Numerical and Experimental Study of Thermal Response of an Electrified Nickel Wire

An electrified nickel wire can produce heat. The heat is transferred to the environment around the wire radiation. However, the temperature produced by the wire will differ depending on the number of voltages supplied by the power source. Here, we do an experiment to measure the temperature of stand-up wire at each voltage of 4.5 V, 6.0 V, 7.5 V, 9.0 V, and 12 V. As a comparison, numerical measurements are done by JavaScript program. We show that the highest temperature of the wire approaches 314 K at 12 V. To equalize the temperature in both methods, the numerical scale factor of time and current in numerical measurements are changed according to the voltage. As a result, temperatures produced in both methods have minimal gap difference with error percentage below 0.5%. In conclusion, the experiment results were used to determine the scaling parameters to approach the ideal thermal response curve in actual values.


Introduction
Heat is a physical phenomenon that commonly occurs every day. Heat is also a form of energy because it can move from one medium to another. Also, the heat effect is equivalent to some works of a system [1]. The simple method of heat transfer is a medium that has higher temperature transfers heat to a medium that has lower temperature [2,3]. One method of heat transfer discussed in this study is radiation.
Radiation does not require a medium to receive heat. It caused by scattering of electromagnetic waves that depend on size, shape and medium properties [4]. The amount of heat produced by a medium depends on the thermal emissivity of the medium. Thermal emissivity is the ability of a medium to deliver heat by radiation. Thermal emissivity values of some materials have been obtained from previous experiments so that they become a general reference. One of the experiments is the determination of thermal emissivity of coated copper and aluminum placed on liquid-nitrogen insulated dewar, a container that has same working principles as vacuum flask [5]. We should identify all thermal emissivity values, especially for metals, because they are essential for material science concept [6]. However, the accuracy of thermal emissivity depends on radiation heat fluxes from the heat source that works as a temperature distributor [7].
A simple experiment for proving the effect of thermal emissivity is by hotwire. A hotwire which is connected to a voltage source (i.e. variable adaptor) can discharge electric current. Yu et al. in Semyonov et al. used hotwire method to measure heat flux between a metallic filament (such as nickel) and a rarefied gas [8]. Hotwire also used in anemometer that based on the measurement of heat transfer [9]. In this research, we use nickel wire as hotwire to know the radiation effect on its temperature at a time. A voltage source which is connected to nickel wire flows electric current, then it converts to heat on this wire. Then, we measure nickel wire temperatures and analyze the correlation between the amount of voltages and temperatures.
However, obtaining the ideal curve of the temperature gradient is difficult due to sensitivity of measurement devices. So, we do numerical simulation as a reference to nickel wire experiment. In this simulation, we use time scale in order to minimize the gap between experimental and simulation data. Time scale is a form of time which is scaled in simulation, so the results fit with observation time of the experiment. Also, a dynamic comparison of different components is part of time scale characteristic [10]. A reference of an experiment involving time scale is detection of evolutionary changes in complex system configuration by generating intervals accordingly [11]. Then, ranges in complex system configuration adjust to the relation between time and space dependencies [12]. Regardless of that, heat transfer phenomena are included in complex system because they have time scale factor which plays very important role in small scale devices [13,14]. We can also add current scale factor, besides time scale factor, to support heat transfer in our nickel wire simulation. Then, we determine both time scale and current scale values towards experimental temperatures.
This study is our original research about comparison of numerical and experimental methods to determine the exact temperature of electrified nickel wire. So far, we cannot discover the previously similar simple research that states the precise temperature of electrified nickel wire at a certain voltage. When its temperature can change because environmental condition, numerical simulation becomes a comparison whether the temperature is accurate. We hope that our research can be developed to other electrified materials, i.e. metals for device manufacturing.

Theories
The current wire which is flowed by electric current can deliver heat at a specific temperature. Radially delivered heat will go to the environment. The heat emitted through radiation is examined in sections 2.1 to 2.5 below.

Dissipation Power
Heat is one type of energy. Thus, the energy quantity can be calculated per unit time. The amount of energy per unit of time is power. The electric wire current can generate power, which is called dissipative power. The dissipative power is lost due to an electric current that flows through electrical resistance on the wire. Dissipative power that occurs at the voltage source and current wire as electrical resistance are as follows. (1)

Heat Source
The heat source of the current wire comes from an electric voltage source. The heat spread is influenced by the mass of the wire m, the specific heat of the wire and the temperature difference between the two ends of the wire Δ . The heat generated from the wire is equal to and is formulated in the following Equation (2).
The derivation of heat energy regarding time can be defined as power . Therefore, the left side of Equation (3) is changed to wire power in Equation (4) below.

Stefan-Boltzmann Law
The radiation process that occurs in the universe is stated in Stefan-Boltzmann's Law. In everyday case, this process happens when a substance or material emits temperature to the environment temperature . This legal formula can be expressed by the radiation power of a material in the following equation (5).
Surface area is found in Equation (5) because radiation occurs per certain area unit. Another factor that affects the heat amount is Stefan-Boltzmann constant σ of 5.67 × 10 -8 W/m 2 ·K 4 and the emissivity of material .

Calculation of Wire Temperature
To calculate wire temperature, a wire detail variable is needed such as wire diameter and the wire sheath area . The wire diameter is formulated in the equation and the wire sheath area is formulated in Equation (7).
Index means lateral (along the long direction ) and index means the cross-sectional area of the wire with diameter . Substitution of Equation (7) in Equation (5) produces Equation (8) below.
Through Equation (8), the power entering the wire is

Energy Conservation
In general, the amount of heat energy transferred from a medium to another medium is equal. This case is included in energy conservation. One important aspect of energy conservation is heat storage from any heat transfer types (including radiation) [15]. When radiation occurs, the power found on the wire will be equal as the difference in the input power with the radiation power . This statement formulated in the following Equation (10).

Experiment
The first step in this research is identifying all properties of nickel wire. Those properties can affect the final experiment results, which are given in Table 1. The experimental setup is shown in Figure 1. The nickel wire with a length of 60 cm was enclosed by two layers of isolator, a tissue paper and a plastic tube. The enclosed wire was placed on a stand as illustrated in Figure 1a.
In order to retain the wire shape, a metal load was attached to the lower end of the wire. The electrical potential difference was given at both ends of the wire. A digital thermometer' sensor was put on nickel wire, as well as another sensor was put down around the experiment area. Both sensors are used to measure nickel wire temperatures and environment temperatures, respectively. This system was examined in five values of voltage 4.5 V, 6.0 V, 7.5 V, 9.0 V and 12 V. The temperature data were extracted at every minute for 35 minutes.

Simulation
We also do research by simulation to obtain numerical temperatures of nickel wire. The simulation is useful as a comparison on experimental temperatures of nickel wire. The simulation is made by JavaScript program shown by HTML program in Google Chrome browser as shown in Figure 2. This program involves forward finite difference method to solve differential equation, i.e. Equation (11) numerically. In order to minimize the difference between experimental and numerical temperatures, we must change SCALE1 and SCALE 2 variable with the appropriate value. SCALE1 and SCALE2 represent time scale and current scale respectively.        Figures 3 -7, we can analyze when the voltage is greater, then the temperature of nickel wire will increase. The highest temperature rising is at the largest voltage, which is 12 V with a maximum temperature reaching 314 K in both methods. The reason is the greater the voltage set on the variable adapter (12 V), the more heat energy is generated. Heat energy per unit time or power is also directly proportional to the voltage stated in Equation (4). Power connected to electric current is also called dissipation. This power causes the actual voltage (voltage on the variable adapter) to fall because it converts almost half of the voltage to heat. To minimalize the difference between experimental temperatures and numerical temperatures, we set SCALE1 (time scale) and SCALE2 (current scale) factors. The purpose of setting both factors is minimizing the gap difference between and curve. Thus, all error percentages between experimental temperatures and numerical temperatures are below 0.5%. In case to keep this error value, experiment and simulation results in Figure 6 is slightly away between zero to 1,000 seconds. Then, they return to approach each other after 1,000 seconds. From Figure 8 below, the higher voltage requires a higher value of SCALE 2. In contrary, the value of SCALE1 decreases with increasing voltage. As a reference to both experimental and numerical methods, all equations in Section 2 are not used. For example, Equation (11) which is the formula towards nickel wire, is not used in experimental method because changes during experiment. Otherwise, Equation (11) is applied for numerical method because some formulas in Section 2 are used in JavaScript simulation. As a consequence, SCALE1 and SCALE2 factors are enough for proving the accuracy of experimental temperatures at certain voltages and times.

Conclusion
Time scale and current scale factors in the nickel wire simulation can prove the accuracy for experimental method. Both factors can scale accurately on nickel wire temperatures in this simulation. They also minimize the gap difference between experimental and numerical temperatures with below 0.5% error percentage. Through the statements above, we can say that our nickel wire experiment is accurate.

Acknowledgment
The authors would like to thank Physics Department -Bandung Institute of Technology for providing Students Activity Grants (Bantuan Kegiatan Mahasiswa) 2019.