Physical and Computational Aspects of Convective Heat Transfer

Cebeci, Tuncer; Bradshaw, P.

doi:10.1007/978-1-4612-3918-5

Cited by 689 publications

(371 citation statements)

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“…It has been implemented in an extensive range of nanofluid and magnetohydrodynamic transport problems and readers are referred to [48]- [52]. Further details of this method are available for convection flows in the monograph of Cebeci and Bradshaw ( [53]). This method has four fundamental steps.…”

Section: Numerical Solution Of Nonlinear Boundary Value Problemmentioning

confidence: 99%

“…Here n k is the  x spacing and Finally, the linearized algebraic equations are solved using a block tri-diagonal elimination scheme implemented in MATLAB software with the suitable initial solution. This method is unconditionally stable (Cebeci and Bradshaw [53]), has a second order accuracy and is relatively easy to program, thus making it highly attractive for engineering analysis. For this iterative scheme to solve the system of equations, a convergence criterion is required.…”

Section: Fig 2 Net Rectangle For Finite Difference Approximationmentioning

confidence: 99%

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Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

Thumma¹,

Bég

Kadir

2017

Journal of Molecular Liquids

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This paper numerically investigates radiative magnetohydrodynamic mixed convection boundary layer flow of nanofluids over a nonlinear inclined stretching/shrinking sheet in the presence of heat source/sink and viscous dissipation. The Rosseland approximation is adopted for thermal radiation effects and the Maxwell-Garnetts and Brinkman models are used for the effective thermal conductivity and dynamic viscosity of the nanofluids respectively. The governing coupled nonlinear momentum and thermal boundary layer equations are rendered into a system of ordinary differential equations via local similarity transformations with appropriate boundary conditions. The non-dimensional, nonlinear, well-posed boundary value problem is then solved with the Keller box implicit finite difference scheme. The emerging thermo-physical dimensionless parameters governing the flow are the magnetic field parameter, volume fraction parameter, power-law stretching parameter, Richardson number, suction/injection parameter, Eckert number and heat source/sink parameter. A detailed study of the influence of these parameters on velocity and temperature distributions is conducted. Additionally the evolution of skin friction coefficient and Nusselt number values with selected parameters is presented. Verification of numerical solutions is achieved via benchmarking with some limiting cases documented in previously reported results, and generally very good correlation is demonstrated. This investigation is relevant to fabrication of magnetic nanomaterials and high temperature treatment of magnetic nano-polymers.

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Section: Numerical Solution Of Nonlinear Boundary Value Problemmentioning

confidence: 99%

Section: Fig 2 Net Rectangle For Finite Difference Approximationmentioning

confidence: 99%

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

Thumma¹,

Bég

Kadir

2017

Journal of Molecular Liquids

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“…Equations in (13) subject to the boundary conditions (14) are solved numerically using the Keller-box method as described in the books by Na [19] and Cebeci and Bradshaw [20]. The solution is obtained in the following four steps.…”

Section: Solution Proceduresmentioning

confidence: 99%

“…The governing boundary layer equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into non-similar equations before they are solved numerically by the Kellerbox method, as described in the books by Na [19] and Cebeci and Bradshaw [20]. To the best of our knowledge, this present problem (for the case of Newtonian heating) has not been considered before, so that the reported results are new.…”

Section: Introductionmentioning

confidence: 99%

Mixed Convection Boundary Layer Flow from a Solid Sphere with Newtonian Heating in a Micropolar Fluid

Salleh

Pop

2010

SRX Physics

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The steady mixed convection boundary layer flow from a solid sphere in a micropolar fluid, generated by Newtonian heating in which the heat transfer from the surface is proportional to the local surface temperature, is considered. The governing boundary layer equations are first transformed into a system of nondimensional equations via the non-dimensional variables, and then into nonsimilar equations before they are solved numerically using an implicit finite-difference scheme known as the Keller-box method. Numerical solutions are obtained for the skin friction coefficient, wall temperature and heat transfer coefficient, as well as the velocity and temperature profiles with several parameters considered, namely the mixed convection parameter, the material or micropolar parameter, and the Prandtl number.

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“…for y (13) where A{x) represents the displacement thickness with sign changed and also the velocity slip at the base of the main-deck, corresponding to the inviscid perturbation of the upstream Blasius solution by the induced pressure gradient. In addition, a boundary condition of the temperature is required to complete this matching with the main-deck and is given by:…”

Section: Lower-deck Equationsmentioning

confidence: 99%

Boundary layer separation by a step in surface temperature

Méndez

Treviño

Liñán

1992

International Journal of Heat and Mass Transfer

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Abstract-The free-interaction influence of thermal expansion process in the boundary layer gas flow is analysed in this paper, using the formalism of the Triple-Deck theory. The physical model considered herein is the forced convection of a gas flowing over a flat plate subject to a step change in the surface temperature, taking place at a certain distance from the leading edge. There is a fundamental parameter 7" w , defined as the ratio of the wall temperature to the free stream temperature. For values of T w close to one, the governing equations can be linearized and solved with the aid of the Fourier transform method. However, for values of this parameter not close to one, a numerical treatment is required to solve the governing equations. Using finite-difference methods, the numerical results for the pressure, skin friction, thickness displacement and Nusselt number are presented for different values of T". Finally, for a critical value of this temperature ratio, the boundary layer separates.

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Physical and Computational Aspects of Convective Heat Transfer

Cited by 689 publications

References 0 publications

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

Numerical study of heat source/sink effects on dissipative magnetic nanofluid flow from a non-linear inclined stretching/shrinking sheet

Mixed Convection Boundary Layer Flow from a Solid Sphere with Newtonian Heating in a Micropolar Fluid

Boundary layer separation by a step in surface temperature

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