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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.

The presence of heavy metals in milk causes many acute and chronic physiological dysfunctions in human organs. The present study aims to investigate the heavy metals in cow's and buffalo's milk of two major cities, Karachi and Gujranwala, Pakistan to estimate metal intake by humans from this source.

In total, 48 milk samples from 2 cities were drawn from animals' udder to avoid contamination. Each sample was digested with nitric acid at 105 ^oC (degree Celsius) on a pre-heated electric hot plate to investigate the metals by atomic absorption spectroscopy (flame type). Air-acetylene technique analyzed chromium, cadmium and lead, and the hydride method analyzed arsenic in the milk samples.

The results revealed the highest mean lead concentration (19.65 ± 43.86 ppb) in the milk samples, followed by chromium (2.10 ± 2.33 ppb) and arsenic (0.48 ± 0.73 ppb). Cadmium was not detected in any sample, assuming cadmium's occurrence was below the detection level. The concentrations of all the metals in the samples of the two cities do not differ statistically. Lead concentrations in the buffalo's milk were higher than in cow's milk (p < 0.05). However, the concentrations of arsenic and chromium between buffalo's and cow's milk do not differ statistically. The present study reveals a lower level of metals in the milk than those conducted elsewhere. The mean concentrations of all the metals met the World Health Organization's (WHO) safety guidelines (1993).

Although cadmium causes toxicity in the human body, cadmium could not be measured because cadmium's concentration was below the detection level, which is 1 ppb.

This study will help reduce the toxic metals in our environment, and the sources of heavy metals, particularly from the industrial sector could be identified. The feed and water consumed by the milking animals could be carefully used for feeding them.

This study will help reduce the diseases and malfunction of human organs and organ systems since these heavy metals cause toxicity and carcinogenicity in humans. Arsenic and chromium cause cancer while lead causes encephalopathy (a brain disease).

The study reports heavy metal concentrations in the two attributes of four independent variables of raw milk samples that were scarcely reported from Pakistan.