NOTE For determining the amount of heating or cooling that can be provided by a radiant source, we have developed the following calculators. While they eliminate a chalkboard fulll of equations, it is important to understand how to use them and what the outputs mean. Feel free to play around with them but we suggest to have the Chiltrix engineering dept. comment/assist before you rely upon any calculations.

1. The first calculator "RADIANT" calculates the net radiant transfer per ft.^2 based on the emissivity and temperature of the radiant surface and, of the surfaces of the room to be heated or cooled. The radiant transfer values must be added to convection values to get a total transfer value. Note that all objects in the universe (>0 degrees K) continuously emit radiant energy. And all objects continuously absorb radiant energy. The calculator calculates and compares both the absorbtion and emission to provide the net energy transfer.

2. the 2nd calculator is for CONVECTION, as with the radiant calculator, this is not the full heating or cooling calculation, as the output will then need to be added to the results of the radiant calculator to get a total value.

3. The 3rd calculator, SURFACE TEMP, can be used to calculate a surface temperature based on a heating or cooling source (heat transfer plate temperature) and an R value of the materials that separate the room facing surface and the source.

4. The 4th calculator, CONVERT K TO R, allows you to find the R value of a material. While only some materials will have a published R value, nearly all materials will have a K value that can be found online. This calculator converts a K value to an R value.

5. The 5th calculator, DEW POINT, allows a calculation of dew point from a known RH% and temperature. This is important for understanding radiant cooling capacity of a system under various conditions.

TIP: The CXRC Radiant Cooling Calculator manual includes a tutorial with additional info on how to use these calculators:
CXRC1 Radiant Cooling Controller Manual

TIP: In most climates, radiant cooling will need a dehumidifier in order to provide best comfort, and, to keep the dew point low enough to obtain maximum radiant cooling capacity. Note that radiant cooling generally requires a dew point controller to prevent unwanted condensation. Suggested indoor humidistat dehumidification target is 50% RH. Here is a dehumidification sizing calculator.

1. RADIANT CALCULATOR (Stefan-Boltzmann)

Radiant Surfaces Calculation

Enter

Radiant Panel Emissivity

Radiant Surface Temperature

deg F

Area Don't Change This

Area =

m^2

K =

C + 273

K =

Q =

e*σ*T^4

Output

Watts/m^2

Avg. Values of Room Surfaces

Enter

Material Surface Emissivity, e =

Avg. Room Surface Temperature

deg F

Area =

m^2

K =

C + 273

K =

Q =

e*σ*T^4

Output

Watts/m^2

Net Radiant Output

BTU

Net Radiant Output

BTU/Ft^2

σ = Stefan-Boltzmann Constant

5.669E-08

*Negative number means cooling

*Positive number means heating

IMPORTANT: ADD RADIANT OUTPUT TO CONVECTION OUTPUT FOR THE TOTAL VALUE

SEE CONVECTION CALCULATOR NEXT

2. Convection Calculator For Heating/Cooling (Wall, Floor, Ceiling)

Celsius

Density

First, in the top section, select function as to heating or cooling, and as to the radiant surface being a ceiling, floor or wall.

Add your inputs in the blue areas.

For air density, air viscosity, air specific heat, air K value - leave them as is or adjust accordingly

Air Density=	1.2 kg/m3 see chart to the right
Air viscosity	.0000187 N-s/m2
Air specific heat		1 J/g-oK
Air, K value	0.027 J/s-m-K

Celsius	Density
Temperature	of air
	ρ (kg/m3)
35	1.1455
30	1.1644
25	1.1839
20	1.2041
15	1.225
10	1.2466
5	1.269
0	1.2922
−5	1.3163
−10	1.3413
−15	1.3673
−20	1.3943
−25	1.4224

Formula For Floor/Ceiling

Equations for Natural Convection - Isothermal Horizontal Plate

Formula For Wall

formula for convection of vertical isothermal; plane

temperature

of air

Helpful Info:

Generally, use the following

θ (°C)

ρ (kg/m3)

Air Density=

1.2 kg/m3 see chart below

1.1455

Air viscosity

.0000187 N-s/m2

1.1644

1.225

Equations for Natural Convection - Isothermal Horizontal Plate

1.2466

1.269

1.2922

Inputs in Blue

Outputs in Green

−5

1.3163

−10

1.3413

Select Function:

−15

1.3673

1= cooling from ceiling

−20

1.3943

2= cooling from floor

−25

1.4224

3= heating from ceiling

4= heating from floor

5= heating- wall

Correlation#1:

6= cooling-wall

Inputs

Calculations

Air Temp, T¥ =

°F

Air Temp, T¥ =

Film Temp.,Tf=

Surface Temp, Tw =

°F

[ Tf = (T¥ + Tw)/2 ]

Dimensionless Numbers used in

Surface Temp, Tw =

Natural Convection Heat Transfer

Coefficient Correlations

Area of Surface, A =

FT^2

Area of Surface, A =

Temp Diff DT =

Correlation #2:

Correlation #1 (for heat transfer from the upper surface of a plate

Perimeter/Surface, P =

Ft. Linear

Perimeter/Surface, P =

M Linear

Abs. Film Temp Tf =

that is hotter than the fluid to a cooler fluid above the plate, or from

If wall radiant, height of wall

Ft.

the lower surface of a plate that is cooler than the fluid to a warmer

If wall radiant, height of wall

Meters

Prandtl Number Pr =

fluid below the plate.)

L = A/P

Grashof Number Gr =

Nu = 0.54 Ra1/4 ( 104< Ra< 107 )

Air Density, r =

kg/m3

Rayleigh No. Ra =

Nu = 0.15 Ra1/3 ( 107< Ra< 1011 )

Air viscosity, m =

N-s/m2

Correlation #2 (for heat transfer from the upper surface of a plate

that is cooler than the fluid to a warmer fluid above the plate, or from

Air, Specific Heat, Cp =

J/g-oK

the lower surface of a plate that is warmer than the fluid to a cooler

fluid below the plate.)

Air, Specific Heat, Cp =

J/kg-oK

Nu = 0.27 Ra1/4 ( 105< Ra< 1010 )

Air Thermal

Conductivity, k =

J/s-m-K

Air Thermal

Expans. Coeff, b =

oK-1

CONVECTIVE HEATING COOLING / FLOOR/WALL/CEILING

Area

m^2

heat transfer coefficient

⍙T

Capacity W

Capacity BTU

BTU / ft^2

Correlation #1.2:

Correlation #1:

for 107 < Ra < 1011 :

for 104 < Ra < 107 :

Nu =

h =

W/m2-K

h =

W/m2-K

Correlation #2 ( for 105 < Ra < 1010 ):

Nu =

h =

W/m2-K

Correlation #3 ( for all values of Ra ):

Nu =

h =

W/m2-K

Correlation #3.2 ( for RaL < 109 ):

Nu =

h =

W/m2-K


3. Solving For Surface Temp
Tc	Radiant Source Temp	PEX or Heat Exchanger F
Ta	Indoor Air Temp	Indoor room air F
R Value	Total R value	R-Value (Separating TC from Ta)
U Value

Th	Indoor Surface Temp	F	C

4. Calculator for Converting K-value to R-value




input		K=(W/m-k)
.		U =BTU inch /(hr ft2 F)
		R per inch
Input		Inches
		R-Value Total





5. Dew Point Calculator
INPUT TEMPERATURE °F			°F
INPUT TEMPERATURE °C			°C
INPUT RH %			%
OUTPUT DEW POINT =			°C
OUTPUT DEW POINT F =			°F

Please contact Chiltrix for a radiant heating and/or cooling evaluation or to get help using these calculators.

Radiant Heating & Cooling Calculators

1. RADIANT CALCULATOR (Stefan-Boltzmann)

2. Convection Calculator For Heating/Cooling (Wall, Floor, Ceiling)

3. Solving For Surface Temp

4. Calculator for Converting K-value to R-value

5. Dew Point Calculator