A criterion for determining the relative importance of the fluctuating component of a periodic heat source

• We derive a novel criterion and validate it numerically.
• It estimates the impact of fluctuating heat sources on temperature response.
• It is useful to analysts who model transient heat sources.
• It is useful to experimentalists who measure transient temperature responses.
• A case study makes clear the implementation and advantage of using the criterion.

Devices such as rotating electrical machines, transformers, and microprocessors experience thermal loading during operation. This is caused by device losses which manifest themselves as heat sources. Whether operated continuously or on a duty cycle these heat sources are often periodic in nature, exhibiting both mean and fluctuating components. This paper proposes a criterion which can be used to estimate the relative importance of the fluctuating component of a periodic heat source on the temperature response of a device, or a component within a device. It may be used by the heat transfer analyst to determine whether a periodic heat source can be modeled accurately by its mean value or whether it must be modeled as a function of time. During thermometric tests it enables the experimentalist to determine whether the measured temperature rise rate represents an instantaneous or a mean value of heat generation rate. The criterion is derived by considering a sinusoidal heat source acting on a thermal network element. A case study is presented where the criterion is used to estimate the relative importance of the fluctuating component of a range periodic heat sources present in a rotating electrical machine. Results are compared with numerical predictions and agreement is found to be fit for purpose.