SNOW_MELT_HEAT

eacb9a4e-2aed-4101-9443-d588b55e1e19 121 SNOW_MELT_HEAT_LOAD Ruben Sidranski 2 8 false false 0 decimal

&[DATE]

Objective and Approach

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Consider one-dimensional conduction in a plane composite wall. The outer surfaces are exposed to a fluid at and a convection heat transfer coefficient. The middle wall B experiences uniform heat generation qdotB, while there is no generation in walls A and C.

⇒ Consistent with the software's operation, variables tend to be defined first, followed by formulas.

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References (Ref)

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The following references were used throughout this calculation (Ref: #)

1) American Society of Heating Refrigeration and Air Conditioning Fundamentals, 2017

2) Email

3) Heat Transfer; A.F. Mills; 1992

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Introduction

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This calculations will solve for the minimum insulation thickness with an assumed and given R-value

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Given

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Fluid Temperature
Ref 2 T.inner 140 °F * :

High Temperature of outer concrete wall
Ref 2 T.C 100 °F * :

This being confirmed with the concrete mix

Surface  Temperature
Ref 2 T.s 90 °F * :

Spray foam "R"/inch
Ref. 4 k.ins 1 6.2 / BTU in * hr ft 2^* Δ°F * / * :

Assumptions

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Concrete and shotconcrete (assumed homogeneous)
Thermal Conductivity
Ref 1, 26.8 Table 4
"cement/lime, mortar and stucco 120 lb/ft" k.C 9.7 BTU in * hr ft 2^* Δ°F * / * : BTU hr ft * Δ°F * / 0.8083

~10 in concrete.  Considered homogeneous with shotcrete
Ref 2 L.C 10 in * :

~2 in shotcrete. Considered homogeneous with the concrete
Ref 2 L.SC 2 in * :

Estimated surface coefficient for concrete and shotconcrete (assumed homogeneous)
per example
Ref 1; 23.19 h.scC 1.0 BTU hr ft 2^* Δ°F * / * :

Initial guess value of the shotcrete T.SC T.C :

Resistance of the concrete wall
NOTE the reciprocal of k/L R.c L.c k.c / : hr ft 2^* Δ°F * BTU / #

Margin to account for wind conduction margin 1.1 :

The following assumptions apply

Calculation is for steady state

There is no heat generated within the volume

Heat flow through a composite layer is the same. When there is more than one layer {in the composite}, the total resistance of the circuit must be calculated as one homogeneous piece.

Areas as the same

negligible contact resistance at the interfaces

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Solve

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T_C

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T_SC

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Fluid Temp T.inner °F 140

Amb. High Temp T.ambh °F #

Sign convention: right direction is + -->

X.A L.C : in 10

X.B L.C L.SC + : in 12

Area "A"

Heat balance for the concrete at the "A" interface gives the heat flux on the "A" side

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Flow rate across the concrete wall
Ref 3 Q.rate k.C L.C / T.inner T.C - (* : BTU hr ft 2^* / 38.8

Area "B" HELP Here FindRoot

Heat balance for the shotcrete at the "B" interface gives the heat flux on the "B" side

Reminder that concrete and shotecrete is homogeneous, so we are solving for T_SC

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Q.rate k.C L.SC / T.C T.SC - (* ≡ T.SC 80 °F * ≡ FindRoot #

3 - appVersion 0.99.6648

<---What's going on here

This is expected T.SC °F 92

test Q.rate L.SC k.C / * (: Δ°F 8

Area "C"

T.inner T.SC - T.SC T.s - / 24

Ref 1; 23.19 Eq 14 X k.ins h.scC / T.inner T.SC - T.SC T.s - / (* : in 3.871