Advanced Mathematical Methods for Scientists and Engineers

The flow of a viscoelastic fluid past a stretching sheet in the presence of a transverse magnetic field is considered. An exact analytical solution of the governing non-linear boundary layer equation is obtained, showing that an external magnetic field has the same effect on the flow as the viscoelasticity.

MHD flow of a viscoelastic fluid past a stretching surface

Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

Solving a nonlinear fractional differential equation using Chebyshev wavelets

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials.

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

The heat transfer in the flow of a second-order fluid, obeying Coleman and Noll's constitutive equation based on the postulate of gradually fading memory, over a stretching sheet has been studied. The boundary layer characteristics of this flow have been obtained. The velocity boundary layer thickness decreases for increasing values of the parameterKC/v. The thermal boundary layer thickness decreases and the Nusselt numberNu
x increases for increasing Prandtl numberP
r orC.

Second-order fluid flow past a stretching sheet with heat transfer

Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets

https://iopscience.iop.org/article/10.1016/j.fluiddyn.2006.05.004/pdf

MHD lubrication flow between rough rectangular plates

The paper presents single-term Haar wavelet series (STHWS) approach to the solution of nonlinear stiff differential equations arising in nonlinear dynamics. The properties of STHWS are given. The method of implementation is discussed. Numerical solutions of some model equations are investigated for their stiffness and stability and solutions are obtained to demonstrate the suitability and applicability of the method. The results in the form of block-pulse and discrete solutions are given for typical nonlinear stiff systems. As compared with the TR BDF2 method of Shampine and Gill’s method, the STHWS turns out to be more effective in its ability to solve systems ranging from mildly to highly stiff equations and is free from stability constraints.

N. M. Bujurke

Papers

Second-order fluid flow past a stretching sheet with heat transfer

Computation of eigenvalues and solutions of regular Sturm-Liouville problems using Haar wavelets

MHD lubrication flow between rough rectangular plates

Numerical solution of stiff systems from nonlinear dynamics using single-term Haar wavelet series

A fast wavelet-multigrid method to solve elliptic partial differential equations