Numerical analysis of channel flow with velocity-dependent suction and nonlinear heat source

Weli, Azubuike; Nwaigwe, Chinedu

doi:10.1080/09720502.2020.1748278

Cited by 6 publications

(9 citation statements)

References 29 publications

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“…5 shows an increase in pressure gradient leads to an increase in fluid velocity. Therefore, the result is physically obtainable; it is in agreement with those of [10,23]. 6 shows the variation of fluid temperature with cooling parameter.…”

Section: Resultssupporting

confidence: 89%

Analytical Solution of a Non-isothermal Flow in Cylindrical Geometry

Nwaigwe

Amadi²

2021

ARJOM

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This study proposes analytical solution to the problem of transport in a Newtonian fluid within a cylindrical domain. The flow is assumed to be dominated along the channel axis, and is taken to be axi-symmetric. No-slip boundary condition is considered for velocity while the temperature and concentration have Dirichlet boundary values. The resulting problem is transformed into a set of non-trivial variable coefficient differential equations in a cylindrical geometry. By adopting the series solution method of Frobenius, the closed-form analytical solutions are derived for the flow variables. We conduct an analysis of the derived model, and showed that, indeed, the flow variables are axi-symmetric. We also state and prove another theorem to show that the derived concentration model is positivity preserving – meaning that it yields positive concentration - provided the boundary value is non-negative. Finally, we present graphical results for the flow variables and discuss the effect of the relevant flow parameters. The results showed that (i) an increase in the cooling parameter, reduces the fluid velocity, (ii) the temperature decreases as the cooling parameter increases and (iii) an increase in the injection parameter, leads to increase in the concentration.

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Section: Resultssupporting

confidence: 89%

Analytical Solution of a Non-isothermal Flow in Cylindrical Geometry

Nwaigwe

Amadi²

2021

ARJOM

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“…An implicit-explicit finite difference scheme for the analysis of a channel flow problem was developed by Nwaigwe [20], which studied transportation phenomena with variable cross-diffusion and nonlinear radiation. The present work extends the work of Nwaigwe [20] by incorporating Forchheimer effects, wall velocity suction (nonlinear convection term), variable permeability, nonlinear pollutant injection, exponentially temperaturedependent heat source [32] and an exponentially moving wall velocity. These conditions are in addition to the existing flow and transport conditions, such as nonlinear radiation and the nonlinear Soret-Dufour effects, considered in the original work of Nwaigwe [20].…”

Section: Introductionmentioning

confidence: 70%

“…Nonlinear cross-diffusion effects, viscous dissipation and uniformly applied magnetic field are equally considered. An external heat generation is assumed to follow the Weli and Nwaigwe formulation [32]. At the initial time t = 0, the velocity, concentration and temperature are functions of position y.…”

Section: A R T I C L E I N P R E S Smentioning

confidence: 99%

“…Moreover, we use the short forms for the value of the transport properties at intermediate grid points Therefore, we extend the scheme from [20] by incorporating the discrete convective and source terms [32]. The convective (first derivative) term is discretized by using an upwind approach [9,10,17,28,29,32], while the diffusion (second derivative) is approached by freezing coefficients [20], see also [4,8,12,13,18,19,26]. The Forchheimer term is discretized by freezing the non-positive coefficient at the previous time level t n , while the velocity factor is evaluated at the new time level t n+1 .…”

Section: Formulation Of the Schemementioning

confidence: 99%

“…for the convective term a(w n i ) ∂w ∂y is consistent, stable and also convergent. However, it is a known and easily provable result in numerical analysis (see, e.g., [2,9,10,28,29]) that the upwind discretization of the first derivative is consistent, stable and has first order of convergence in space, see also the recent paper [32]. Furthermore, since the coefficient in the first derivative term is freezed (evaluated at time level t n ), it means that the scheme is also first order in time, see [32] for a proof of this.…”

Section: A R T I C L E I N P R E S Smentioning

confidence: 99%

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Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

Nwaigwe

Oahimire²,

Weli

2023

ACM

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This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.

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