**2. Experimental Method**

The experimental set-up of the integrated system with serial and parallel circuits is shown in Figure 1. To control the experimental ambient conditions, the experimental set-up is housed inside the psychrometric calorimeter which is controlled using PID controller. The experimental set-up comprises of serial and parallel circuits with components namely, battery, HVAC heater core, heater, water pump, working fluid tank, radiator, temperature sensors, flow meters and valves. The specifications of various components of experimental set-up are presented in Table 1. Both the circuits are operated using three valves, named valve1, valve2 and valve3. For the integrated system with serial circuit, valve1 and valve3 are cutoff and only valve2 is operated. Whereas, for the integrated system with parallel circuit, valve2 is cutoff and valve1 and valve3 are operated. The valve1 supplies working fluid for the battery heating and valve3 supplies working fluid for HVAC heating in the integrated system with parallel circuit. The battery is not the actual battery but the mimic of GM Volt (2010) battery model whose specifications are: weight = 198 kg, specific heat = 143 J/kg K and battery capacity = 16 kWh. The total working fluid flow rate of 24 L/min is divided for battery heating and HVAC heating in the integrated system with parallel circuit using valve1 and valve3. For the integrated system with parallel circuit, the flow ratio term is defined which is the ratio of battery flow rate to HVAC flow rate. In the case of an integrated system with serial circuit, full working fluid flow rate of 24 L/min is either supplied for battery heating or HVAC heating using valve2. The working of the integrated system with serial and parallel circuits involves a supply of working fluid using water pumped to a heater, where it is heated to higher temperature. From the heater, the heated working fluid is divided between the battery and HVAC in the case of an integrated system with a parallel circuit, and totally supplied for either the battery or HVAC in the case of an integrated system with serial circuit. The collected heated working fluid in tank is transferred through the radiator where it is cooled and again transferred to the heater using a water pump. To analyze the heating performances of the battery and HVAC, two modes (serial and parallel) of operation are employed. In addition, the heater power is varied as 2 kW, 4 kW and 6 kW in both the modes, and the flow ratio is varied as 2/8, 3/7, 5/5, 7/3 and 8/2 in a parallel mode of operation, to investigate the behavior of battery and HVAC heating performances. Battery out temperature, battery temperature rise rate, battery heating capacity, HVAC heating capacity and total heating capacity are investigated under various operating conditions. The accuracy of various experimental devices and instruments is shown in Table 2. Additionally, Figure 1b shows the picture of an experimental set-up of the integrated system with serial and parallel circuits.

cuits.

*Symmetry* **2021**, *13*, x FOR PEER REVIEW 4 of 25

(**a**) Schematic diagram

(**b**) Picture

**Figure 1.** (**a**) Schematic diagram and (**b**) picture for experimental set-up of integrated system with serial and parallel cir-**Figure 1.** (**a**) Schematic diagram and (**b**) picture for experimental set-up of integrated system with serial and parallel circuits.



Core size: 147 × 206 × 28 mm

Radiator Applied vehicle: GM Volt

HVAC Applied vehicle: Kona

**Table 1.** *Cont*.


**Table 2.** Accuracy of various experimental devices and instruments.


The poor calibration, instrumental errors, positional errors of probes, environmental error etc., are responsible for the uncertainty in the experimental results [33]. Therefore, the uncertainty analysis is conducted on the experimental results of the integrated system with serial and parallel circuits, to ensure the accuracy and reliability of the experimental test results [34]. The errors in experimental data of temperature and flow rate measurements cause uncertainties in the heating performances of battery and HVAC of the integrated system with serial and parallel circuits. The uncertainties in the output parameter due to uncertainties in the input parameters are calculated using Equation (1) [35]. The uncertainties in various parameters for the experimental study on integrated system with serial and parallel circuits could be calculated using the concept of linear fraction approximation [36].

$$\mathcal{U}I\_F = \left[ \left( \frac{\partial F}{\partial X\_1} \mathcal{U}\_1 \right)^2 + \left( \frac{\partial F}{\partial X\_2} \mathcal{U}\_2 \right)^2 + \dots + \left( \frac{\partial F}{\partial X\_n} \mathcal{U}\_n \right)^2 \right]^{\frac{1}{2}} \tag{1}$$

Here, *X*1, *X*2, . . . *X<sup>n</sup>* are the input parameters, *U*1, *U*2, . . . *U<sup>n</sup>* are the uncertainties in the input parameters, *F* is the output parameter and *U<sup>F</sup>* is the uncertainty in the output parameter. Using Equation (1), the uncertainties in flow rate, battery out temperature and HVAC heating capacity are calculated as 1.50%, 0.75% and 1.68%, respectively.
