scholarly journals Unsteady Stagnation-Point Flow and Heat Transfer Over a Permeable Exponential Stretching/Shrinking Sheet in Nanofluid with Slip Velocity Effect: A Stability Analysis

2018 ◽  
Vol 8 (11) ◽  
pp. 2172 ◽  
Author(s):  
Nor Dzulkifli ◽  
Norfifah Bachok ◽  
Nor Yacob ◽  
Norihan Md Arifin ◽  
Haliza Rosali
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Skin Friction ◽  
Stagnation Point ◽  
Velocity Slip ◽  
Shrinking Sheet ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Flow And Heat Transfer ◽  
Exponential Stretching

A model of unsteady stagnation-point flow and heat transfer over a permeable exponential stretching/shrinking sheet with the presence of velocity slip is considered in this paper. The nanofluid model proposed by Tiwari and Das is applied where water with Prandtl number 6.2 has been chosen as the base fluid, while three different nanoparticles are taken into consideration, namely Copper, Alumina, and Titania. The ordinary differential equations are solved using boundary value problem with fourth order accuracy (bvp4c) program in Matlab to find the numerical solutions of the skin friction and heat transfer coefficients for different parameters such as stretching/shrinking, velocity slip, nanoparticle volume fraction, suction/injection, and also different nanoparticles, for which the obtained results (dual solutions) are presented graphically. The velocity and temperature profiles are presented to show that the far field boundary conditions are asymptotically fulfilled, and validate the findings of dual solutions as displayed in the variations of the skin friction and heat transfer coefficients. The last part is to perform the stability analysis to determine a stable and physically-realizable solution.

Stability analysis on the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet with heat source effect

2018 ◽  
Vol 28 (11) ◽  
pp. 2650-2663 ◽  
Author(s):  
Fatinnabila Kamal ◽  
Khairy Zaimi ◽  
Anuar Ishak ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Source ◽  
Skin Friction ◽  
Stagnation Point ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Content Type ◽  
Source Effect ◽  
Flow And Heat Transfer

PurposeThis paper aims to analyze the behavior of the stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet in the presence of the viscous dissipation and heat source effects.Design/methodology/approachThe governing partial differential equations are converted into ordinary differential equations by similarity transformations before being solved numerically using the bvp4c function built in Matlab software. Effects of suction/injection parameter and heat source parameter on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented in the forms of tables and graphs. A temporal stability analysis will be conducted to verify which solution is stable for the dual solutions exist for the shrinking case.FindingsThe analysis indicates that the skin friction coefficient and the local Nusselt number as well as the velocity and temperature were influenced by suction/injection parameter. In contrast, only the local Nusselt number, which represents heat transfer rate at the surface, was affected by heat source effect. Further, numerical results showed that dual solutions were found to exist for the certain range of shrinking case. Then, the stability analysis is performed, and it is confirmed that the first solution is linearly stable and has real physical implication, while the second solution is not.Practical implicationsIn practice, the study of the steady two-dimensional stagnation-point flow and heat transfer past a permeable stretching/shrinking sheet in the presence of heat source effect is very crucial and useful. The problems involving fluid flow over stretching or shrinking surfaces can be found in many industrial manufacturing processes such as hot rolling, paper production and spinning of fibers. Owing to the numerous applications, the study of stretching/shrinking sheet was subsequently extended by many authors to explore various aspects of skin friction coefficient and heat transfer in a fluid. Besides that, the study of suction/injection on the boundary layer flow also has important applications in the field of aerodynamics and space science.Originality/valueAlthough many studies on viscous fluid has been investigated, there is still limited discoveries found on the heat source and suction/injection effects. Indeed, this paper managed to obtain the second (dual) solutions and stability analysis is performed. The authors believe that all the results are original and have not been published elsewhere.

scholarly journals Unsteady Stagnation Point Flow of Hybrid Nanofluid Past a Convectively Heated Stretching/Shrinking Sheet with Velocity Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1649
Author(s):  
Nurul Amira Zainal ◽  
Roslinda Nazar ◽  
Kohilavani Naganthran ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Skin Friction ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Velocity Slip ◽  
Slip Condition ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Unsteady stagnation point flow in hybrid nanofluid (Al2O3-Cu/H2O) past a convectively heated stretching/shrinking sheet is examined. Apart from the conventional surface of the no-slip condition, the velocity slip condition is considered in this study. By incorporating verified similarity transformations, the differential equations together with their partial derivatives are changed into ordinary differential equations. Throughout the MATLAB operating system, the simplified mathematical model is clarified by employing the bvp4c procedure. The above-proposed approach is capable of producing non-uniqueness solutions when adequate initial assumptions are provided. The findings revealed that the skin friction coefficient intensifies in conjunction with the local Nusselt number by adding up the nanoparticles volume fraction. The occurrence of velocity slip at the boundary reduces the coefficient of skin friction; however, an upward trend is exemplified in the rate of heat transfer. The results also signified that, unlike the parameter of velocity slip, the increment in the unsteady parameter conclusively increases the coefficient of skin friction, and an upsurge attribution in the heat transfer rate is observed resulting from the increment of Biot number. The findings are evidenced to have dual solutions, which inevitably contribute to stability analysis, hence validating the feasibility of the first solution.

Dual Solutions in Magnetohydrodynamic Stagnation-Point Flow and Heat Transfer Over a Shrinking Surface With Partial Slip

2014 ◽  
Vol 136 (10) ◽  
Author(s):  
Tapas Ray Mahapatra ◽  
Samir Kumar Nandy ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Stagnation Point ◽  
Fluid Velocity ◽  
Velocity Slip ◽  
Stagnation Point Flow ◽  
Partial Slip ◽  
Shrinking Sheet ◽  
Slip Parameter ◽  
Similarity Transformations ◽  
Flow And Heat Transfer

In this paper, the problem of steady two-dimensional magnetohydrodynamic (MHD) stagnation-point flow and heat transfer of an incompressible viscous fluid over a stretching/shrinking sheet is investigated in the presence of velocity and thermal slips. With the help of similarity transformations, the governing Navier–Stokes and the energy equations are reduced to ordinary differential equations, which are then solved numerically using a shooting technique. Interesting solution behavior is observed for the similarity equations with multiple solution branches for certain parameter domain. Fluid velocity increases due to the increasing value of the velocity slip parameter resulting in a decrease in the temperature field. Temperature at a point increases with increase in the thermal slip parameter. The effects of the slips, stretching/shrinking, and the magnetic parameters on the skin friction or the wall shear stress, heat flux from the surface of the sheet, velocity, and temperature profiles are computed and discussed.

scholarly journals Stability Analysis on Stagnation-Point Flow and Heat Transfer towards a Permeable Stretching/Shrinking Sheet with Heat Source in a Casson Fluid

CFD letters ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1-15
Author(s):  
Ubaidullah Yashkun ◽  
Fatinnabila Kamal ◽  
Khairy Zaimi ◽  
Nor Ashikin Abu Bakar ◽  
Norshaza Atika Saidin
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Heat Source ◽  
Stagnation Point ◽  
Casson Fluid ◽  
Stagnation Point Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer
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