This paper deals with the road map generation of an unknown environment by an autonomous vehicle using a proposed trapezoidal approximation. Subsequently a novel shortest path calculation method named smallest road segment (SRS) detection method has been proposed. At first we have generated a blind map of an unknown environment in a computer. Image of the unknown environment is captured by the vehicle and sent to the computer using wireless transmitter module. The image is pre-processed and the detected road boundaries help to update the blind map with road positions. When the complete map having all possible road branches is generated then based on the source and destination point, the shortest path is calculated using the proposed SRS method. This shortest path is forwarded to the vehicle to reach at the destination through the best path available.

We consider a two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity and thermal conductivity past a vertical impermeable flat plate. The equations governing the flow are transformed for three different regimes appropriate to the forced convection, free convection and forced-free convection regimes. The reduced equations for the forced convection and free convection regime are solved using the perturbation technique treating x the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained using the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. The effects of the viscosity variation parameter, e, and thermal conductivity parameter, g, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 1 to 100 are shown. The perturbation solutions obtained for small and large values of x are found in excellent agreement with the finite difference solutions for the entire x regime. We also present the values of the dimensionless velocity, viscosity and thermal conductivity showing the effects of viscosity and thermal conductivity parameter.

A steady, two‐dimensional natural convection flow of a viscous, incompressible fluid having temperature‐dependent viscosity and thermal conductivity about a truncated cone is considered. We use suitable transformations to obtain the equations governing the flow in convenient form and integrate them by using an implicit finite difference method. Perturbation solutions are employed to obtain the solution in the regimes near and far away from the point of truncation. The results are obtained in terms of the local skin friction and the local Nusselt number. Perturbation solutions are compared with the finite difference solutions and found to be in excellent agreement. The dimensionless velocity, viscosity and thermal conductivity distributions are also displayed graphically, showing the effects of various values of the pertinent parameter for smaller values of Prandtl number.

Free convection over an isothermal vertical wavy cone immersed in a fluid with variable viscosity is studied in this paper. We consider the boundary-layer regime where the Grashof number is very large and assume that the wavy surfaces have O(1) amplitude and wavelength. Using the appropriate variables, which reduce the wavy cone to a flat one, the basic equations are transformed to nonsimilar boundary-layer equations. These equations are then solved numerically using a very efficient implicit finite-difference method known as Keller box scheme. Detailed results for the streamlines, isotherms, reduced skin friction and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, wavy surface amplitude, half cone angle and Prandtl number.

The effect of variable viscosity and thermal conductivity on natural convection over an isothermal vertical wavy cone is studied in this paper. We consider the boundary-layer regime having larger Grashof number and assume the wavy surfaces with O(1) amplitude and wavelength. Using the appropriate variables the basic equations are transformed to nonsimilar boundary-layer equations which reduce the wavy cone to a flat one. These equations are then solved numerically using a very efficient implicit finite-difference method known as Keller box scheme. Detailed results for the streamlines, isotherms, reduced skin friction and heat transfer rates for a selection of parameter sets consisting of the viscosity parameter, thermal conductivity parameter, wavy surface amplitude and half cone angle.

We consider a steady two-dimensional laminar forced flow and heat transfer of a viscous incompressible fluid having temperature dependent viscosity and thermal conductivity past a wedge with a uniform surface heat flux. The governing equations, reduced to local nonsimilarity boundary layer equations using suitable transformations, have been integrated employing an implicit finite difference method. Perturbation techniques are employed to obtain the solutions near the leading edge as well as far from it. The perturbation solutions are compared with the finite difference solutions and found to be in excellent agreement. The results are presented in terms of local skin friction coefficient and rate of heat transfer for various values of the governing parameters, such as the Prandtl number Pr , the pressure gradient parameter m , the viscosity variation parameter ε and thermal conductivity variation parameter γ , against the local permeability parameter ξ . The effect of variations in ξ , ε and γ on the dimensionless velocity, viscosity and thermal conductivity distributions are also depicted graphically for Pr=0.7 .

A two-dimensional mixed convection flow of a viscous incompressible fluid of temperature dependent viscosity past a vertical impermeable fluid is considered. The governing equations for the flow are transformed for the regions appropriate to the forced convection, free convection and forced-free convection regimes. Solutions of the reduced equation appropriate in the forced convection and free convection regime are obtained using the perturbation technique treating ξ, the buoyancy parameter, as the perturbation parameter and those for the forced-free convection regime are obtained by the implicit finite difference method. Numerical results thus obtained are presented in terms of the local shear stress and local surface heat-flux. Effect of the viscosity variation parameter, ε, on the surface shear stress and the surface heat-flux for the fluid appropriate for Prandtl number ranging from 0.02 to 100 is shown. The perturbation solutions obtained for small and large values of ξ are found in excellent agreement with the finite difference solutions for the entire ξ regime.