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

Synchronization of chaotic systems which is defined based on the exponential stability for encrypts of signals is presented in this paper. An adaptive control scheme is proposed, and the convergence of the synchronized error is guaranteed. Masking and modulation methods are applied for encryption. To verify the effectiveness of the proposed schemes, numerical simulation was applied on a well-known system without linear term chaotic using MatLab software. The comparison of the proposed chaotic synchronization in the case of the synchronization rate and in the decryption precision of sent signal and image are shown.

/pdf/application-adaptive-exponential-synchronization-of-chaotic-53or1rpvwt.pdf

Application adaptive exponential synchronization of chaotic dynamical systems in secure communications

This paper investigates the influence of suction on the flow, heat and mass transfer characteristics over a permeable shrinking sheet immersed in a doubly stratified micropolar fluid. The model which consists of partial differential equations is converted into a set of nonlinear equations using similarity transformations and then solved using the bvp4c solver. Numerical results obtained are presented graphically for the distributions of velocity, angular velocity, temperature and concentration profiles within the boundary layer for various values of the magnetic parameter and wall mass suction parameter. It is visualized that the enhancement of suction parameter will increase the skin friction, heat transfer rate (local Nusselt number) and Sherwood number. It is also found that as the magnetic parameter increase, there is an increment in the skin friction while opposite results are obtained for the local Nusselt number and Sherwood number.

/pdf/effect-of-suction-on-the-mhd-flow-in-a-doubly-stratified-2m3ubv4c.pdf

Effect of suction on the MHD flow in a doubly-stratified micropolar fluid over a shrinking sheet

In many applications, hybrid nanofluids showed superior heat transfer outcomes; nevertheless, further study is needed to expand the range of applications for hybrid nanofluids. Therefore, in this study, the radiative magnetohydrodynamic (MHD) mixed convective alumina-copper/water hybrid nanofluid flow past an inclined shrinking plate is analyzed. By incorporating similarity transformations, the PDEs of the flow model is converted to ODEs. The boundary value problem of the fourth-order accuracy code (bvp4c) is implemented to solve the mathematical model numerically. When preliminary assumptions are appropriate, the above-proposed method may provide non-unique outcomes. Due to the plate’s shrinking motion, two solutions are possible. The first solution is stable based on a stability study. Therefore, we only rely on the first solution for effective practical uses. The findings reported that using less copper concentration (1 % volume fraction instead of 2 %) and applying more thermal radiation and MHD effect, the heat transfer rate might increase significantly when the plate is inclined considerably (at 70 degrees). It is possible to avoid the flow separation by upsurging the copper volume fraction from 1 % to 2 % at a higher MHD effect. The boundary layer separation is not affected by the employment of various inclination angles, variable thermal radiation, and mixed convection. This study offers valuable insight into fundamental transport phenomena such as the transmission of heat, momentum, or mass. Thus, it provides valuable information on the gradients of essential factors to control the boundary layer flow pattern. 

Mixed convection MHD hybrid nanofluid over a shrinking permeable inclined plate with thermal radiation effect

Hybrid nanofluid has emerged as a remarkable heat transfer fluid due to its promising thermal characteristics. Despite that, a continuous investigation should still be conducted to overcome certain challenges in actual applications and provide a solution in controlling fluid behavior. Therefore, in this study, the authors intend to model and analyze the three-dimensional magnetohydrodynamic radiative hybrid nanofluid flow over a permeable stretching/shrinking surface with slips and joule heating. The similarity transformation is adapted to convert the leading equations into ordinary differential equations. The resulting equations are then evaluated with the facilitation of the BVP4C solver in MATLAB. The skin-friction coefficient and the local Nusselt number are presented in the form of graph for the selected pertinent effects. The solutions are found to be nonunique. Therefore, stability analysis is conducted, and the flow is only stable for the first solution. The presence of high copper volumetric concentration and velocity slip condition has delayed the boundary-layer separation process, which occurred at the shrinking surface region. A lower amount of volumetric concentration of copper is sufficient to enhance the heat transfer rate. 

Three-Dimensional Stretching/Shrinking Flow of Hybrid Nanofluid with Slips and Joule Heating

Dual solutions are discovered in the problem of magnetohydrodynamics (MHD) boundary layer flow of Carreau fluid over a permeable shrinking sheet with thermal radiation. Therefore, a stability analysis is carried out to identify the stable solution of this problem. For the stability analysis, the problem is considered to be unsteady with time derivative introduced into the governing equations. Next, time-dependent solutions are substituted into these equations to form linear eigenvalue equations. The smallest eigenvalue of these equations is then computed using the bvp4c solver in MATLAB. The results showed that the first solution is stable, while the second solution is unstable. The first solution is physically meaningful and realizable in practice, and thus significant to the problem.

/pdf/stability-analysis-of-mhd-carreau-fluid-flow-over-a-2mgoux1zk1.pdf

Norihan Md Arifin

Papers

Application adaptive exponential synchronization of chaotic dynamical systems in secure communications

Effect of suction on the MHD flow in a doubly-stratified micropolar fluid over a shrinking sheet

Mixed convection MHD hybrid nanofluid over a shrinking permeable inclined plate with thermal radiation effect

Three-Dimensional Stretching/Shrinking Flow of Hybrid Nanofluid with Slips and Joule Heating

Stability analysis of MHD carreau fluid flow over a permeable shrinking sheet with thermal radiation