Solvability of a system of integral equations in two variables in the weighted Sobolev space W(1,1)-omega(a,b) using a generalized measure of noncompactness

In this paper, we deal with the existence of solutions for a coupled system of integral equations in the Cartesian product of weighted Sobolev spaces E = Wω1,1 (a,b) x Wω1,1 (a,b). The results were achieved by equipping the space E with the vector-valued norms and using the measure of noncompactness constructed in [F.P. Najafabad, J.J. Nieto, H.A. Kayvanloo, Measure of noncompactness on weighted Sobolev space with an application to some nonlinear convolution type integral equations, J. Fixed Point Theory Appl., 22(3), 75, 2020] to applicate the generalized Darbo’s fixed point theorem [J.R. Graef, J. Henderson, and A. Ouahab, Topological Methods for Differential Equations and Inclusions, CRC Press, Boca Raton, FL, 2018]

Machine learning based analysis of heat transfer in tangent hyperbolic fluid at heat generating magnetized surface

An artificial intelligence-based study is conducted to examine the heat transfer in the tangent hyperbolic fluid using a stretchable magnetized surface. To be more specific, heat and mass transfer are considered in the flow regime of tangent hyperbolic fluid. The magnetic field is applied externally. The heat generation, velocity, and thermal slip effects are considered. The flow is formulated in terms of coupled non-linear PDEs. Lie groups of transformations are constructed to reduce the order of PDEs. The reduced equations are solved by using the shooting method. The impact of the Weissenberg number, power law index, Prandtl number, and heat generation parameter is evaluated on the heat transfer coefficient by using artificial intelligence. 88 samples are divided at random into training 62 (70 %), validation 13 (15 %), and testing 13 (15 %). The hidden layer contains 10 neurons. The Levenberg-Marquadt backpropagation algorithm is used to train the model. The developed model is evaluated by mean square error and regression analysis. According to ANN anticipated values, the heat transfer coefficient shows decreasing trends towards higher values of Weissenberg number, power law index, and heat generation parameter. The tangent hyperbolic fluid temperature admits an increase for heat generation and magnetic field parameter while the opposite is the case for thermal slip parameter

Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been developed by using the Lie symmetry method. PDE's (Partial Differential Equations) are transformed into ODE's (Ordinary Differential Equations) by implementing the suitable transformation. A numerical method called bvp4c is used to explain the dimensionless system (ODE's). Graphs and tables are used to interpret the impact of the significant physical parameters. The curves of temperature function declined due to enchanting the values of the thermophoresis Parameter. The temperature is produced at a low level due to enchanting the values of thermophoresis because this force transports burn at a low 10 μm diameter so the temperature becomes lessor. Increments of thermophoresis parameter which enhanced the values of concentration Function. As the concentration boundary layer increased which declined the mass transfer due increment in thermophoresis. The curves of temperature function are increasing due to enhancing the values of the Brownian parameter because addition in the Brownian motion, improved the movement of particles ultimately increasing the kinematic energy of fluid which improved the heat transfer phenomena. Increments of Brownian parameter which declined the values of concentration function. Physically, the kinematic energy improved which declined the mass transfer rate near the surface

Darcy resistant of Soret and Dufour impact of radiative induced magnetic field sutterby fluid flow over stretching cylinder

The incompressible two-dimensional steady flow of Sutterby fluid over a stretching cylinder is taken into account. The magnetic Reynolds number is not deliberated low in the present analysis. Radiation and variable thermal conductivity are considered to debate the impact on the cylindrical surface. The Dufour and Soret impacts are considered on the cylinder. The mathematical model is settled by employing boundary layer approximations in the form of differential equations. The system of differential equations becomes dimensionless using suitable transformations. The dimensionless nonlinear differential equations are solved through a numerical scheme(bvp4c technique). The flow parameters of physical effects on the velocity, temperature, heat transfer rate, and friction between surface and liquid are presented in tabular as well as graphical form. The velocity function declined by improving the values of the Sponginess parameter. The fluid temperature is reduced by increment in curvature parameter