The purpose of mathematical model is to measure the heating behavior and to evaluate the changes in the heating programs without conducting the real and actual live experiments on the designed system in early hour of the day. It is possible to formulate the parameters in replicated way and how the individual heating system is working [4]. The model of the system starts from the theory and by using the actual observations to determine some constants used in the formula [5]. The constants are outside temperature and the heat input for the building. The theoretical formula connects time consideration with the building temperature. The equation given below, provides internal temperature of the building at time t. The constants a, b, and c are considered with special number e. The change in temperature can be measured for the church.    

        When boiler is running to heat up the building the values of constant a and b is negative and curve becomes increasing steeply and then leveled off over time for the values of c. The measurement provides actual temperature against the time for the actual recording of the church and there are different distinct patterns as according to the nature of material used in the window and walls of the church. The curves for the cooling of system are similar to the heating pattern. The heating curves are like elbow and the cooling curves are similar to the elbow shape trend.  

        All the temperature values are selected and corresponding average of temperature at window surfaces, wall, and indoor air are evaluated by the heat balance and transmission losses [2]. The different sensor measures the wall temperature and the transfer coefficient values are obtained for the conduction and convection process. The heat losses from the floor and transmission losses from the walls reduces the temperature [6].

Where height is W1 = 0, 6 m height of W2 1, 6 m

The total height of the wall is . The focus of the heat balance in the church for all the energy categories are identified. The transmission and the ventilation losses are negatively connected with the heat losses and the gain induces positive influence. The U-values are obtained as

        In the equation of the transmission losses calculations the value of A is the area of the studying, H defines heat loss coefficient, and Tin  and Tout are indoor and outdoor temperatures. The building air temperature consists of two cooling and heating cycles and model is calibrated on the basis of heating system to predict the change in the heating controls [3].

        The complete analysis indicates the estimated system for the heating and how the change in the external system can induce impact on the total heating cost. The energy estimation is necessary for the operation of the boiler [5]. There are two ways for the operation of the boiler in the Tucson AZ or Minneapolis MN churches including the conventional gas and oil boiler and the electric heater that runs on the maximum capacity for the water boiling and the radiator surface approaches to the set temperature. The drop in the amount is in the range of 0.5 to 5.0 deg C [6].

        Opposite to the modern condensing boilers the full capacity of design is to circulate the water and to reach the required temperature. The fuel flow is considered for water at different temperatures as mentioned in the graph below appendix. The simple and reliable fuel consumption method is used as temperature of the pipe increases when water leaves the boiler and when boiled water enters in the boiler [6]. The data is collected at the top of the pipe where a different metal is exposed to temperature and by using a small battery powered USB logger. The energy that is initially provided to the water in pipe is directly proportional to the difference in temperature for the flowing water. The electrical consumption measured for the boiler is associated with the time lag that is between the starting up of boiler and flow of temperature that is rising. The temperature of the boiler drops when turned off. The electrical consumption is estimated as the fuel consumption and monitoring equipment’s were used to measure it [2].      

        In a previous research Ramsden method estimated details from the people for they experience the warmth of church [6]. On the basis of his research, the people experience comfort at the temperature of the air and if the radiant heat is reaching to the bodies. A number of sources are used for the analysis for instance besides the heating system, in the day timing the sunshine coming from the window increases the surface heating of church [1]. The relative contribution was related to the two sources as fabric of building, the sunshine coming straight from the windows, surface of different types of heating equipment, and bodies of the other people in the church. Globe thermometer was used to determine the radiant heat that is similar to the ordinary thermometer. The center of thermometer is black metal sphere, and research explored effects and comfort of using the thermometer for analysis of air temperature [6].

References of Modelling temperature of church of HVAC project