This study uncovered a numerical simulation of the Williamson hybrid nanofluid's MHD on “heat and mass transfer flow” over a porous stretched sheet. The model made use of Cattaneo-Christov heat and mass fluxes. The situation's underlying physics is modelled using governing equations. Using an appropriate similarity transformation, these equations were transformed into a system of ordinary differential equations. Methodology/Approach: MATLAB software along with BVC4C tool is used to find the numerical solution of the problem. The study's findings show that while boosting the mass relaxation flux increases concentration distributions, doing so also increases temperature distributions. Thermal radiation, heat generation, and an additional value to improve temperature and velocity distributions, the Eckert number was measured. Major findings: Higher magnetic field values are shown to result in an increase in the velocity distribution because of the applied electromagnetic force. Additionally, a rise in the thermal radiation parameter is seen to broaden the distributions of velocity and temperature. Astrophysics, geophysics, biological sciences, and biomedical engineering are all helpful to this study. The findings of this study are generally well supported by the literature.

The objective of this paper is to analyze the impact of thermophoresis parameter, Brownian motion, velocity ratio parameter, similarity radius of the slim needle, magnetic parameter, Prandtl number and thermal radiation on the steady state, laminar, MHD hybrid nanofluid composed of MgO-Ag/H2O flowing along a horizontal hot thin needle. To achieve this, the BVP-5C shooting technique is employed through MATLAB to solve the transformed nonlinear ODEs governing the fluid flow. This study investigates the impact of non-dimensional parameters on the flow velocity, temperature and concentration profiles within the hybrid nanofluid. The effects of skin friction, local Nusselt number and Sherwood number are demonstrated through the use of tables. The observation reveals that elevating the thermophoresis parameter results in a simultaneous reduction in the temperature and concentration profiles, while an opposite behavior is observed for Brownian motion. The magnetic parameter and thermal radiation values result in a rising temperature profile, while the trend is reversed for the velocity ratio parameter, Prandtl number and Schmidt number. The Nusselt number demonstrates an upward trend with higher values of thermophoresis parameter, velocity ratio parameter and thermal radiation. Further, Sherwood number experiences an increase with greater values of Brownian motion and magnetic parameter but it displays a contrasting pattern for thermophoresis, velocity ratio parameter and thermal radiation parameter. Validation of this model with existing data has been excellent.

This article introduces the idea of (fuzzy soft Boolean rings) FSBRs and investigates their algebraic properties. The concepts of fuzzy soft ideals (FSIs) of FSBRs, and idealistic fuzzy soft Boolean rings (IFSBRs) are then defined and discussed.

The present paper gives direct product of finite interval-valued intuitionistic fuzzy ideals.  Furthermore, we add more useful results and also prove that, let be interval-valued intuitionistic fuzzy ideal of BF-algebra X. If  and for any, then  is an interval-valued intuitionistic fuzzy H-ideal of BF-algebra X.Â

In previous papers, it has been introduced a generalized hypergeometric function of two variables. The present paper aims at to derive different types of integral representations for the generalized hypergeometric function. The results derived here are very general in nature and are interesting and can obtain some known and new integrals for various polynomials. Each result is followed by its applications to the classical orthogonal polynomials.