An Approach of Numerical Solution and Uncertainty Measure of MHD Viscous Flow Over a Shrinking Sheet with Second Order Slip Flow Model Under Fuzzy Environment

Abstract

Abstract : The specified problem for our consideration is MHD viscous flow over a shrinking sheet with second order slip flow model. In this paper, we investigate MHD viscous flow with a second order slip flow model over a permeable shrinking surface under fuzzy environment. The governing differential equation can be obtained by using similarity variable technique and then using the Zadeh extension theorem for the same equation to fuzzify. The  technique is used to show the validation for the uncertainty of the equation of the motion. The effect of magnetic parameter, mass transfer parameter, first order velocity slip parameter and second order velocity slip parameter  has been investigated in fuzzy environment. It is observed that the effect of uncertainty due to change of the parameter  and  not for the parameter  and. A suitable range in which magnetic parameter, mass transfer parameter, first order velocity slip parameter and second order velocity slip parameter is evaluated that gives the accuracy in the velocity profile and finally the solution is carried out and presented graphically. It has been found that in crisp case whenever   decreases the velocity also decreases. A Comparison of skin friction coefficient is also shown for crisp and fuzzy valued.

Keyword : Triangular Fuzzy Set, Fuzzified, Crisp, Magnetic Parameter

Abstract : The specified problem for our consideration is MHD viscous flow over a shrinking sheet with second order slip flow model. In this paper, we investigate MHD viscous flow with a second order slip flow model over a permeable shrinking surface under fuzzy environment. The governing differential equation can be obtained by using similarity variable technique and then using the Zadeh extension theorem for the same equation to fuzzify. The  technique is used to show the validation for the uncertainty of the equation of the motion. The effect of magnetic parameter, mass transfer parameter, first order velocity slip parameter and second order velocity slip parameter  has been investigated in fuzzy environment. It is observed that the effect of uncertainty due to change of the parameter  and  not for the parameter  and. A suitable range in which magnetic parameter, mass transfer parameter, first order velocity slip parameter and second order velocity slip parameter is evaluated that gives the accuracy in the velocity profile and finally the solution is carried out and presented graphically. It has been found that in crisp case whenever   decreases the velocity also decreases. A Comparison of skin friction coefficient is also shown for crisp and fuzzy valued.