Abstract
The uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. In this article, we discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems (namely, Couette flow, Poiseuille flow, and Couette–Poiseuille flow) of a third-grade fluid over an inclined channel with heat transfer. The dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). The fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost. In the first case, proposed problems are analyzed in a crisp environment, while in the second case, they are discussed in a fuzzy environment with the help of α -cut approach, which controls the fuzzy uncertainty. It is observed that the fuzzy gravitational and magnetic parameters are less sensitive for a better flow and heat situation. Using triangular fuzzy numbers (TFNs), the left, right, and mid values of the velocity and temperature profile are presented due to various values of the involved parameters in tabular form. For validation, the present results are compared with existing results for some special cases, viz., crisp case, and they are found to be in good agreement.
Highlights
Academic Editor: Dragan Pamucar e uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information
We discuss the combined effects of the gravitational and magnetic parameters for both crisp and fuzzy cases in the three basic flow problems of a third-grade fluid over an inclined channel with heat transfer. e dimensionless governing equations with the boundary conditions are converted into coupled fuzzy differential equations (FDEs). e fuzzified forms of the governing equations along with the boundary conditions are solved by employing the numerical technique bvp4c built in MATLAB for both cases, which is very efficient and has a less computational cost
The physical problems with involved geometry, coefficients, parameters, and initial and boundary conditions greatly affect the solutions of DEs. en, the coefficients, parameters, and initial and boundary conditions are not crisp due to the mechanical defect, experimental error, measurement error, etc. erefore, in this situation, fuzzy set theory is an effective tool for a better understanding of the considered phenomena, and it is more accurate than assuming the crisp or classical physical problems
Summary
Academic Editor: Dragan Pamucar e uncertainties or fuzziness occurs due to insufficient knowledge, experimental error, operating conditions, and parameters that give the imprecise information. We analyze the effects of the uncertain gravitational parameter k and uncertain magnetic parameter M through α-cut approach (0 ≤ α ≤ 1) as discussed in detail, on velocity and temperature profiles for Couette and Poiseuille flow graphically and tabularly.
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