Recent development of microfluidic applications in various areas like cooling of silicon chips, VLSI, aircraft avionics, X-Ray and laser equipments has led to an increased study of coupled fluid flow and heat transfer in microchannels. A major issue in the mathematical modeling of these phenomena is the applicability of the no-slip boundary condition at solid-fluid interfaces. Most of such micro-scale investigations consider a slip velocity at solid boundaries, which has been observed in a number of experiemntal studies [1], [2]. In cases involving the heating of substrate and/or transport fluid, definite formation of nanobubbles from the fluid has been established [3]. These bubbles migrate to the channel walls and deposit on them in the form of random clusters. As a result, due to the minimized shear resistance offered by the surfaces of such bubbles to the fluid, variation in slip length is observed along the channel walls. Hence, in order that theoretical studies lead to physically acceptable results required for the fabrication of microfluidic devices, such variation of slip length encountered by a fluid in a microchannel must be included in these analysis.

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