There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)

This article reports on the International Nanofluid Property Benchmark Exercise, or INPBE, in which the thermal conductivity of identical samples of colloidally stable dispersions of nanoparticles or “nanofluids,” was measured by over 30 organizations worldwide, using a variety of experimental approaches, including the transient hot wire method, steady-state methods, and optical methods. The nanofluids tested in the exercise were comprised of aqueous and nonaqueous basefluids, metal and metal oxide particles, near-spherical and elongated particles, at low and high particle concentrations. The data analysis reveals that the data from most organizations lie within a relatively narrow band (±10% or less) about the sample average with only few outliers. The thermal conductivity of the nanofluids was found to increase with particle concentration and aspect ratio, as expected from classical theory. There are (small) systematic differences in the absolute values of the nanofluid thermal conductivity among the various experimental approaches; however, such differences tend to disappear when the data are normalized to the measured thermal conductivity of the basefluid. The effective medium theory developed for dispersed particles by Maxwell in 1881 and recently generalized by Nan et al. [J. Appl. Phys. 81, 6692 (1997)], was found to be in good agreement with the experimental data, suggesting that no anomalous enhancement of thermal conductivity was achieved in the nanofluids tested in this exercise.

A Benchmark Study on the Thermal Conductivity of Nanofluids

Nanofluid flow and heat transfer in porous media: A review of the latest developments

Hydrodynamic and hydromagnetic stability

The effect of control on the onset of Marangoni-B\'{e}nard convection in a horizontal layer of fluid with internal heat generation heated from below and cooled from above is investigated. The resulting eigenvalue problem is solved exactly. The effects of control are studied by examining the critical Marangoni numbers and wave numbers. It is found that the onset of Marangoni-B\'{e}nard convection with internal heat generation can be delayed through the use of control.

			Keywords: Marangoni-B\'{e}nard convection; control; internal heat generation.

https://www.matematika.utm.my/index.php/matematika/article/download/219/212

Effects of Control on the Onset of Marangoni-Benard Convection with Uniform Internal Heat Generation

The stagnation-point flow in a Darcy porous medium toward a shrinking sheet with the presence of thermal radiation, suction, velocity, and thermal slips is numerically studied. The partial differentiation equations have been transformed into ordinary differentiation equations by a similarity transformation. Numerical results show the existence of dual solutions in a certain range of the governing parameters. A stability analysis to identify which solutions are stable and physically realizable by using the bvp4c solver implemented in Matlab has also been presented.

/pdf/the-effects-of-suction-on-forced-convection-boundary-layer-2dof1pmfth.pdf

The effects of suction on forced convection boundary layer stagnation point slip flow in a darcy porous medium towards a shrinking sheet with presence of thermal radiation: a stability analysis

New 4(3) pairs Diagonally Implicit Runge-Kutta-Nystrom (DIRKN) methods with reduced phase-lag are developed for the integration of initial value problems for second-order ordinary differential equations possessing oscillating solutions. Two DIRKN pairs which are three- and four-stage with high order of dispersion embedded with the third-order formula for the estimation of the local truncation error. These new methods are more efficient when compared with current methods of similar type and with the L-stable Runge-Kutta pair derived by Butcher and Chen (2000) for the numerical integration of second-order differential equations with periodic solutions.

/pdf/new-4-3-pairs-diagonally-implicit-runge-kutta-nystrom-method-5cy68k0bgd.pdf

New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

An analysis is performed for mixed convection thermal and solute concentration Marangoni boundary layer that can be formed along the surface, which separates two immiscible fluids in surface tension flows. Similarity equations for the case in which an external pressure gradient is imposed are derived. The dimensionless governing equations of the flow field are solved numerically using the shooting method. The effect of flow parameters on the velocity, temperature and concentration are computed and presented in tables and figures.

/pdf/thermal-and-solutal-marangoni-mixed-convection-boundary-1i7u636sc1.pdf

Thermal and solutal Marangoni mixed convection boundary layer flow

A similarity solution of the steady magnetohydrodynamic (MHD) mixed convection boundary layer flow due to a stretching vertical heated sheet in a power law nanofluid with thermal radiation effect is theoretically studied. The governing system of partial differential equations is first transformed into a system of ordinary differential equations. The transformed equations are solved numerically using the shooting method. The influence of pertinent parameters such as the nanoparticle volume fraction parameter, the magnetic parameter, the buoyancy or mixed convection parameter and the radiation parameter on the flow and heat transfer characteristics is discussed. Comparisons with published results are also presented.

/pdf/mhd-mixed-convection-flow-of-a-power-law-nanofluid-over-a-vjvwqqei7n.pdf

Norihan Md Arifin

Papers

Effects of Control on the Onset of Marangoni-Benard Convection with Uniform Internal Heat Generation

The effects of suction on forced convection boundary layer stagnation point slip flow in a darcy porous medium towards a shrinking sheet with presence of thermal radiation: a stability analysis

New 4(3) Pairs Diagonally Implicit Runge-Kutta-Nyström Method for Periodic IVPs

Thermal and solutal Marangoni mixed convection boundary layer flow

MHD mixed convection flow of a power law nanofluid over a vertical stretching sheet with radiation effect