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This paper investigates the impact of Darcy number and variable thermal conductivity on MHD free convective heat transfer in a microchannel. Approximate solution of the problem is obtained by using semi‐analytical method. Most of the fluid physical properties associated with flow are displayed, analyzed, and discussed. From the results, it is found that Darcy number reduces fluid velocity in case of asymmetric heating of the microchannel at the lower plate while fluid velocity is enhanced at the upper plate. It is also observed that variable thermal conductivity enhances fluid velocity in case of both asymmetric and symmetric heating of the microchannel bounding walls. It is further seen that there is point of intersection around the center of the microchannel when both variable thermal conductivity and Darcy number are increased. [ABSTRACT FROM AUTHOR]

This paper presents a hybrid conjugate gradient (CG) approach for solving nonlinear equations and signal reconstruction. The CG parameter of the approach is a convex combination of the Dai‐Yuan (DY)‐like and Hestenes‐Stiefel (HS)‐like parameters. Independent of any line search, the search direction is descent and bounded. Under some reasonable assumptions, the global convergence of the hybrid approach is proved. Numerical experiments on some benchmark test problems show that the proposed approach is efficient compared with some existing algorithms. Finally, the proposed approach is applied in signal reconstruction. [ABSTRACT FROM AUTHOR]