Numerical study of natural convection heat transfer of 𝐀𝐥𝟐𝐎𝟑/𝐖𝐚𝐭𝐞𝐫 nanofluid in a T -shaped microchannel

Finite-volume procedure is presented for solving the natural convection of the laminar 𝐴𝑙2𝑂3/𝑊𝑎𝑡𝑒𝑟 nanofluid flow in a Γ shaped microchannel in this article. Modified Navier-Stokes equations for nanofluids are the basic equations for this problem. Slip flow region, including the effects of velocity slip and temperature jump at the wall, are the main characteristics of flow in the slip flow region. Steady state equations were solved by using time marching method. In provided FORTRAN code, the finite volume method and an explicit fourth-order Runge–Kutta integration algorithm were applied to find the steady state solutions. Also an artificial compressibility technique was used to couple the continuity to the momentum equations as it is simpler and converges faster. The Grashof numbers from 102 to 105 were considered. The results showed that Nusselt number increases with the Grashof number and the parameter R (the ratio of minimum diameter of nanoparticles and maximum one).. As the parameter R increases, the distortion of the isotherm lines increases to some extent.