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The biomagnetic fluid flow (blood flow) and heat transfer in channels with various physical configurations are simulated. A blood model consistent with biomagnetic fluid dynamics (BFD), which includes the principles of MHD and FHD, is considered. The fluid is assumed to be Newtonian, and both electrically conducting and nonconducting fluid flows are separately considered. The FEM and DRBEM applications are introduced for the steady biomagnetic fluid flow model where the fluid is considered as electrically non-conducting. The effects of the externally applied magnetic field on the flow and heat distribution are analyzed in details. FEM applications are presented for the solution of biomagnetic fluid flow through channels between plates with differing constriction profiles. Alterations in the behaviors of the flow and temperature of the biomagnetic fluid due to the stenoses in the channel and location and intensity of the magnetic source are analyzed.