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Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator

Easily calculate and compute geothermal ground-source heat pump borehole temperature (kelvin line source) calculator with accurate equations, live formulas, and expert guidance.

Calculated Result
-0.53 C

Borehole Wall Temperature (T_b)

Borehole Wall Temperature (T_b)

-0.53 C

Borehole Wall Temperature C

-0.5339267242586541

Temperature Drop Deg C

12.533926724258654

Kelvin E1 Value

8.750331581680838

Undisturbed Ground Temp C

12

-0.53 — C

Calculation Breakdown

  1. Applied FormulaModels long-term borehole wall temperature evolution and thermal ground depletion for ground-source heat pump (GSHP) closed-loop vertical U-tube heat exchangers using Carslaw & Jaeger’s Kelvin infinite line source.T_b(t) = T_0 + \frac{q}{4 \pi k} \int_{\frac{r_b^2}{4\alpha t}}^\infty \frac{e^{-u}}{u} du

Borehole Kelvin Line Source Metric Output

Interactive visualization based on your current inputs

Calculated Value
-0.5-0.20.20.61.0Borehole Wall Temperature (T_b)

What Is the Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator?

The Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator computes results using established domain formulas, verified conversion factors, and user-entered parameters.

How Does the Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator Work?

Models long-term borehole wall temperature evolution and thermal ground depletion for ground-source heat pump (GSHP) closed-loop vertical U-tube heat exchangers using Carslaw & Jaeger’s Kelvin infinite line source.

Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Tb(t)=T0+q4πk∫rb24αt∞e−uuduT_b(t) = T_0 + \frac{q}{4 \pi k} \int_{\frac{r_b^2}{4\alpha t}}^\infty \frac{e^{-u}}{u} du

Models long-term borehole wall temperature evolution and thermal ground depletion for ground-source heat pump (GSHP) closed-loop vertical U-tube heat exchangers using Carslaw & Jaeger’s Kelvin infinite line source.

How to Use the Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Geothermal Ground-Source Heat Pump Borehole Temperature (Kelvin Line Source) Calculator Example

Input Values:

undisturbedGroundTempC:12
heatExtractionRateWPerM:45
soilThermalConductivityWPerMK:2.5
boreholeRadiusMm:75
operatingTimeMonths:6
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required C.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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