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In this work, the flow of ternary hybrid nanomaterials filling porous spaces is investigated in the presence of magnetohydrodynamics (MHD) and nonlinear convection. Three dissimilar nanoparticles copper (Cu), alumina (Al2O3), and magnesium oxide (MgO) are employed. Various features including Ohmic heating, heat generation, and variable thermal conductivity are studied, along with nonlinear radiation and entropy analysis. Solutions are developed using the ND Solve (shooting) method in Mathematica software. Analysis of parameters of interest is conducted, with conclusions highlighting key outcomes. Results show an increase in the thermal field for Eckert number and radiation, while a decrease in liquid flow is observed with increasing the magnetic parameter. The heat transport rate exhibits an opposite trend between heat generation and radiation. Temperature ratio parameter and Prandtl number show opposite trends in the thermal field, while the temperature gradient decreases against variable thermal conductivity. The drag force follows a similar trend against nonlinear convective and porosity variables. The entropy rate increases with the Brinkman number, and both porosity and radiation have an increasing impact on entropy rate. An increase in liquid flow is noted with the nonlinear convection variable. A comparative study of heat transport rate through the Prandtl number shows good agreement.

In this work, the flow of ternary hybrid nanomaterials filling porous spaces is investigated in the presence of magnetohydrodynamics (MHD) and nonlinear convection. Three dissimilar nanoparticles copper (C u) , alumina (Al 2 O 3) , and magnesium oxide (M g O) are employed. Various features including Ohmic heating, heat generation, and variable thermal conductivity are studied, along with nonlinear radiation and entropy analysis. Solutions are developed using the ND Solve (shooting) method in Mathematica software. Analysis of parameters of interest is conducted, with conclusions highlighting key outcomes. Results show an increase in the thermal field for Eckert number and radiation, while a decrease in liquid flow is observed with increasing the magnetic parameter. The heat transport rate exhibits an opposite trend between heat generation and radiation. Temperature ratio parameter and Prandtl number show opposite trends in the thermal field, while the temperature gradient decreases against variable thermal conductivity. The drag force follows a similar trend against nonlinear convective and porosity variables. The entropy rate increases with the Brinkman number, and both porosity and radiation have an increasing impact on entropy rate. An increase in liquid flow is noted with the nonlinear convection variable. A comparative study of heat transport rate through the Prandtl number shows good agreement. [ABSTRACT FROM AUTHOR]

The studies conducted in the recent past reveals that the non-Newtonian are extensively applied in several engineering applications. The atypical Oldroyd-B fluid, a specific sub-category of non-Newtonian fluids, with fractional derivative constitutive equations, is very expedient to determine the approximation of many dilute polymer liquids. Since very few studies regarding the numerical solution of the aforesaid model are conducted, so the literature that can be referred to in this regard is scarce. The current article investigates the unsteady magneto-hydrodynamic flow of irregular Oldroyd-B fluid with a modified thermal flux restricted between two infinite parallel plates. Here, it is assumed that the thermal conductivity of the fluid is variable, and the impact of body forces like gravity is accordingly analyzed in terms of non-linear convection. The linear acceleration of the lower permeable plate in its plane prompts the flow. Further, we have investigated the heat transfer in the flow field through a modified fractional thermal gradient and internal heat source. The temperature gradient accelerates with time and exists among the flow boundaries. In order to determine the approximate solution unified with finite difference approximation for Caputo fractional time derivatives, we have utilized the standard Galerkin finite element method. Moreover, we have conducted a convergence analysis of the suggested numerical scheme and offered some valid error approximations. In the non-integer viscoelastic model, the local number and coefficient of skin friction are also deliberated. We have also performed some upright numerical simulations to highlight the ascendency of characteristic flow parameters of velocity and temperature fields in the proposed scheme. Here, we have analyzed that the resistive force increases by 40%, corresponding to an increment in α ranging from 0 to 0.4. Further, the heat transfer rate is diminish by 10.94% against an increase in variable thermal conductivity while it is enhanced by 37.78% corresponding to increased in Pr.

The studies conducted in the recent past reveals that the non-Newtonian are extensively applied in several engineering applications. The atypical Oldroyd-B fluid, a specific sub-category of non-Newtonian fluids, with fractional derivative constitutive equations, is very expedient to determine the approximation of many dilute polymer liquids. Since very few studies regarding the numerical solution of the aforesaid model are conducted, so the literature that can be referred to in this regard is scarce. The current article investigates the unsteady magneto-hydrodynamic flow of irregular Oldroyd-B fluid with a modified thermal flux restricted between two infinite parallel plates. Here, it is assumed that the thermal conductivity of the fluid is variable, and the impact of body forces like gravity is accordingly analyzed in terms of non-linear convection. The linear acceleration of the lower permeable plate in its plane prompts the flow. Further, we have investigated the heat transfer in the flow field through a modified fractional thermal gradient and internal heat source. The temperature gradient accelerates with time and exists among the flow boundaries. In order to determine the approximate solution unified with finite difference approximation for Caputo fractional time derivatives, we have utilized the standard Galerkin finite element method. Moreover, we have conducted a convergence analysis of the suggested numerical scheme and offered some valid error approximations. In the non-integer viscoelastic model, the local number and coefficient of skin friction are also deliberated. We have also performed some upright numerical simulations to highlight the ascendency of characteristic flow parameters of velocity and temperature fields in the proposed scheme. Here, we have analyzed that the resistive force increases by 40 % , corresponding to an increment in α ranging from 0 to 0.4. Further, the heat transfer rate is diminish by 10.94 % against an increase in variable thermal conductivity while it is enhanced by 37.78 % corresponding to increased in Pr. [ABSTRACT FROM AUTHOR]