A new solution method for nonsimilarity boundary layers, applicable locally and independently of information from other stream wise positions, is described and implemented. The governing equations generated by the local nonsimilarity solution method are of the same type as those encountered in the treatment of similarity boundary layers. In addition to its local applicability, the utility of the new method is enhanced by its simplicity and directness, both in concept and in actual computations. Several nonsimilar velocity boundarylayer problems are solved herein with a view to illustrating the method, the participating nonsimilarities stemming from the freestream velocity distribution, surface mass transfer, and transverse curvature. On the basis of comparisons with available published information as well as of comparisons internal to the method itself, it may be concluded that the local nonsimilarity method provides results of high accuracy at all streamwise locations, except those near a point of separation.

Local nonsimilarity boundary-layer solutions

Influence of radiation on unsteady hydromagnetic natural convection transient flow near an impulsively moving vertical flat plate with ramped wall temperature in a porous medium is studied. Exact solution of momentum and energy equations, under Boussinesq approximation, is obtained in closed form by Laplace transform technique. The variations in fluid velocity and temperature are shown graphically whereas numerical values of skin friction and Nusselt number are presented in tabular form.

MHD natural convection flow with radiative heat transfer past an impulsively moving plate with ramped wall temperature

The unsteady natural convective flow of an incompressible viscous fluid near a vertical plate has been considered. It is assumed that the bounding plate has a ramped temperature profile. The exact solutions of the energy and momentum equations, under the usual Boussinesq approximation, have been obtained in closed form. There are two different solutions for the fluid velocity—one valid for the fluids of Prandtl numbers different from unity, and the other for which the Prandtl number is unity. The variations of the fluid temperature, velocity as well as the Nusselt number and wall skin friction have been presented graphically. The natural convection near a ramped temperature plate has also been compared with the flow near a plate with constant temperature.

Natural convection near a vertical plate with ramped wall temperature

This article aims to study the unsteady convection flow of nanofluids induced by free convection and the oscillating plate condition. The fluid is confined to the region over an infinite vertical flat plate with ramped wall temperature. Five different types of water-based nanofluids containing copper (Cu), silver (Ag), copper oxide (CuO), alumina ( Al2O3 and titanium oxide (TiO2 are chosen for this analysis. The Laplace transform technique is applied to obtain exact solutions of velocity and temperature for both cases of ramp and isothermal plate conditions. Ramp and isothermal solutions are compared graphically and it is found that the ramp velocity and the temperature are smaller in magnitude than isothermal velocity and temperature. Corresponding expressions for skin-friction and Nusselt number are also evaluated. The results are plotted for various physical parameters contained in the governing equations and discussed in details. Comparison with earlier results provides an excellent agreement.

Exact solutions for free convection flow of nanofluids with ramped wall temperature

Hydromagnetic natural convection flow with heat and mass transfer of a chemically reacting and heat absorbing fluid past an accelerated moving vertical plate with ramped temperature and ramped surface concentration through a porous medium

R. A. McGraw

Papers

Free Convection From a Vertical Flat Plate With Step Discontinuities in Surface Temperature

On laminar boundary-layer flows of a dissociated gas past catalytic surfaces☆