Forced Convection

Nield, D. A.; Bejan, Adrian

doi:10.1007/978-3-319-49562-0_4

Cited by 10 publications

(20 citation statements)

References 763 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…( 2) -(4) now become ... (7) ... (8) ... (9) Solving Eq. ( 9) using the corresponding boundary conditions, we get ... (10) where…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…This convective instability problem is referred to as the Darcy-Bénard problem and it has been studied widely in the last few decades by considering various additional effects depending on the varied state of affairs. The gargantuan works available on this topic is aptly acknowledged in the books (Straughan [15], Nield and Bejan [10], Nield and Simmons [13]). One such extension work that has been carried out is the vertical throughflow effect on the Darcy-Bénard problem because of its application in in-situ coal gasification and also in controlling the convective instability by altering the vertical throughflow (Sutton [19], Homsy and Sherwood [3], Jones and Persichetti [5], Nield [11], Khalili and Shivakumara [6], Zhao et al [25], Shivakumara and Sureshkumar [14], Brevdo and Ruderman [2], Barletta et al [1]).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Yallappa¹

2022

jmmf

View full text Add to dashboard Cite

The vertical throughflow effect is investigated on the onset of porous convection by considering a cubic density-temperature relationship and using the Forchheimer-Darcy model. The stability eigenvalue problem is explained numerically using the Galerkin technique. Contrary to the linear density-temperature relationship, the direction of throughflow alters the onset of convection. The throughflow dependent Péclet number is found to stabilize the fluid motion against convection and the upflow is found to be either stabilizing or destabilizing than the downflow depending on the values of thermal condition parameters λ1 and λ2. A destabilizing effect on the onset is observed with increasing λ1 and λ2. The Darcy number Da and the Forchheimer drag co-efficient, cb instability characteristics have been investigated and depicted graphically.

show abstract

“…( 2) -(4) now become ... (7) ... (8) ... (9) Solving Eq. ( 9) using the corresponding boundary conditions, we get ... (10) where…”

Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Yallappa¹

2022

jmmf

View full text Add to dashboard Cite

show abstract

“…This result was supported experimentally by Li and Zou (2016), where they found 33.84% increment of thermal conductivity with 1.0% nanofluid. Important references on nanofluids and hybrid nanofluids are presented in the papers by Roşca and Pop (2017), Roşca et al (2019a, 2019b, 2021) and in the books by Das et al (2008), Nield and Bejan (2017), Shenoy et al (2016) and Merkin et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Dual solutions on three-dimensional nanofluid flow and heat transfer over a permeable non-linearly shrinking surface with second-order velocity slips

Roşca

Roşca²,

Pop³

2023

HFF

View full text Add to dashboard Cite

Purpose This paper aims to present the steady dual solutions on three-dimensional flow and heat transfer of nanofluid over a permeable non-linearly shrinking surface with two-order velocity slips conditions. Boundary layer assumption is considered in the mathematical modelling. Authors comprehend from previous studies and papers that the shrinking surfaces are extremely important in current engineering and environmental systems. Design/methodology/approach Using appropriate similarity variables, the full partial differential equations (PDF) are modified into a specific set of ordinary (similar) differential equations (ODE). The resulting non-linear ordinary differential system is then solved both analytically for some particular cases and numerically for the general case using the function bvp4c from MATLAB for characteristic values of the parameters which govern the equations. The transformed mathematical model is analysed using the bvp4c procedure. Based on the given assumptions, this study is able to produce multiple solutions of the problem. Findings The ordinary (similarity) differential equations have two branches solutions, upper and lower branch solutions, given some interval of shrinking and velocity slip parameters. The authors consider here a temporal stability analysis, as they want to establish which of the solutions are stable and which are not. In a distinct paragraph, the authors discuss in detail and present in a graphical manner the effects of shrinking and second-order slip flow model on the skin friction coefficient, surface wall heat flux and dimensionless velocity and temperature profiles. The analysis reveals that the second order slip has a big influence on the flow and heat transfer characteristics. Originality/value The present discoveries are unique and truly new for the research of the three-dimensional stretching/shrinking forced convection flow and heat transfer nanofluids. The nanofluid is a water-based nanofluid (H2O), which contains one type of nanoparticles, namely, copper (Cu). Of course, the analysis can be further extended considering other types of nanoparticles such as alumina (Al2O3). The authors assume that the thermal equilibrium is reached for the base fluid together with the suspended nanoparticles and that the nanoparticles are uniform in dimension and form.

show abstract

“…According to the comment in Nield and Bejan (2017), achieving a large magnetic field is thought impractical; hence, small magnetic field effects should be taken into account. This argument though was disputed by the earlier work in Bergman and Fearn (1994), where the chimney-type convection rolls could have arisen from strong magnetic field.…”

Section: Introductionmentioning

confidence: 99%

Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow

Türkyılmazoğlu

2023

HFF

View full text Add to dashboard Cite

Purpose The onset of Darcy–Benard convection in a fluid-saturated porous layer within channeled walls can be through either the convectively amplified perturbations or absolutely unstable modes. The convective type route to formation of cellular forms has received much more interest in the literature than the absolute mode. This paper aims to explore the absolute instability mechanism on triggering the Benard convection in the presence of a uniform magnetic field acting perpendicular to the channel walls. Design/methodology/approach Pursuing a completely theoretical linear stability approach, the locus of wavenumbers and critical Rayleigh numbers with respect to varying Peclet numbers leading to zero complex group velocity, and hence the absolute instability onset, is formulated in closed form. The formulae also incorporate the influence of fluid movement through the porous layer. Findings Wanenumbers are found to be increasing in magnitude under the effect of the magnetic field. Although the magnetic field expectedly behaves in favor of stabilizing the convection through both convective and absolute instabilities by pushing the threshold value of Rayleigh number to higher values, a peculiarity exists in such a manner that the stabilizing effect of magnetic field can no longer compete against the absolute instability mechanism within the magnetized field after some critical location possessing negative part of the wavenumber. Originality/value The significant outcome is attributed to the exchange of instabilities as far as the absolute instability mechanism is concerned. Magnetic field is always stabilizing and no such trend is observed regarding the convective type instability.

show abstract

Forced Convection

Cited by 10 publications

References 763 publications

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Outlook of Density Maximum on the Onset of Forchheimer-Bénard Convection with throughflow

Dual solutions on three-dimensional nanofluid flow and heat transfer over a permeable non-linearly shrinking surface with second-order velocity slips

Uniform magnetic field impact on absolute versus convective onset of Darcy–Benard convection with horizontal throughflow

Contact Info

Product

Resources

About