OTTV: what it is and how to calculate it

PAUL HAY Capital Projects

http://www.phcjam.com/

            

Overall Thermal Transmission Value (OTTV)

Author:            Paul Hay

e-mail:              paul.hay@phcjam.com

profile:             www.linkedin.com/in/phcjam

1.0  WHAT IS OTTV?        

1.1            Overall Thermal Transmission Value (OTTV) is the measure of external heat-gain transmitted through a unit area of a building’s wall or roof;

1.2       OTTV is recorded in units of W/m².

1.3       OTTV concerns conductive & radiative heat-gains transmitted through glazing and opaque components.

2.0  OTTV VARIABLES  

2.1       Equivalent Temperature Differential (TD_eq) is the theoretical difference between outdoor and indoor temperatures that would result in a heat transfer equivalent to the effects of solar heat-gains, thermal storage and actual temperature difference on an opaque component, as a roof [unit = K];

2.2       Solar Factor (SF) is the average hourly value of solar insolation [unit = W/m²];

            2.2.1.  EEBC-94 states that SF = 435 W/m² for roofs; and

            2.2.2.  SF = 372 W/m² for walls.

2.3       Shading Coefficient (SC) is the ratio of solar heat-gain through any fenestration compared to that through an unshaded, 3-mm thick double-strength glass.

            SC =   Solar Heat-Gain through any fenestration                                              [2.1]

                        Solar Heat-Gain through reference glass

3.0  CALCULATING OTTV OF ROOFS

3.1       EEBC-94 specifies the maximum OTTV for roofs as 20 W/m² ;

3.2       There are two equations for calculating OTTVs for roofs.

            3.2.1   For roofs without skylights,

            OTTV_r =          [DT x U_r] + [(TD_eq - DT) x A_c x U_r]                                                    [3.1]

            where,

            OTTV_r = Overall Thermal Transmission Value of a roof, W/m²

                        DT       = Temperature Difference, K

                                    = T_d - T_i

                        T_d        = Design Temperature, C  

                                    = 33.9 C, for Kingston

                        T_i         = Thermostat set-point, C

                        TD_eq    =  Equivalent Temperature Differential, K

                        A_c        = Solar absorptance (0<A_c<1)

                        U_r        = Overall Thermal Transmission Coefficient of roof, W/m-K  

Fig. 1:  Shading Coefficients for Fenestration

            3.2.2   For roofs with skylights,

            OTTV_r =          [DT x U_r x (1-SRR)] + [(TD_eq - DT) x A_c x U_r x (1-SRR)] +

                                    [DT x U_s x SRR] + [SF x SC_s x SRR]                                             [3.2]

            where,

                        SRR   = Skylight-to-Roof Ratio (0<SRR<1)

                        SF       = Solar Factor for roof, W/m²

                        SC_s     = Shading Coefficient of skylights (0<SC_s <1)

                        U_s        =  Overall Thermal Transmission Coefficient of roof, W/m-K

4.0  CALCULATING OTTV OF WALLS

4.1       EEBC-94 species the maximum OTTV for walls as (a) 67.7 W/m² for large offices [Area > 3,700 m²] (b) 61.7 W/m², for smaller offices and (c) 53.1 W/m² for other buildings;

4.2       OTTVi for a wall is calculated as follows:

            OTTV_i =          [DT x U_i x (1-WWR_i)] + [(TD_eq - DT) x CF_i x A_c x U_i x (1-WWR_i)] +

                                    [DT x U_f x WWR_i] + [SF x CF_i x SC_i x WWR_i]                               [4.1]

            where,

            OTTV_i = Overall Thermal Transmission Value of a wall “i”, W/m²

                        U_i         =  Overall Thermal Transmission Coefficient of wall “i”, W/m-K

                        WWR_i = Window-to-Wall Ratio for wall “i” (0<WWR_i<1)

                        SF       = Solar Factor for wall, W/m²

                        CF_i      = Correction Factor for orientation of wall “i”

                        SC_i      = Shading Coefficient of fenestration on wall “i” (0<SC_i <1)

                        U_f        =  Overall Thermal Transmission Coefficient of fenestration, W/m-K

4.3       Overall OTTV for walls is calculated as follows:

            OTTV_w =         [(A₁ x OTTV₁ ) + (A₂ x OTTV₂) +.........+ (A_i  x OTTV_i )]                  [4.2]

                                                            (A₁ + A₂ + ..............+ A_i)

            where,

                        OTTV_w = Overall OTTV for walls “1" to “i”

                        A_i         =   Area of wall “i”

5.0  SAMPLE OTTV CALCULATIONS

Calculate the OTTV for an office building constructed as follows:

Location:        Kingston, Jamaica                               T_in                = 24.4 deg.C

Dimensions:    18 m x 18 m x 3.6 m high                    Orientation    = North

A_c(r)               = 0.35                                                 TD_eq(r)         = 23.0 deg.C

A_c(w)              = 0.70                                                 TD_eq(w)          = 23.0 deg.C

SRR               = 0.01                                                 U_r                 = 1.10 W/m²-K

WWR            = 0.33                                                 U_s                 = 5.40 W/m²-K

SC_s                = 0.50                                                 U_w                = 3.01 W/m²-K

SC_s                = 0.50                                                 U_f                 = 4.60 W/m²-K

            DT       = T_d - T_in

Where,

            T_d        = Design temperature         = 33.9 deg.C, for Kingston

ˆ          DT       = 33.9 - 24.4  = 9.5 K

(A)         For a roof with skylights,

            OTTV_r =          [DT x U_r x (1-SRR)] + [(TD_eq(r) - DT) x A_c(r) x U_r x (1-SRR)] +

                                    [DT x U_s x SRR] + [SF_(r) x SC_s x SRR]                                          [5.1]

            where,

                        SF_(r)     = Solar Factor for roof         = 435 W/m², for Jamaica

ˆ          OTTV_r =          [9.5 x 1.10 x (1- 0.01)] + [(23.0 - 9.5) x 0.35 x 1.10 x (1- 0.01)] +

                                    [9.5 x 5.4 x 0.01] + [435 x 0.5 x 0.01]

                        =          10.35 + 5.15 + 0.51 + 2.18

                        =          18.2 W/m²

(B)         OTTVi for a wall is as follows:

            OTTV_i =          [DT x U_i x (1-WWR_i)] + [(TD_eq(w) - DT) x CF_i x A_c(w) x U_i x (1-WWR_i)] +

                                    [DT x U_f x WWR_i] + [SF_(w) x CF_i x SC_i x WWR_i]                            [5.2]

            where,

                        SF_(w)    = Solar Factor for wall         = 372 W/m², for Jamaica

                        CF_i      = Correction Factor for orientation of wall “i”

            CF₁     = 0.96, for east wall

ˆ          OTTV₁ =         [9.5 x 3.01 x (1 - 0.33)] + [(23.0 - 9.5) x 0.96 x 0.7 x 3.01 x (1 - 0.33) +

                                    [9.5 x 4.60 x 0.33] + [372 x 0.96 x 0.5 x 0.33]

                        =          19.16 + 18.30 + 14.42 + 58.92

                        =          110.8 W/m²

Similarly, CF₂           =          1.09, for south wall

ˆ          OTTV₂ =         19.16 + 20.77 + 14.42 + 66.90       =          121.3 W/m²

            CF₃     =          1.36, for west wall

ˆ          OTTV₃ =         19.16 + 25.92 + 14.42 + 83.48       =          143.0 W/m²

            CF₄     =          0.58, for north wall

ˆ          OTTV₄ =         19.16 + 11.05 + 14.42 + 35.60       =          80.2 W/m²

(C)         Overall OTTV for walls is as follows:

            OTTV_w =         [(A₁ x OTTV₁ ) + (A₂ x OTTV₂) +.........+ (A_i  x OTTV_i )]                  [5.3]

                                                            (A₁ + A₂ + ..............+ A_i)

Where,

            A₁          =  A₂    =  A₃    =  A₄    = 18 x 3.6       = 64.8 m²

ˆ          OTTV_w =         [(64.8 x 110.8) + (64.8 x 121.3) + (64.8 x 143.0) + (64.8 x 80.2)]

                                                            (64.8 + 64.8 + 64.8+ 64.8)

                        =          113.8 W/m²