 # Directive Heat Transfer Lab Report

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Background
Goals:
This lab will investigate the correlation between increasing the coefficient of convective heat transfer and increasing the maximum current-carrying capacity of nichrome wire. The coefficient of convective heat transfer obtained from the previous lab will be employed. In addition, the experimental values will be compared to the computational and theoretical values.
Theory:
Whenever energy is transferred into a system, the system’s energy level increases. When the energy exceeds the functional capacity of the system, thermal failure may occur in various modes including but not limited to melting, fracturing or oxidation. Internal Joule heating is responsible for melting that occurs in electrically
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Q_conv=hA*(T_wire-T_∞ )
Where Qconv is the rate of heat transfer, Twire -T∞ denote the temperature difference between the wire and its surroundings, A, is surface area of the wire, and h is the coefficient of heat transfer (Armstrong p.5). The latter varies depending on the interaction between the surrounding air and the heated surface, and varies from 0.5 – 1000 W/m2K in air (forced and free).
Radiative Heat Transfer
The energy emitted, Eb, varies proportionately with the fourth power of temperature, T, of the radiator’s surface, as follows:
E_b = ∂T^4
Where: Ԑ is the emissivity of the material, which indicates how a material compares to a “blackbody”; ∂ = 5.67e-8W/m2K4= Stefan-Boltzmann constant. Thus, equation  can be rewritten as:
E_b = ԐT^4
The rate of radiative heat loss also varies proportionately with the surface area, A, of the radiating surface, and is expressed as follows:

Q_rad = Ԑ*Ϭ*A(T_wire-T_∞^4 )
Equation  below illustrates the final energy balance equation that describes the temperature of the wire a function of varied parameters. mc dT/dt=i^2 R- ∂ԐA_s (T_wire^4-T_∞^4 )-hA_s