User:BademiChetan

Introduction

This is the model of a flat plate solar water heater.

It's basically follows the equations and relations in Chapter 6, Solar Engineering for Thermal Processes by Duffie and Beckman,

In the method on_load, certain parameters have been fixed. These can be varied and results for different parameters can be obtained. Some sample screen shots are attached.

The model has been tested with all the data(example problems) mentioned in the book and give correct results. Improvements to the model would be deciding the angle of incidence based on the position of the sun, varying the wind transfer coefficient by using the data reader, etc.

Salient features

1. Calculates HeatLossCoefficient and TempPlateMean by solving equations 6.4.9 and 6.9.4 iterativelys(Duffie and Beckman). This is very accurate compared to a model with approximations.

2. Number of glass covers, length, width, insulation properties, thickness of the insulation, temperature of fluid inlet and outlet can be varied.

3. Takes into account the transmission-absorptance product for various angles of incidences.

Assumptions

Following are the assumptions(as mentioned in the book).

1. Performance is steady state.

2. Construction is of parallel sheet and tube type.

3. The headers cover small area and can be neglected.

4. The headers provide uniform flow to the collector tubes.

5. There is no absorption of solar energy by covers insofar as it affects losses from the collector.

6. Heat flow through the covers is one dimensional.

7. There is negligible temperature drop through the cover.

8. The covers are opaque to infra red radiation.

9. There is one dimensional heat flow from the black insulation.

10. The sky can be considered a black body for long wavelength radiation at equivalent sky temperature.

11. The temperature gradients around the tubes can be neglected.

12. The temperature gradients in the direction of flow and between the tubes can be neglected.

13. Loss through the front and the back are to the same temperature.

14. Dust and dirt on the collector are negligible.

15. Shading of the collector absorber is negligible.

16. Wind transfer coefficient of assumed to be zero.

Source

REQUIRE "atoms.a4l";

(* New Definition: for overall collector loss coefficient. *) 

ATOM heat_loss_coeff REFINES solver_var
DIMENSION M/T^3/TMP
DEFAULT 10{W/m^2/K};            
lower_bound := 0{W/m^2/K};
upper_bound := 1e100 {W/m^2/K};
nominal := 1{W/m^2};
END heat_loss_coeff;

ATOM heat_capacity REFINES solver_var
DIMENSION L^2/T^2/TMP
DEFAULT 4181.3{J/kg/K};         (* heat_capacity of water at 25 degree celcius *) 
lower_bound := -1e60{J/kg/K};
upper_bound :=  1e60{J/kg/K};
nominal :=      1{J/kg/K};
END heat_capacity;


MODEL FlatPlate;


N                   "number of plates"                                      IS_A factor;
beta                "collector angle( in degree )"                          IS_A factor;
C                   "A function of beta, for intermediate calculations."    IS_A factor;
E                   "A function of TempPlateMean. For calculations only"    IS_A factor;
TempAmbient         "Ambient temperature"                                   IS_A temperature;
TempPlateMean       "Mean plate temperature"                                IS_A temperature;
TempFluidInlet      "Fluid inlet temperature"                               IS_A temperature;
TempFluidOutlet     "Fluid outlet temperature"                              IS_A temperature;
EmittanceGlass      "Emittance of glass"                                    IS_A factor;
EmittancePlate      "Emittance of plate"                                    IS_A factor;
HeatLossCoeffTop    "Heat loss coefficient of the top surface"              IS_A heat_loss_coeff;
HeatLossCoeffSide   "Heat loss coefficient of the side surface"             IS_A heat_loss_coeff;
HeatLossCoeffBack    "Heat loss coefficient of the back surface"            IS_A heat_loss_coeff;
HeatLossCoeff       "Overall heat loss coefficient of the collector"        IS_A heat_loss_coeff;
HeatUseful          "Useful heat"                                           IS_A energy_rate;
MassRate            "Rate of flow of mass"                                  IS_A mass_rate;
HeatCapacity        "Amount of heat required to change temperature"         IS_A heat_capacity;
RemovalFactor       "Heat removal factor"                                   IS_A factor;
CollectorArea       "Area of the collector"                                 IS_A area;
BackConductivity    "Conductivity of the back insulation"                   IS_A thermal_conductivity;
SideConductivity    "Conductivity of the side insulation"                   IS_A thermal_conductivity;
CollectorLength     "Length of the Collector"                               IS_A distance;
CollectorWidth      "Width of the Collector"                                IS_A distance;
CollectorThickness  "Thickness of the collector"                            IS_A distance;
SideThickness       "Thickness of the side insulator"                       IS_A distance;
BackThickness       "Thickness of the back insulator"                       IS_A distance;
Efficiency          "Efficiency of the collector"                           IS_A factor;
SolarRadiation      "Solar Radiation at the surface"                        IS_A irradiance;
NetRadiation        "Effective solar radiation"                             IS_A irradiance;
TransmittanceNormal "Normal transmittance of the glass plate"               IS_A factor;
AbsorptanceNormal   "Normal absorptance of the glass plate"                 IS_A factor;
AngleModifier       "Incidence angle modifier"                              IS_A factor;
AngleModifierCoeff  "Incidence angle modifier coefficient"                  IS_A factor;
IncidenceAngle      "Incidence angle"                                       IS_A factor;

(* EQUATIONS *) 




find_area_of_collector:
CollectorArea = CollectorLength * CollectorWidth ;

find_intermediate_const_C:
C = 520 * ( 1 -0.00005 * beta * beta ) ;

find_intermediate_const_E:
E = 0.430 * ( 1 - 100 / TempPlateMean ) ; 

find_heat_removal_factor:
RemovalFactor = MassRate * HeatCapacity * ( TempPlateMean - TempAmbient ) / CollectorArea / ( NetRadiation -  HeatLossCoeff*( TempFluidInlet - TempAmbient)  ) ;

find_heat_loss_coeff_top:
HeatLossCoeffTop    = C / TempPlateMean / N * ( ( TempPlateMean - TempAmbient ) / ( 1.07886 * N + 1)  )^E 
+ 5.67E-8 * (TempPlateMean + TempAmbient) *(TempPlateMean^2 + TempAmbient^2)/( 1 / EmittancePlate - N + ( 2.07886 * N + 0.133 *EmittancePlate ) / EmittanceGlass) ;

find_heat_loss_coeff_back:
HeatLossCoeffBack = BackConductivity / BackThickness ;

find_heat_loss_coeff_side:
HeatLossCoeffSide = SideConductivity * 2 * ( CollectorLength + CollectorWidth ) * CollectorThickness / SideThickness / CollectorArea ;


calc_incidence_angle_modifier:
AngleModifier = 1 + AngleModifierCoeff * (1 / cos(IncidenceAngle * 1{PI} / 180 ) - 1 ) ;


calc_net_radiation_at_collector:
NetRadiation = SolarRadiation * TransmittanceNormal * AbsorptanceNormal * AngleModifier ;

(* Calculate HeatLossCoefficient and TempPlateMean by solving equations 6.4.9 and 6.9.4 iterativelys(Duffie and Beckman) *) 

find_overall_heat_loss_coeff:
HeatLossCoeff = HeatLossCoeffTop + HeatLossCoeffBack + HeatLossCoeffSide ;

find_mean_plate_temperature:
TempPlateMean = TempFluidInlet + ( NetRadiation - HeatLossCoeff * ( TempFluidInlet - TempAmbient )  ) * ( 1 - RemovalFactor ) / HeatLossCoeff ;


(* Calculating the amount of heat that can be used. *) 
calc_useful_heat:
HeatUseful = CollectorArea * RemovalFactor * ( NetRadiation - HeatLossCoeff * ( TempFluidInlet - TempAmbient ) ) ; 


(* Calculate efficiency of the collector. *) 
calc_efficiency:
Efficiency = HeatUseful / CollectorArea / SolarRadiation ;

METHODS
    METHOD on_load;
    
    FIX N;
    N := 1 ;
    
    FIX beta;
    beta := 45 ;
    
    FIX TempAmbient;
    TempAmbient := 300{K};
    
    (* Initial guess for the solver. *) 
    TempPlateMean := TempAmbient + 10{K} ;
    
    FIX TempFluidInlet;
    TempFluidInlet := 310{K};
    
    FIX TempFluidOutlet ;
    TempFluidOutlet := 350{K};
    
    FIX EmittanceGlass;
    EmittanceGlass := 0.88 ;
    
    FIX EmittancePlate;
    EmittancePlate := 0.95 ;
    
    FIX MassRate;
    MassRate := 0.03{kg/s};
    
    FIX HeatCapacity;
    HeatCapacity := 4181.3{J/kg/K};
    
    FIX SolarRadiation;
    NetRadiation := 1400 {kg/s^3} ;
    
    FIX CollectorLength;
    CollectorLength := 2{m};
    
    FIX CollectorWidth ;
    CollectorWidth := 1{m};
    
    FIX CollectorThickness;
    CollectorThickness := 7.5{mm};
    
    FIX SideThickness;
    SideThickness := 25{mm};
    
    FIX BackThickness;
    BackThickness := 50{mm};
    
    FIX BackConductivity;
    BackConductivity := 0.045 {kg*m/s^3/K};
    
    FIX SideConductivity;
    SideConductivity := 0.045 {kg*m/s^3/K};
    
    FIX AbsorptanceNormal; 
    AbsorptanceNormal := 0.96;
    
    FIX TransmittanceNormal;
    TransmittanceNormal := 0.96;
    
    (* Enter the angle of incidence in degrees *) 
    FIX IncidenceAngle;
    IncidenceAngle := 60;
    
    FIX AngleModifierCoeff;
    AngleModifierCoeff := -0.10;
    
    END on_load;
END FlatPlate;

Incidence Graph

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Incidence Graph generated by ASCEND for the model of simple flat plate solar water heater

Screenshot1

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Values obtained after solving the model of simple flat plate solar water heater part I

Screenshot2

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Values obtained after solving the model of simple flat plate solar water heater part II