Liquid Temperature Given Useful Heat Gain Calculator

Formula Used:

\[ T_l = T_{fo} - \frac{q_u}{m \times C_{p \text{ molar}}} \]

Temperature of Liquid from Collector (T_fo):

Useful Heat Gain (q_u):

Mass Flow Rate (m):

kg/s

Molar Specific Heat Capacity at Constant Pressure (C_{p molar}):

J/K·mol

Temperature of Liquid in Tank (T_l):

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1. What is the Liquid Temperature Given Useful Heat Gain Formula?

The formula calculates the temperature of liquid in a tank based on the temperature from the collector, useful heat gain, mass flow rate, and molar specific heat capacity. It's essential for thermal energy storage system analysis and design.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ T_l = T_{fo} - \frac{q_u}{m \times C_{p \text{ molar}}} \]

Where:

\( T_l \) — Temperature of liquid in tank (K)
\( T_{fo} \) — Temperature of liquid from collector (K)
\( q_u \) — Useful heat gain (W)
\( m \) — Mass flow rate during charging and discharging (kg/s)
\( C_{p \text{ molar}} \) — Molar specific heat capacity at constant pressure (J/K·mol)

Explanation: The formula calculates the temperature decrease in the liquid tank based on the heat transfer characteristics and fluid properties.

3. Importance of Liquid Temperature Calculation

Details: Accurate temperature calculation is crucial for thermal energy storage system efficiency, heat transfer optimization, and proper system sizing in solar thermal applications.

4. Using the Calculator

Tips: Enter all values in appropriate units (K for temperature, W for heat gain, kg/s for mass flow rate, J/K·mol for specific heat capacity). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is useful heat gain in thermal systems?
A: Useful heat gain is the net amount of thermal energy absorbed by the working fluid after accounting for system losses.

Q2: Why use molar specific heat capacity instead of mass-specific?
A: Molar specific heat capacity is used when working with molar quantities and provides consistency in thermodynamic calculations involving gases.

Q3: What factors affect the temperature of liquid in the tank?
A: The temperature depends on initial collector temperature, heat transfer rate, fluid flow rate, and the thermal properties of the fluid.

Q4: When is this formula most applicable?
A: This formula is particularly useful for well-mixed liquid storage tanks in solar thermal systems and heat exchanger applications.

Q5: Are there limitations to this calculation?
A: The calculation assumes perfect mixing in the tank and constant fluid properties, which may not hold true in all real-world scenarios.