MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet

A new variational principle for the generalized theory of heat conduction with finite wave speed is considered. The corresponding transition to the classical case, when the speed of thermal disturbance is infinite, is performed by setting the relaxation time equal to zero. The concept of generalized coordinate (penetration depth) and the method of partial integration are basic tools for obtaining the approximative solutions. By means of the variational technique developed here a nonlinear boundary value problem can be reduced to an ordinary differential equation whose solution is often capable of being expressed in analytic closed form. Several examples are solved in details. The results are found to be in good agreement with those obtained by other methods.

An approach to linear and nonlinear heat transfer problem using a Lagrangian

The MHD flow and heat transfer of a non-Newtonian power-law fluid over a continuously moving surface with a parallel free stream have been investigated. The partial differential equations governing the non-similar flow have been solved numerically using an implicit finite-difference scheme. The skin friction and heat-transfer coefficients increase with the magnetic parameter, and they are more for the pseudoplastic fluid than for the dilatant fluid. The heat-transfer coefficient increases significantly with the Prandtl number. The gradient of the velocity at the surface is negative when the wall velocity is greater than the free stream velocity, and it is positive when the wall velocity is less than the free stream velocity.

MHD boundary-layer flow of a non-Newtonian fluid over a continuously moving surface with a parallel free stream

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. The solution of this highly non-linear problem is obtained by means of the transformation group theoretic approach. The one-parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u (y, t) has been studied and the results are plotted.

http://inspirehep.net/record/580812/files/Badran49-56.pdf

Solution of the Rayleigh Problem for a Power Law Non-Newtonian Conducting Fluid via Group Method

Heat transfer analysis in convective flow of Jeffrey nanofluid by vertical stretchable cylinder

An investigation is made of the magnetic Rayleigh problem where a semi-infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non-Newtonian power law fluid of infinite extent. The nonstationary flow of this electrically conducting fluid in a transverse magnetic field is then analyzed. The solution to this highly non-linear problem is obtained by means of a new variational principle developed by the authors. This new principle allows one to obtain the solution in a straightforward manner. Unlike other variational techniques in dissipative physics the authors' possesses a pure Hamiltonian structure and obeys all the laws of the classical variational calculus. It is shown that the influence of the magnetic field is greater on the coefficient of friction of dilatant fluids than pseudo-plastic fluids. In the absence of a magnetic field the thickness of the boundary layer increases with increasing powers of the fluid. Finally, the shape of the velocity profile is more strongly dependent on the magnetic field strength for pseudo-plastic fluids than for dilatant fluids.

A. M. Strauss

Papers

A variational solution of the Rayleigh problem for a power law non-Newtonian conducting fluid

On two variational methods for obtaining solutions to transport problems