In the present study, the forced air convection heat transfer for unconfined and confined heat sinks by considering flow bypass effect is studied on a semi-empirical basis. The flow bypass effect for unconfined heat sinks is firstly investigated. For unconfined heat sinks with specified fin spacing and fin height, the results reveal that the value of Ui/(ε·Us), which represents the flow bypass capability, increases from a very small Reynolds number up to a certain Reynolds number, say Rei = 60–200; and then gradually decrease with further increasing Reynolds number. At a specified Reynolds number, the Ui/(ε·Us) will generally increase when the fin spacing decreases or the fin height increases. For heat sinks partially confined in a channel, a novel concept to estimate an imaginative flow domain, in which the flow is influenced due to the existence of heat sink in the channel, is postulated in the study. Accordingly, an effective method for predicting the flow velocity between fins, flow rate through the heat sink and the fin heat transfer coefficient in both unconfined flow and confined flow is presented. Finally, in order to explore the optimal number of fins, a performance parameter defined as the ratio of thermal conductance to the required pumping power is introduced; an optimal procedure to determine the maximum performance parameter for a heat sink partially confined in a channel is postulated. The results manifest that the optimal number of fins increases with increasing inlet flow velocity.

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