This work investigates the unsteady natural convection flow of a viscous, incompressible and electrically conducting fluid near an infinite vertical plate with ramped temperature and ramped motion. A unified closed form solution is obtained for the velocity field and skin friction coefficient corresponding to the case when the magnetic field fixed relative to the fluid or the moving boundary. It is assumed that the boundary plate has a ramped temperature profile and ramped motion subject to a uniform transverse magnetic field under the supposition of negligible induced magnetic field. Exact solutions of energy and momentum equations are obtained using the Laplace transform techniques. Graphical representations are attained for different values of the Prandtl number, magnetic field and heat sink parameter. Results show that wall ramped temperature and ramped motion tend to decrease fluid temperature, velocity, Nusselt number and skin friction.

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature-dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well-known Laplace transform. The time-domain solution is obtained using the Riemann-sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.

This study analyzes time-dependent magnetohydrodynamics natural convective flow of a viscous incompressible fluid in an annulus with ramped motion of the boundaries. The governing momentum and energy equations are solved analytically, in terms of the modified Bessel function of the first and second kinds. The influence of governing parameters such as the Hartman number, radius ratio, Grashof number, heat absorption parameter, and Prandtl number are discussed with the help of line graphs. It is found that the Hartmann number has a retarding effect on fluid velocity when K = 0.0 and K = 0.5, while the reverse effect is noticed when K = 1.0. The Hartman number also decreases the mass flow rate for all cases of K while it enhances the skin friction at the inner surface of the outer cylinder. It increases the skin friction at the outer surface of the inner cylinder when K = 1.0 and K = 0.0, but decreases the skin friction at the outer surface of the inner cylinder when K = 0.5.

The use of wastewater for the irrigation of vegetables is on the increase because of its richness in nutrients and it reduces the pressure on available freshwater resources. Untreated wastewater may, however, be a source of contamination of the vegetables by potentially toxic elements, which may, in turn, constitute a health risk to consumers. Samples of seven vegetables: cabbage, onion bulbs, bitter leaf, jute mallow, spinach, tomato, and lettuce irrigated with wastewater were collected and analysed for potentially toxic elements using Energy Dispersive X-ray Fluorescence. The Target Hazard Quotient (THQ) and Health Index (HI) were determined based on the estimated daily metal intake of Cd, Ni, Pb, Zn, Cu, Fe Mg, and Mn through the consumption of these vegetables. Cancer Risk was assessed for Cd, Ni, and Pb. Except for Mg, for which no guideline value was found for vegetables, the concentration of Cu in cabbage and Mn in tomato were found to be within the permissible limit, whereas Cd, Ni, Pb Zn, and Fe were found to be above the permissible limits of the FAO/WHO in all the vegetables. The Target Hazard Quotient (THQ) shows that adult consumers of all seven vegetables are at risk of non-carcinogenic toxicity of Cd, Ni, and Pb, while in children, the risk extends to Zn, Cu, Fe, and Mn (with tomato as the only exception for Mn). The Health Index being greater than 1in all vegetables means there is a non-carcinogenic risk health risk associated with the consumption of all vegetables by children and adults. The Target cancer Risk shows that adults are exposed to cancer risk from the consumption of all the vegetables due to Ni and Cd contamination (except onion for cadmium), while in children, the risk extends to Pb (except for onion). The consumption of vegetables irrigated with untreated wastewater from the Sabon Gari market drain is an exposure route to potentially toxic elements such as Cd, Ni, Pb, Zn, Cu, Fe, and Mn, with resultant non-carcinogenic and carcinogenic health risks. These health risks were found to be higher in children.

An unsteady MHD flow of a temperature dependent heat source/sink in an annulus due to ramped motion and ramped temperature of the boundaries has been analyzed. The partial differential equations of the fluid flow are formulated taking into account the ramped temperature and ramped velocity of the inner cylinder. The closed form solution are obtained for three cases of the magnetic field being fixed relative the fluid, cylinder and when the velocity of the magnetic field is less than the velocity of the moving cylinder. The problem is solved using Laplace transform technique to obtain the Laplace domain solution and Riemann sum approximation to obtain the time domain solution. The effect of the governing parameters on the fluid flow are illustrated graphically. It is found that, Hartmann number has a retarding effect on the skin friction at the outer surface of the inner cylinder and mass flow rate. It also decreases fluid velocity for cases K=0.0andK=0.5 the reverse effect is noticed for case K=1.0. Increase in Hartmann number lead to an increase in skin friction at the inner surface of the outer cylinder for case K=0.0 but decreases it for cases K=0.0andK=0.5.