Effects of magnetic field are encountered in some engineering applications such as in geothermal energy extraction, nuclear reactor coolers, and metal casting. In convective heat transfer applications, an external magnetic field may be used to control the fluid flow and heat transfer characteristics. In many cavity flow applications with convection, magnetic field dampens the fluid motion and reduces the convective heat transfer rate [
1,
2]. In jet flow configurations, magnetic field effects reduce the unsteady effects. A potential application of magnetic field is to enhance the heat transfer for the configurations with separated flows such as encountered in a backward-facing step and branching channel. The size of the re-circulation zones can be altered with an externally imposed magnetic field in a convective heat transfer with separated flow. Magnetic field effects in convection can be altered by adding nano-sized particles to the base fluid, which changes both the thermal and electrical conductivity of the fluid [
3,
4]. The inclusion of a very small amount of nanoparticles to the base fluid may result in significant enhancement of heat transfer, and various factors affect the amount of enhancement, such as size, shape and type of the particles. Nanofluid technology has been successfully implemented in various thermal engineering application [
5,
6]. Mehryan et al. [
7] examined the entropy generation study of Fe
O
–water nanofluid in an enclosure under the effect of variable magnetic field. A spatially sinusoidal varying magnetic field in y-direction was imposed and differences were noted when compared to a case with uniform magnetic field. Sheikholeslami and Ganji [
8] analyzed ferrofluid flow in a semi annulus with an external magnetic field by using control volume based finite element method (CVFEM) considering both ferrodynamics and magnetohydrodynamics. Magnetic number was found to influence the heat transfer differently depending on the Rayleigh number while both increasing nanoparticle volume fraction and decreasing Hartmann number were found to enhance the heat transfer rate. In the numerical study by Sheikholeslami et al. [
9], forced convection of magnetic nanofluid in a lid-driven semi annulus was examined with CVFEM. The average Nusselt number was observed to increase with nanoparticle volume fraction while the heat transfer enhancement was found to decrease with higher values of Reynolds number and lower values of Hartmann number. Selimefendigil and Oztop [
10] performed a numerical Magneto-hydrodynamic nanofluid convection of a vented cavity with elastic step-wise corrugation of the walls by using finite element method. The presence of the magnetic field was found to affect the distribution of multiple recirculation zones within the vented cavity filled with nanofluid. In a recent numerical study, efficiency of a direct absorption solar collector was examined with nanofluid and magnetic field effects. In the case of magnetic nanofluid, efficiencies up to 30% were obtained.
Flow separation is important in many engineering applications, e.g. in aerodynamics, power generation systems, thermal energy storage, and many others [
11,
12]. Fluid flow geometries are prone to such fluid phenomena as branching channels and backward or forward facing steps [
13,
14]. Fluid flow and heat transfer characteristics in branching channel are important in many applications ranging from biomedical to pharmaceutical industry. Matos and Oliveira [
15] performed numerical simulation for fluid flow of non-Newtonian inelastic fluid in a bifurcating channel. Fluid flow characteristic were found to be influenced by the variation of Reynolds number, mass flow rate ratio and power-law index values. Senn and Poulikakos [
16] performed numerical study for analyzing the effects of secondary flow on the thermal mixing in a tree-like micro-channel net. Selimefendigil and Oztop [
17] numerically analyzed convection of nanofluid flow for a backward-facing step geometry with a uniform magnetic field, which was imposed at various inclination angles. It was observed that, for vertically and inclined application of magnetic field, re-circulation zone behind the step was reduced and heat transfer augmented for higher values of Hartmann number. In the study by Abbassi and Nassrallah [
18], laminar flow of electrically conducting fluid in a backward-facing step geometry was analyzed. Various values of Stuart number and Prandtl number were considered for Reynolds number of 380. For higher values of Prandtl number, magnetic field was found to enhance the heat transfer, whereas, except in the regions of recirculation zone, fluid motion was dampened by the magnetic field. An experimental study of pulsating fluid flow in laminar conditions through a 90-degree bifurcation was performed by Khodadadi et al. [
19]. They observed that the Reynolds number, dividing mass flow rate of the branching channels and Stokes number have influence on the formation and size of the re-circulation regions. A theoretical study for the forced convective heat transfer in a branch network was conducted by Luo et al. [
20]. The heat transfer rate was found to increase with trunk diameter and deteriorate with the length of the branched structure. In a recent study, Selimefendigil et al. [
21] performed numerical study of branching channel of CuO–water nanofluid under the effects of uniform magnetic field. The influences of inclination angle of lower branching channel and Hartmann number in uniform magnetic field on the convective heat transfer features were examined. The average Nusselt number was found to be higher for higher values of Hartmann umber, while the addition of nanoparticle was found to be efficient for higher values of Hartmann number. Selimefendigil and Oztop [
22] made a numerical study on the convective heat transfer features of a branching channel filled with carbon nanotube (CNT)-water nanofluid under the effects of rotating surface at the junction. Significant enhancement was observed with the inclusion of CNT nanoparticles to the base fluid, while the convective heat transfer features were found o be strongly influenced by the rotation of the surface at the junction.