Browsing by Author "Lund, Liaquat Ali"

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Citation Count: Lund, Liaquat Alia...et al. (2020). "Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions", Symmetry-Basel, Vol. 12, No. 8.
Convective Effect on Magnetohydrodynamic (MHD) Stagnation Point Flow of Casson Fluid over a Vertical Exponentially Stretching/Shrinking Surface: Triple Solutions
(2020) Lund, Liaquat Ali; Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In the current study, the characteristics of heat transfer of a steady, two-dimensional, stagnation point, and magnetohydrodynamic (MHD) flow of shear thickening Casson fluid on an exponentially vertical shrinking/stretching surface are examined in attendance of convective boundary conditions. The impact of the suction parameter is also considered. The system of governing partial differential equations (PDEs) and boundary conditions is converted into ordinary differential equations (ODEs) with the suitable exponential similarity variables of transformations and then solved using the shooting method with the fourth order Runge-Kutta method. Similarity transformation is an important class of phenomena in which scale symmetry allows one to reduce the number of independent variables of the problem. It should be noted that solutions of the ODEs show the symmetrical behavior of the PDES for the profiles of velocity and temperature. Similarity solutions are obtained for the case of stretching/shrinking and suction parameters. It is revealed that there exist two ranges of the solutions in the specific ranges of the physical parameters, three solutions depend on the opposing flow case where stagnation point (A) should be equal to 0.1, two solutions exist when lambda(1)= 0where lambda(1)is a mixed convection parameter andA > 0.1, and a single solution exists when lambda(1)> 0. Moreover, the effects of numerous applied parameters on velocity, temperature distributions, skin friction, and local Nusselt number are examined and given through tables and graphs for both shrinking and stretching surfaces.
Citation Count: Lund, Liaquat Ali...et al. (2020). "Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis", Scientific Reports, Vol. 10, No. 1.
Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis
(2020) Lund, Liaquat Ali; Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.
Citation Count: Lund, Liaquat Ali...et al. (2020). "Magnetized flow of Cu + Al2O3 + H2o hybrid nanofluid in porous medium: Analysis of duality and stability", Symmetry, Vol. 12, No. 9.
Magnetized flow of Cu + Al2O3 + H2o hybrid nanofluid in porous medium: Analysis of duality and stability
(2020) Lund, Liaquat Ali; Omar, Zurni; Dero, Sumera; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of Sc ≤ S and Mc ≤ M (Sc > S and Mc > M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised. © 2020 by the authors.
Citation Count: Lund, Liaquat Ali...at all (2020). "Rotating 3d flow of hybrid nanofluid on exponentially shrinking sheet: Symmetrical solution and duality", Symmetry, Vol. 12, No. 10, pp. 1-14.
Rotating 3d flow of hybrid nanofluid on exponentially shrinking sheet: Symmetrical solution and duality
(2020) Lund, Liaquat Ali; Omar, Zurni; Dero, Sumera; Baleanu, Dumitru; Khan, Ilyas; 56389
This article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (Al2 O3 ), and copper (Cu) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Ω).
Citation Count: Lund, Liaquat Ali...et al. (2020). "Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition", Symmetry-Basel, Vol. 12, No. 1.
Stability Analysis and Dual Solutions of Micropolar Nanofluid over the Inclined Stretching/Shrinking Surface with Convective Boundary Condition
(2020) Lund, Liaquat Ali; Omar, Zurni; Khan, Umair; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
The present study accentuates the heat transfer characteristics of a convective condition of micropolar nanofluid on a permeable shrinking/stretching inclined surface. Brownian and thermophoresis effects are also involved to incorporate energy and concentration equations. Moreover, linear similarity transformation has been used to transform the system of governing partial differential equations (PDEs) into a set of nonlinear ordinary differential equations (ODEs). The numerical comparison has been done with the previously published results and found in good agreement graphically and tabular form by using the shooting method in MAPLE software. Dual solutions have been found in the specific range of shrinking/stretching surface parameters and the mass suction parameter for the opposing flow case. Moreover, the skin friction coefficient, the heat transfer coefficient, the couple stress coefficient, and the concentration transfer rate decelerate in both solutions against the mass suction parameter for the augmentation of the micropolar parameter respectively. The first (second) solution is the stable (unstable) solution and can (not) be considered as a real solution as the values of the smallest eigenvalues are positive (negative).
Citation Count: Lund, Liaquat Ali...et al. (2020). "Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface", Crystals, Vol. 10, No. 4.
Triple Solutions and Stability Analysis of Micropolar Fluid Flow on an Exponentially Shrinking Surface
(2020) Lund, Liaquat Ali; Omar, Zurni; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; 56389
In this article, we reconsidered the problem of Aurangzaib et al., and reproduced the results for triple solutions. The system of governing equations has been transformed into the system of non-linear ordinary differential equations (ODEs) by using exponential similarity transformation. The system of ODEs is reduced to initial value problems (IVPs) by employing the shooting method before solving IVPs by the Runge Kutta method. The results reveal that there are ranges of multiple solutions, triple solutions, and a single solution. However, Aurangzaib et al., only found dual solutions. The effect of the micropolar parameter, suction parameter, and Prandtl number on velocity, angular velocity, and temperature profiles have been taken into account. Stability analysis of triple solutions is performed and found that a physically possible stable solution is the first one, while all leftover solutions are not stable and cannot be experimentally seen.