ORIGINAL Heat transfer in circular microchannels during volumetric heating with magnetic field Muhammad M. Rahman Æ Abdullatif A. Gari Æ Shantanu Shevade Received: 10 August 2006 / Accepted: 8 March 2007 / Published online: 12 April 2007 Ó Springer-Verlag 2007 Abstract Convective heat transfer within circular mi- crochannels in a rectangular solid substrate with heat generation due to imposed magnetic field was studied. A detailed parametric study was performed by varying Rey- nolds number, magnetic field strength, working fluid, and the diameter of the channel. It was found that the heat transfer coefficient decreases downstream along the chan- nel. Nusselt number increased with Reynolds number. The tube diameter, properties of the working fluid, and mag- netic field strength affected the temperature distribution and heat transfer rate at the solid-fluid interface. List of symbols d channel diameter, m D dimensionless channel diameter, d/H g o heat generation rate, W/m 3 G magnetic field strength, T h heat transfer coefficient, W/m 2 -K H height of the substrate, m k thermal conductivity, W/m-K L channel length, m nx number of intervals in x-direction ny number of intervals in y-direction nr number of intervals in r-direction within the tube nz number of intervals in z-direction p pressure, Pa r distance in radial direction, m Re Reynolds number, Vd/m S volume of the solid substrate, m 3 T temperature, °C V Average velocity of fluid in the channel, m/s W half of the tube spacing, m x distance along x-direction, m y distance along y-direction, m z distance along z-direction, m Z dimensionless distance along axial direction, z/L Greek symbols a thermal diffusivity, m 2 /s q density, kg/m 3 m kinematic viscosity, m 2 /s u angular coordinate, radian h dimensionless temperature, (T–T in )/[(g o S)/(k s L)] Subscripts f fluid in inlet max maximum r radial s solid z axial u angular 1 Introduction Convective heat transfer in microchannels is critical in the design and process control of various MEMS: Micro- Electric-Mechanical-Systems and biomedical lab-on-a-chip devices. Studies in the literature showed that high rate of heat transfer in microchannels results in better M. M. Rahman (&)  A. A. Gari  S. Shevade University of South Florida, Tampa, FL 33620, USA e-mail: rahman@eng.usf.edu 123 Heat Mass Transfer (2008) 44:463–472 DOI 10.1007/s00231-007-0257-4