MHD Pulsatile Blood Flow Through an Inclined Stenosed Artery with Body Acceleration and Slip Effects
Emeka Amos,
Ekakitie Omamoke,
Chinedu Nwaigwe
Issue:
Volume 8, Issue 1, February 2022
Pages:
1-13
Received:
11 January 2022
Accepted:
26 January 2022
Published:
9 February 2022
Abstract: In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angle with the fluid considered to be electrically conducting non-Newtonian elastic-viscous fluid. The momentum equation was transformed from dimensional form to dimensionless form with the Frobenius power series method used to solve the axially symmetric differential momentum equation with suitable boundary conditions. For clarity of the applicability of the study, results was shown graphically with behavior of the blood flow through the artery with stenosis shown for the velocity in the axial direction, blood acceleration, wall shear stress and volumetric flow rate. Results showed that, an increase in the body acceleration Go and pulsatile pressure Pl causes an increase in the blood flow, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the magnetic field M causes a decrease in the blood flow velocity, blood acceleration, shear stress at the artery walls and volumetric flow rate. The increase in the artery inclination ϕ results to an increase in the blood flow velocity, wall shear stress and the volumetric flow rate but an irregular behavior in the blood acceleration while the increase in slip velocity h at the wall decreases the velocity and blood acceleration, while the shear stress at the wall increases and the volumetric flow rate decreases.
Abstract: In this work, the combined effect of slip velocity, pulsatility of the blood flow and body acceleration effect on Newtonian unsteady blood flow past an artery with stenosis and permeable wall is theoretically studied with results discussed. The magnetic field is applied to the stenosed artery with permeable walls which is inclined at a varying angl...
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An Analytic Proof of Some Part of Keith-Xiong’s Theorem
Issue:
Volume 8, Issue 1, February 2022
Pages:
14-29
Received:
8 March 2021
Accepted:
4 March 2022
Published:
15 March 2022
Abstract: In the theory of partitions, Euler’s partition theorem involving odd parts and different parts is one of the famous theorems. It states that the number of partitions of an integer n into odd parts is equal to the number of partitions of n into different parts. By intepretting odd parts as parts congruent to 1 modulo 2, the second author and Keith provided a completely generalization about Euler’s partition theorem involving odd parts and different parts for all moduli and provide new companions to Rogers-Ramanujan-Andrews-Gordon identities related to this theorem. They gave a combinatorial proof of the theorem by establishing bijection. In this note, we will offer an anclytic view point of this beautiful theorem. We use q-series and generating function theories to provide an analytic style proof for some cases of Keith-Xiong’s theorem. By defining basic units and special units, the basic units in the partitions are divided into two categories, and then the number between the basic units in the special units is classified, and all the cases when m = 3 and alternative sum type (Σ,2) are given, our method is verifying the generating functions of both sides satisfying the same recurrences.
Abstract: In the theory of partitions, Euler’s partition theorem involving odd parts and different parts is one of the famous theorems. It states that the number of partitions of an integer n into odd parts is equal to the number of partitions of n into different parts. By intepretting odd parts as parts congruent to 1 modulo 2, the second author and Keith p...
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