment is significant as it ensures the uniform distribution of energy. The graphs do not start from the point (0,0) because the heat exchanger was not initially in a stable state until the agitator achieved uniform heat distribution. The use of a data logger recording temperatures at one-second intervals was crucial, as manual recording could introduce human errors when reading thermocouples. It's important to note that our calculations may not be precise due to the standard error of the balance used to weigh the water, with an uncertainty of ±0.05g, impacting the measurements.
In conclusion, this experiment demonstrates that increasing the flow rate of the hot fluid results in a shorter time required to heat the tank to a specific temperature. As evidenced by Equation (3), the rate of heat transfer is directly influenced by the temperature difference. This finding is consistent with theoretical expectations and supports the hypothesis that a higher flow rate accelerates the heating process.
The following nomenclature was used throughout the experiment:
This comprehensive experiment report provides valuable insights into transient heat transfer and its practical applications. Understanding heat transfer processes is essential in various industries, and the results obtained in this experiment contribute to this knowledge.
Transient Heat Transfer Experiment Report. (2024, Jan 06). Retrieved from https://studymoose.com/document/transient-heat-transfer-experiment-report
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