Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium following a sudden change in surface heat flux

Rees, D. Andrew S.; Bassom, Andrew P.

doi:10.1016/j.ijheatmasstransfer.2015.10.021

Cited by 9 publications

(5 citation statements)

References 9 publications

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“…Figure 8 shows how the temperature field evolves with time. Once more a thin boundary layer develops at early times, and it may easily be shown that θ ∼ 2t 1/2 ierfc[(1 − r )/2 √ t]; see Rees and Bassom (2016). Therefore, we expect the outer surface temperature to rise initially as 2(t/π) 1/2 before curvature effects become significant.…”

Section: Case 2: Constant Heat Fluxmentioning

confidence: 94%

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Rees

Bassom

2018

Transp Porous Med

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We consider two unsteady free convection flows of a Bingham fluid when it saturates a porous medium contained within a vertical circular cylinder. The cylinder is initially at a uniform temperature, and such flows are then induced by suddenly applying either a new constant temperature or a nonzero heat flux to the exterior surface. As time progresses, heat conducts inwards and this may or may not overcome the yield threshold for flow. For the constant temperature case, flow begins immediately should the parameter, Rb, which is a nondimensional yield parameter, be sufficiently large. The ultimate fate, though, is full immobility as the cylinder eventually tends towards a new constant temperature. For the constant heat flux case, the fluid remains immobile but will begin to flow eventually should Rb be sufficiently large. The two cases have different critical values for Rb.

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Section: Case 2: Constant Heat Fluxmentioning

confidence: 94%

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Rees

Bassom

2018

Transp Porous Med

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“…Most of these are boundary layer flows; see Rees 11 for a discussion of these works. A series of four papers by Rees and Bassom [12][13][14][15] is devoted to different aspects of onedimensional flows and it covers similar ground to works by Yang and Yeh 16 , Kleppe and Marner 17 , Patel and Ingham 18 , Bayazitoglu et al 19 and Barletta and Magyari 20 . Rees 21 has also presented nonlinear computations for convection in a sidewall-heated cavity and found that the presence of a Bingham fluid means that there is a critical value of the Darcy-Rayleigh number above which convection arises.…”

Section: Introductionmentioning

confidence: 94%

Darcy–Bénard–Bingham convection

Rees

2020

Physics of Fluids

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The present paper is the first to consider Darcy-Bénard-Bingham convection. A Bingham fluid saturates a horizontal porous layer which is subjected to heating from below. It is shown that this simple extension to the classical Darcy-Bénard problem is linearly stable to small-amplitude disturbances but nevertheless admits strongly nonlinear convection. The Pascal model for a Bingham fluid occupying a porous medium is adopted, and this law is regularized in a frame-invariant manner to yield a set of two-dimensional governing equations which are then solved numerically using finite difference approximations. A weakly nonlinear theory of the regularized Pascal model is used to show that the onset of convection is via a fold bifurcation. Some parametric studies are performed to show that this nonlinear onset of convection arises at increasing values of the Darcy-Rayleigh number as the Rees-Bingham number increases, and that for a fixed Rees-Bingham number the wavenumber at which the rate of heat transfer is maximised increases with the Darcy-Rayleigh number.

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“…In this study, the fluid of interest is Bingham plastic fluid, a well‐known representation of yield stress fluids, proposed by Bingham 27,28 . Yield stress fluids are observed in a wide range of circumstances both in the environment and industry 6,29–33 . Bingham plastic fluid exhibits a linear stress‐strain relationship, unlike Casson and Herschel‐Bulkley fluids, once the yield stress is surpassed.…”

Section: Mathematical Representation Of Fluid Modelmentioning

confidence: 99%

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

Khan

Sultan

2020

Heat Trans

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This article presents flow, heat and mass transfer phenomena in Bingham plastic fluid. The flow channel is considered to be a rotating disk with a slip which is different in span and streamwise directions, and heat transfer is investigated using dissipation term of the fluid. Arrhenius activation energy and binary chemical reaction are the imperative features of the study of mass transfer. Bingham plastic fluid and anisotropic slip arethe key factors of the study due to their numerous applications in manufacturing industries. On the other hand, the radiative heat transfer phenomenon is considered which is widely used in nuclear and power generating systems. The partial differential equations that govern the flow, and heat and mass transfer are converted into ordinary differential equations by utilizing von Kármán's similarity transformation for rotating disk flows. The velocity, temperature, and concentration profiles and some important physical quantities are examined against important flow parameters. It is observed that the thermal radiation showed an increasing effect on temperature profile and the activation energy enhanced the mass transfer rate. The radial slip increased the volumetric flow rate and reduced the boundary layer thickness. The tangential slip reduced the volumetric flow rate and increased the boundary layer thickness. K E Y W O R D S activation energy, anisotropic slip, Bingham fluid, rotating disk, thermal radiation | INTRODUCTIONThe motivation for investigating the flows due to rotating disk drives from their occurrence in various real-world phenomena like aerospace engineering, centrifugal pumps, rotational air cleaners, gas turbine engineering, computer storage devices, turbomachinery, and chemical engineering. This area of research was initially explored by Kármán 1 in which he proposed a similarity transformation for flows over a rotating disk. Some of the recent research in this area focused on the flow of different non-Newtonian fluids under various flow conditions. [2][3][4][5][6][7][8] In 1889, Arrhenius 9 introduced the term activation energy; the minimum energy that a chemical system with potential reactants requires to produce a chemical reaction. The phenomenon of chemical reaction in the mass transfer has attracted a great deal of interest due to its numerous applications in geothermal engineering, oil reservoir, nuclear reactor cooling, and chemical engineering, and so on. All of these applications include the collective effect of binary chemically reactive species and Arrhenius activation energy. The idea of boundary layer fluid flow under the influence of activation energy and binary chemical reaction attracted the attention of many researchers in the last decade, whereas, this concept was disclosed by Bestman 10 in 1990. Some of the recent research studies on the topic are Ijaz, 2 Dhlamini et al, 11 Majeed et al, 12 and Kiran Kumar et al. 13 The radiative heat transfer phenomenon has gained massive attention due to numerous applications of radiative effect. It is mainly use...

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Unsteady thermal boundary layer flows of a Bingham fluid in a porous medium following a sudden change in surface heat flux

Cited by 9 publications

References 9 publications

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Unsteady Free Convection Boundary Layer Flows of a Bingham Fluid in Cylindrical Porous Cavities

Darcy–Bénard–Bingham convection

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

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