Ritz method for slip flow in super-elliptic ducts

This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

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“…where Bðw, wÞ and F are, respectively, bilinear and linear forms [21]. Hence, the BVP (23), ( 24), ( 26) is equivalent to the following system…”

Section: Ritz Methodsmentioning

confidence: 99%

Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

Chuchalerm

Wiwatanapataphee

Sawangtong

2020

Journal of Applied Mathematics

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“…However, due to the difficult Robbins boundary conditions, slip flow requires a new formulation. Recently, Wang [44] introduced the Ritz method for slip flow using variational methods. The purpose of the present paper is to extend the method of Wang [44], which deals with the flow problem only, to constant flux convective heat transfer.…”

Section: Ritz Methods For General Cross Sectionsmentioning

confidence: 99%

“…Recently, Wang [44] introduced the Ritz method for slip flow using variational methods. The purpose of the present paper is to extend the method of Wang [44], which deals with the flow problem only, to constant flux convective heat transfer. Briefly, Wang [44] proved the following Theorem 1.…”

Section: Ritz Methods For General Cross Sectionsmentioning

confidence: 99%

Slip Flow and Constant Flux Heat Transfer in Isosceles Triangular Ducts

Wang

2017

Journal of Thermophysics and Heat Transfer

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“…Wang [18] analysed the slip flow in super-elliptic ducts governed by the Poisson equation (1) with f = -1 subject to Navier's slip condition. The Ritz method was applied for the solution of the problem.…”

Section: Introductionmentioning

confidence: 99%

Oscillating pressure-driven slip flow and heat transfer through an elliptical microchannel

et al. 2019

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This paper studies the transient slip flow and heat transfer of a fluid driven by the oscillatory pressure gradient in a microchannel of elliptic cross section. The boundary value problem for the thermal-slip flow is formulated based on the assumption that the fluid flow is fully developed. The semi-analytical solutions of velocity and temperature fields are then determined by the Ritz method. These solutions include some existing known examples as special cases. The effects of the slip length and the ratio of minor to major axis of the elliptic cross section on the velocity and temperature distribution in the microchannel are investigated.

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Ritz method for slip flow in super-elliptic ducts

Cited by 5 publications

References 22 publications

Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

Pressure-Driven Thermal Slip Flow in the Elliptical Channel with Radial Oscillatory Wall

Slip Flow and Constant Flux Heat Transfer in Isosceles Triangular Ducts

Oscillating pressure-driven slip flow and heat transfer through an elliptical microchannel

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