“…It is found that the effect of increase in the value of internal heat source, magnetic Rayleigh number and nonlinearity of the magnetization parameter is to hasten, while increase in the value of Biot number, the ratio of viscosities and reciprocal of Darcy number is to delay the onset of thermo-magnetic convection in a ferrofluid saturated porous layer. Ziabakhsh et al [47] studied the analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation using homotopy analysis method (HAM). On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium was studied by Bararnia et al [48].…”
“…It is found that the effect of increase in the value of internal heat source, magnetic Rayleigh number and nonlinearity of the magnetization parameter is to hasten, while increase in the value of Biot number, the ratio of viscosities and reciprocal of Darcy number is to delay the onset of thermo-magnetic convection in a ferrofluid saturated porous layer. Ziabakhsh et al [47] studied the analytical solution of non-Newtonian micropolar fluid flow with uniform suction/blowing and heat generation using homotopy analysis method (HAM). On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium was studied by Bararnia et al [48].…”
“…The governing partial differential equation are first transformed into a system of ordinary differential equations before being solved numerically by a shooting method. The numerical results obtained are then compared with those reported by Wang [35], Ishak et al [36] and Ziabakhsh et al [44].…”
“…23,25,26 In this paper, neither constants are used, instead m = 1/2 is employed to meet the requirements of a dilute MF, which means the vanishing of the anti-symmetrical part of the stress tensor. [24][25][26] We introduce the non-dimensional similarity variables for a transformation of the original physical governing equation systems with the boundary conditions as follows:…”
Section: Basic Governing Equationsmentioning
confidence: 99%
“…[13][14][15][16] Recently, more investigations into the physical and engineering problems involving MFs have begun to emerge. The main research topics concern stagnation point flow; [17][18][19] heat transfer by free/mixed convection (with inclined enclosure) [20][21][22] and forced convection; 23,24 the stretching/shrinking sheet problems; [25][26][27] incorporating the boundary conditions such as suction/injection, velocity slip, heat radiation and generation, magneto hydrodynamics (MHDs); [26][27][28][29] and even a wavy differentially heated cavity. 30 Also, the flow and heat transfer of a MF through a horizontal/vertical channel 31,32 and applications in biological science 33 have been performed.…”
The rheological and heat-conduction constitutive models of micropolar fluids (MFs), which are important non-Newtonian fluids, have been, until now, characterized by simple linear expressions, and as a consequence, the non-Newtonian performance of such fluids could not be effectively captured. Here, we establish the novel nonlinear constitutive models of a micropolar fluid and apply them to boundary layer flow and heat transfer problems. The nonlinear power law function of angular velocity is represented in the new models by employing generalized "n-diffusion theory," which has successfully described the characteristics of non-Newtonian fluids, such as shear-thinning and shear-thickening fluids. These novel models may offer a new approach to the theoretical understanding of shear-thinning behavior and anomalous heat transfer caused by the collective micro-rotation effects in a MF with shear flow according to recent experiments. The nonlinear similarity equations with a power law form are derived and the approximate analytical solutions are obtained by the homotopy analysis method, which is in good agreement with the numerical solutions. The results indicate that non-Newtonian behaviors involving a MF depend substantially on the power exponent n and the modified material parameter K 0 introduced by us. Furthermore, the relations of the engineering interest parameters, including local boundary layer thickness, local skin friction, and Nusselt number are found to be fitted by a quadratic polynomial to n with high precision, which enables the extraction of the rapid predictions from a complex nonlinear boundary-layer transport system. Published by AIP Publishing.
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