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The purpose of the current flow configurations is to bring to attention the thermophysical aspects of magnetohydrodynamics (MHD) Williamson nanofluid flow under the effects of Joule heating, nonlinear thermal radiation, variable thermal coefficient and activation energy past a rotating stretchable surface.

A mathematical model is examined to study the heat and mass transport analysis of steady MHD Williamson fluid flow past a rotating stretchable surface. Impact of activation energy with newly introduced variable diffusion coefficient at the mass equation is considered. The transport phenomenon is modeled by using highly nonlinear PDEs which are then reduced into dimensionless form by using similarity transformation. The resulting equations are then solved with the aid of fifth-order Fehlberg method.

The rotating fluid, heat and mass transport effects are analyzed for different values of parameters on velocity, energy and diffusion distributions. Parameters like the rotation parameter, Hartmann number and Weissenberg number control the flow field. In addition, the solar radiation, Joule heating, Prandtl number, thermal conductivity, concentration diffusion coefficient and activation energy control the temperature and concentration profiles inside the stretching surface. It can be analyzed that for higher values of thermal conductivity, Eckret number and solar radiation parameter the temperature profile increases, whereas opposite behavior is noticed for Prandtl number. Moreover, for increasing values of temperature difference parameter and thermal diffusion coefficient, the concentration profile shows reducing behavior.

This paper is useful for researchers working in mathematical and theoretical physics. Moreover, numerical results are very useful in industry and daily-use processes.

Petroleum hydrocarbons are naturally occurring flammable fossil fuels used as conventional energy sources. It has carcinogenic, mutagenic properties and is considered a hazardous pollutant. Soil contaminated with petroleum hydrocarbons adversely affects the properties of soil. This paper aim to remove pollutants from the environment is an urgent need of the hour to maintain the proper functioning of soil ecosystems.

The ability of micro-organisms to degrade petroleum hydrocarbons makes it possible to use these microorganisms to clean the environment from petroleum pollution. For preparing this review, research papers and review articles related to petroleum hydrocarbons degradation by micro-organisms were collected from journals and various search engines.

Various physical and chemical methods are used for remediation of petroleum hydrocarbons contaminants. However, these methods have several disadvantages. This paper will discuss a novel understanding of petroleum hydrocarbons degradation and how micro-organisms help in petroleum-contaminated soil restoration. Bioremediation is recognized as the most environment-friendly technique for remediation. The research studies demonstrated that bacterial consortium have high biodegradation rate of petroleum hydrocarbons ranging from 83% to 89%.

Proper management of petroleum hydrocarbons pollutants from the environment is necessary because of their toxicity effects on human and environmental health.

This paper discussed novel mechanisms adopted by bacteria for biodegradation of petroleum hydrocarbons, aerobic and anaerobic biodegradation pathways, genes and enzymes involved in petroleum hydrocarbons biodegradation.

This study aims to analyse the non-linear losses of a porous media (stack) composed by parallel plates and inserted in a resonator tube in oscillatory flows by proposing numerical correlations between pressure gradient and velocity.

The numerical correlations origin from computational fluid dynamics simulations, conducted at the microscopic scale, in which three fluid channels representing the porous media are taken into account. More specifically, for a specific frequency and stack porosity, the oscillating pressure input is varied, and the velocity and the pressure-drop are post-processed in the frequency domain (Fast Fourier Transform analysis).

It emerges that the viscous component of pressure drop follows a quadratic trend with respect to velocity inside the stack, while the inertial component is linear also at high-velocity regimes. Furthermore, the non-linear coefficient b of the correlation ax + bx² (related to the Forchheimer coefficient) is discovered to be dependent on frequency. The largest value of the b is found at low frequencies as the fluid particle displacement is comparable to the stack length. Furthermore, the lower the porosity the higher the Forchheimer term because the velocity gradients at the stack geometrical discontinuities are more pronounced.

The main novelty of this work is that, for the first time, non-linear losses of a parallel plate stack are investigated from a macroscopic point of view and summarised into a non-linear correlation, similar to the steady-state and well-known Darcy–Forchheimer law. The main difference is that it considers the frequency dependence of both Darcy and Forchheimer terms. The results can be used to enhance the analysis and design of thermoacoustic devices, which use the kind of stacks studied in the present work.