The impact of thermal radiation on viscous dissipative boundary layer flow of heat absorbing magneto-nanofluid over a permeable exponentially stretching sheet with Navier's velocity and thermal slips has been analyzed. The prevailing mathematical equations are changed to nonlinear ordinary differential equations using the appropriate similarity variables and then the equations are numerically solved by Runge-Kutta scheme of fourth order together with the shooting technique. Three kinds of water based nanofluids having aluminum oxide, copper and titanium oxide as nanoparticles are considered for this investigation. The consequence of relevant flow parameters on nanofluid velocity, temperature distribution, wall velocity gradient and local Nusselt number are displayed by means of various graphs. In addition, analysis of quadratic regression estimation on the numerical data of coefficient of skin friction and local Nusselt number has been presented to verify the relationship among the controlling physical parameters and transfer rate parameters. Our result reveals that the velocity and temperature distribution profiles are lower for Cu-water nanofluid followed by Al2O3 and TiO2 water base nanofluids in the regime of boundary layer. The thermal radiation and viscous dissipation have tendency to augment the Cu-water temperature over the stretching sheet.

The key objective of this analysis is to examine the flow of hydromagnetic dissipative and radiative graphene Maxwell nanofluid over a linearly stretched sheet considering momentum and thermal slip conditions. The appropriate similarity variables are chosen to transform highly nonlinear partial differential equations (PDE) of mathematical model in the form of nonlinear ordinary differential equations (ODE). Further, these transformed equations are numerically solved by making use of Runge-Kutta-Fehlberg algorithm along with the shooting scheme. The significance of pertinent physical parameters on the flow of graphene Maxwell nanofluid velocity and temperature are enumerated via different graphs whereas skin friction coefficients and Nusselt numbers are illustrated in numeric data form and are reported in different tables. In addition, a statistical approach is used for multiple quadratic regression analysis on the numerical figures of wall velocity gradient and local Nusselt number to demonstrate the relationship amongst heat transfer rate and physical parameters. Our results reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. Finally, we have compared our numerical results with those of earlier published articles under the restricted conditions to validate our solution. The comparison of results shows an excellent conformity among the results.

The hydromagnetic dissipative, heat-absorbing, chemically reactive and optically thick radiative flow of nanofluid over a stretchable surface together with heat and mass transport phenomena is investigated. The prevailing partial differential equations (PDE) of the mathematical model are changed by incorporating apt similarity variables in the form of nonlinear similarity equations. Further, these similarity equations are solved numerically utilizing the Runge-Kutta Fehlberg technique in conjunction with the shooting method. For the numerical explorations, three kinds of nanofluids are prepared by disseminating very fine nanoparticles of titanium oxide (TiO2), aluminium oxide (Al2O3) and copper (Cu) into water. The significance of numerous regulatory flow parameters on the nanofluid velocity, nanofluid temperature, local Nusselt number, species concentration, wall velocity gradient and mass flow rates are examined through different graphical results. Additionally, a quadratic regression approximation analysis is accomplished to analyze the connection between the heat transport rate and regulatory flow parameters. The numerical results reveal that the temperature of Cu-water based nanofluid temperature gets enhanced owing to improvement in the strength of radiation, viscous dissipation and magnetic effects. Further, regression approximation analysis unveils that a slight change in the velocity slip parameter leads in the optimal perturbation in both the shear stress values and heat transfer rate at the stretchable surface. Finally, the validation of numerical results and the developed algorithm of employed computational technique have been done by making a comparison of computed results with the available results under restricted situations.

In this paper, we compute compactly supported biorthogonal Riesz basis of wavelets. We solve the Bezout equation resulting from biorthogonality of the scaling function with its dual in a simple and algebraic way. We provide some examples of the biorthogonal wavelets showing their detail construction. Two algorithms for their construction are also given.

Abstract:In this paper, we give two algorithms to compute compactly supported biorthogonal Riesz basis of wavelets. The input to these algorithms are filters of the transfer and the dual transfer functions, which are obtained by solving the Bezout equation. This Bezout equation arises from biorthogonality of the scaling function and the dual scaling function. We solve the Bezout equation in a simple and algebraic way. We also give a case study of the biorthogonal wavelets showing their detail construction. Some references to Sobolev regularity of the wavelets which is a qualitative property of the wavelet is also made by us.