scholarly journals Time-space dependent fractional viscoelastic MHD fluid flow and heat transfer over accelerating plate with slip boundary

2017 ◽  
Vol 21 (6 Part A) ◽  
pp. 2337-2345
Author(s):  
Shengting Chen ◽  
Liancun Zheng ◽  
Chunrui Li ◽  
Jize Sui
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Fluid Model ◽  
Mhd Flow ◽  
Constitutive Relationship ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Slip Boundary ◽  
Flow And Heat Transfer ◽  
Time Space

The MHD flow and heat transfer of viscoelastic fluid over an accelerating plate with slip boundary are investigated. Different from most classical works, a modified time-space dependent fractional Maxwell fluid model is proposed in depicting the constitutive relationship of the fluid. Numerical solutions are obtained by explicit finite difference approximation and exact solutions are also presented for the limiting cases in integral and series forms. Furthermore, the effects of parameters on the flow and heat transfer behavior are analyzed and discussed in detail.

scholarly journals On the MHD flow and heat transfer of a micropolar fluid in a rectangular duct under the effects of the induced magnetic field and slip boundary conditions

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Hassan Nasr Ahamed Ismail ◽  
Aly Maher Abourabia ◽  
D. A. Hammad ◽  
Nasrelden A. Ahmed ◽  
A. A. El Desouky
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Boundary Conditions ◽  
Micropolar Fluid ◽  
Mhd Flow ◽  
Slip Boundary Conditions ◽  
Rectangular Duct ◽  
Induced Magnetic Field ◽  
Slip Boundary ◽  
Flow And Heat Transfer

MHD flow and heat transfer over a permeable stretching/shrinking sheet in a hybrid nanofluid with a convective boundary condition

2019 ◽  
Vol 29 (9) ◽  
pp. 3012-3038 ◽  
Author(s):  
Emad H. Aly ◽  
Ioan Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Numerical Solutions ◽  
Mhd Flow ◽  
Convective Boundary Condition ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid ◽  
Convective Boundary ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid. Design/methodology/approach Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter. Findings It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid. Originality/value The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

MHD FLOW AND HEAT TRANSFER IN A CASSON FLUID OVER A NONLINEARLY STRETCHING SHEET WITH NEWTONIAN HEATING

2018 ◽  
Vol 49 (12) ◽  
pp. 1185-1198 ◽  
Author(s):  
Abid Hussanan ◽  
Mohd Zuki Salleh ◽  
Hamzeh Taha Alkasasbeh ◽  
Ilyas Khan
Keyword(s):  
Heat Transfer ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Casson Fluid ◽  
Newtonian Heating ◽  
Flow And Heat Transfer ◽  
Nonlinearly Stretching Sheet

scholarly journals Unsteady MHD Flow and Heat Transfer over a Stretching Permeable Surface with Suction or Injection

2015 ◽  
Vol 127 ◽  
pp. 703-710 ◽  
Author(s):  
Mohan Kumar Choudhary ◽  
Santosh Chaudhary ◽  
Ritu Sharma
Keyword(s):  
Heat Transfer ◽  
Mhd Flow ◽  
Permeable Surface ◽  
Flow And Heat Transfer ◽  
Suction Or Injection

Unit Mobility Ratio Displacement Calculations for Pattern Floods in Homogeneous Medium

1966 ◽  
Vol 6 (03) ◽  
pp. 217-227 ◽  
Author(s):  
Hubert J. Morel-Seytoux
Keyword(s):  
Oil Recovery ◽  
Numerical Solutions ◽  
Mobility Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Numerical Techniques ◽  
Sweep Efficiency ◽  
Closed Form Solutions ◽  
Regular Patterns ◽  
Quantities Of Interest

Abstract The influence of pattern geometry on assisted oil recovery for a particular displacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presentsvery briefly, the methods and mathematical derivations required to obtain the results of engineering concern, andtypical results in the form of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston-like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M=1 and the numerical results for non-Piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed form solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected. BACKGROUND Pattern geometry is a major factor in making water-flood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Numerical solutions of non-alignment stagnation-point flow and heat transfer over a stretching/shrinking surface in a nanofluid

2016 ◽  
Vol 26 (6) ◽  
pp. 1747-1767 ◽  
Author(s):  
Ioan Pop ◽  
Kohi Naganthran ◽  
Roslinda Nazar
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Numerical Solutions ◽  
Dual Solutions ◽  
Stagnation Point Flow ◽  
Content Type ◽  
Boundary Layer Equations ◽  
Flow And Heat Transfer ◽  
Shrinking Surface

Purpose – The purpose of this paper is to analyse numerically the steady stagnation-point flow of a viscous and incompressible fluid over continuously non-aligned stretching or shrinking surface in its own plane in a water-based nanofluid which contains three different types of nanoparticles, namely, Cu, Al2O3 and TiO2. Design/methodology/approach – Similarity transformation is used to convert the system of boundary layer equations which are in the form of partial differential equations into a system of ordinary differential equations. The system of similarity governing equations is then reduced to a system of first-order differential equations and solved numerically using the bvp4c function in Matlab software. Findings – Unique solution exists when the surface is stretched and dual solutions exist as the surface shrunk. For the dual solutions, stability analysis has revealed that the first solution (upper branch) is stable and physically realizable, while the second solution (lower branch) is unstable. The effect of non-alignment is huge for the shrinking surface which is in contrast with the stretching surface. Practical implications – The results obtained can be used to explain the characteristics and applications of nanofluids, which are widely used as coolants, lubricants, heat exchangers and micro-channel heat sinks. This problem also applies to some situations such as materials which are manufactured by extrusion, production of glass-fibre and shrinking balloon. In this kind of circumstance, the rate of cooling and the stretching/shrinking process play an important role in moulding the final product according to preferable features. Originality/value – The present results are original and new for the study of fluid flow and heat transfer over a stretching/shrinking surface for the problem considered by Wang (2008) in a viscous fluid and extends to nanofluid by using the Tiwari and Das (2007) model.

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