Calculating Buried Pipe Heat Transfer for Ice Slabs

After the flow, tube spacing, thermal properties, and boundary loads are entered on one consistent basis, the calculation separates hydraulic capacity from slab conductance and predicts both coolant temperature rise and ice-surface capacity. A single heat-transfer coefficient cannot describe the entire assembly.

Design Inputs and Boundary Conditions

Before anything else, confirm the geometry and operating conditions. The stated case uses 1-inch-ID polyethylene pipe embedded in a 5-inch concrete floor, with 50% ethylene glycol entering at 18°F. The pipe crown is 1.75 in. below the concrete surface. The proposed comparison changes center spacing from 4 in. to 3.5 in.; the initial flow is 5 US gpm.

Input	Stated value	Required clarification
Pipe	1-inch ID polyethylene	Outside diameter and wall conductivity
Slab	5 inches thick	Concrete conductivity and pipe position relative to slab bottom
Pipe cover	1.75 inches from pipe crown to surface	Confirm this is not centerline depth
Coolant	50% ethylene glycol at 18°F inlet	Density, heat capacity, conductivity, viscosity, and basis of concentration
Flow	5 US gpm	Flow per tube, per circuit, or total system flow
Spacing	4 inches; proposed 3.5 inches	Confirm centerline-to-centerline spacing
Ice	Proposed 1.5-inch layer	Ice conductivity and target surface temperature
Air	60°F dry bulb, 45°F wet bulb	Air velocity and radiation environment
Concrete	25°F reported temperature	Measurement location and operating state
Ground	Not stated	Ground temperature and insulation construction

Do not move on until circuit length, number of parallel circuits, supply/return routing, and every missing property are taken from drawings, measured, or read from the applicable property table at the operating concentration and temperature.

Refrigeration-Load Definition

Calculate the required surface duty before selecting spacing or flow. During ice formation, the refrigeration system must remove the sprayed water's sensible heat, its latent heat of freezing, and any ongoing heat entering from the room and ground. During holding operation, the water-freezing term may fall, but convection, radiation, moisture deposition, lighting, occupants, and ground heat remain.

For a water mass m, write the pull-down energy as:

Q_water = m[c_p,water(T_initial − T_freeze) + h_fusion + c_p,ice(T_freeze − T_final)]

Include the final ice-cooling term only when the design requires cooling below the freezing point. Divide total energy by the permitted freezing time to obtain an average refrigeration rate, then add simultaneous surface and ground loads. Use the 2006 ASHRAE Refrigeration Handbook, Chapter 35, as a rink-load calculation reference and verify the selected design conditions against the project requirements.

The stated 60°F dry-bulb and 45°F wet-bulb conditions help define air-side loads, but air velocity and surrounding surface temperatures are also needed. Lighting and other warm surfaces raise radiant load even when the air temperature remains unchanged.

Check: express the final requirement as heat rate and surface heat flux, both with an explicit time basis. Do not proceed with a value stated only as Btu/ft².

Coolant Flow and Circuit Capacity

Set flow from the required heat pickup and the allowable coolant temperature rise. For one circuit:

Q_circuit = m_dot × c_p × (T_return − T_supply)

with m_dot = density × volumetric flow. Obtain density and specific heat for 50% ethylene glycol at the circuit's mean temperature. Do not substitute water properties; glycol concentration and low temperature materially change heat capacity and viscosity.

1. Assign the design heat load to each circuit from its served slab area.
2. Select an allowable supply-to-return temperature rise from the refrigeration and surface-uniformity requirements.
3. Calculate the required mass flow, then convert it to volumetric flow using glycol density.
4. Calculate velocity, Reynolds number, and internal convection from the actual pipe inside diameter and glycol properties.
5. Calculate circuit pressure loss, including pipe, fittings, headers, and balancing devices.
6. Compare total system flow and head with the pump curve and the chiller's permitted evaporator flow range.

Reducing flow increases coolant temperature rise for the same heat load. It can also reduce internal convection when the flow approaches a less effective regime. Excess flow may improve internal convection only modestly while sharply increasing pumping power and pressure loss.

A reported operating reference used approximately 3 US gpm per tube, with nominal coolant temperatures of 18°F entering and above 20°F leaving. That is a comparison point, not a design setting; circuit length, glycol properties, and heat duty decide whether it transfers to this installation. Lowering circulation can also drive a refrigeration system toward low evaporator pressure or low leaving-solution-temperature limits. Do not change protective settings to compensate for an unverified flow selection.

Check: at the selected flow, calculated circuit heat pickup must equal its assigned load, and measured or predicted pressure drop must lie on the pump operating curve.

Tube Spacing and Slab Conductance

Changing spacing from 4 in. to 3.5 in. places more tube length under each unit of floor area and shortens the lateral conduction path between adjacent pipes. It therefore raises area-based heat-transfer capacity and reduces the warm stripe midway between tubes. It does not proportionally increase the internal pipe coefficient, which is governed mainly by coolant properties, tube diameter, and flow.

Treat the slab as a two-dimensional conduction field. A one-dimensional calculation using only the 1.75-in. cover misses lateral spreading resistance and the interaction between neighboring tubes. Model a repeating section extending halfway to the adjacent tube on each side. Include the pipe wall, concrete above and below the tube, the ice layer, surface boundary conditions, and any bottom insulation or ground resistance.

Reported comparison values were 42 Btu/ft² at 4-in. centers and 47 Btu/ft² at 3.5-in. centers for 1-in. ice and approximately 3 US gpm per tube. Their time basis was not stated, so they cannot be entered as heat fluxes until that basis is identified. They also do not directly apply to the proposed 1.5-in. ice layer. Thicker ice adds conduction resistance and generally requires a colder coolant condition for the same surface load.

Check: compare both spacings at identical coolant temperatures, flow basis, ice thickness, concrete properties, and room and ground boundaries. Accept a spacing only after both average heat flux and maximum midpoint surface temperature meet the design target.

Composite Heat-Transfer Calculation

Calculate component resistances before reporting an overall coefficient. On a consistent reference-area basis, the thermal path contains internal coolant convection, polyethylene wall conduction, concrete spreading, ice conduction, and the surface boundary. A conceptual resistance expression is:

1/U = R_internal + R_pipe + R_concrete,2D + R_ice + R_surface

The resistances cannot be added until each is converted to the same reference area. For the cylindrical pipe terms, use the actual inside and outside diameters. Obtain internal convection from the calculated flow regime and glycol properties. Obtain slab spreading resistance from a validated embedded-tube correlation or a two-dimensional numerical model.

1. Solve the hydraulic model to obtain local coolant temperature along the circuit.
2. Apply that temperature to successive slab sections rather than treating the entire tube as being at 18°F.
3. Solve conduction through the pipe, concrete, and ice to the surface.
4. Apply convection, radiation, and moisture-related loads at the ice surface and ground or insulation conditions at the slab bottom.
5. Iterate until the heat removed by the coolant equals the heat crossing the slab boundaries.

Check: the model's coolant-side heat gain must match the integrated slab heat flow within the chosen numerical tolerance, and the predicted return temperature must follow from the same energy balance.

End-to-End Commissioning Verification

1. Confirm glycol concentration and record supply and return temperatures with calibrated sensors.
2. Measure total flow and individual circuit flow; verify that the reported 5 US gpm basis matches the design interpretation.
3. Record pump differential pressure and compare it with calculated system resistance.
4. Map concrete or ice-surface temperature above a tube and midway between tubes. A large repeating temperature difference points to excessive spacing, inadequate cover conduction, circuit imbalance, or insufficient coolant capacity.
5. Record room dry-bulb, wet-bulb, air movement, lighting state, and ground-side conditions during the test.
6. Calculate measured refrigeration pickup from glycol mass flow, specific heat, and supply/return temperature difference, then compare it with the modeled slab load.

Do not move on until flow, temperature rise, pump head, surface-temperature pattern, and calculated heat balance agree under one documented operating condition.

Frequently Asked Questions