scholarly journals MHD Flow and Heat Transfer of Double Stratified Micropolar Fluid over a Vertical Permeable Shrinking/Stretching Sheet with Chemical Reaction and Heat Source

2020 ◽  
Vol 21 (1) ◽  
pp. 1-14
Author(s):  
Ansab Azam Khan ◽  
Suliadi Firdaus Sufahani ◽  
Khairy Zaimi ◽  
Mohammad Ferdows
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Sherwood Number ◽  
Micropolar Fluid ◽  
Numerical Solutions ◽  
Mhd Flow ◽  
Shrinking Sheet ◽  
Local Sherwood Number

The present study analyses the magnetohydrodynamic (MHD) flow of a double stratified micropolar fluid across a vertical stretching/shrinking sheet in the presence of suction, chemical reaction, and heat source effects. The governing equations in the form of partial differential equations are transitioned into coupled nonlinear ordinary differential equations by means of similarity transformation. The numerical solutions are obtained with the aid of the boundary value problem bvp4c solver in the MATLAB software. Numerical results have been confirmed with the previous results for a certain case and the comparison is found to be in an excellent agreement. Results for related profiles and heat transfer characteristics are displayed through plots and tabulated for the governing parameters involved. It is found that the reduced skin friction coefficient and the local Nusselt number increase with the increasing chemical reaction and heat source parameters. The rising values of the chemical reaction parameter have increased the magnitude of the local Sherwood number. In contrary, the heat source parameter has the tendency to decrease the magnitude of the local Sherwood number.

scholarly journals MHD Mixed Convection Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Over a Vertical Stretching/ Shrinking Sheet With Suction, Chemical Reaction and Heat Source

CFD letters ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 106-120
Author(s):  
Ansab Azam Khan ◽  
Khairy Zaimi ◽  
Suliadi Firdaus Sufahani ◽  
Mohammad Ferdows
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Sherwood Number ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Shrinking Sheet ◽  
Flow And Heat Transfer ◽  
Local Sherwood Number

The purpose of this study was to investigate the magnetohydrodynamic (MHD) mixed convection flow and heat transfer of a dual stratified micropolar fluid over a vertical permeable stretching/ shrinking sheet with chemical reaction and heat source. The governing nonlinear partial differential equations are reduced into a system of nonlinear ordinary differential equations using an appropriate similarity transformation. Then, the obtained ordinary differential equations are solved numerically using the boundary value problem solver (bvp4c) in MATLAB software. The numerical results are tabulated and plotted for the heat transfer characteristics, namely, the skin friction coefficient, the local Nusselt number, the local Sherwood number as well as the velocity, temperature and concentration profiles for some values of the governing parameters. The present numerical results also have been compared with the previous reported results for a particular case and the comparisons are found to be in an excellent agreement. The results indicate that the skin friction coefficient and the local Nusselt number increase with chemical reaction and heat source. The magnitude of the local Sherwood number increases with the increasing of chemical reaction parameter. However, the magnitude of the local Sherwood number decreases with heat source effect.

scholarly journals Mixed Convective Flow and Heat Transfer of a Dual Stratified Micropolar Fluid Induced by a Permeable Stretching/Shrinking Sheet

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1162 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
Nadihah Wahi ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Convective Flow ◽  
Mhd Flow ◽  
Similarity Solutions ◽  
Surface Velocity ◽  
Shrinking Sheet ◽  
Transfer Characteristics ◽  
Flow And Heat Transfer

The present study accentuates the magnetohydrodynamics (MHD) flow and heat transfer characteristics of a dual stratified micropolar fluid over a permeable stretching/shrinking sheet. Thermal and solutal buoyancy forces are also included to incorporate with the stratification effect. Similarity, transformation is applied to reduce the governing model (partial differential equations) into a set of nonlinear ordinary differential equations (ODEs) due to its complexity. Using bvp4c solver in the MATLAB software, numerical results for some limiting cases are in favorable agreement with the earlier published results. Both assisting and opposing buoyancy flows have dual similarity solutions within specific range of suction and stretching/shrinking parameters, whereas only a distinctive solution is observed for pure forced convective flow. The micropolar fluid shows a disparate pattern of flow, heat and mass transfer characteristics between stretching and shrinking cases. Unlike the shrinking flow, the surface velocity gradient, local Nusselt and Sherwood numbers for stretching flow intensify with the increment of the material parameter. The result from stability analysis reveals that the first solution is the real solution, whereas the second solution is virtual.

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.

scholarly journals Flow and Heat Transfer at a Nonlinearly Shrinking Porous Sheet:The Case of Asymptotically Large Powerlaw Shrinking Rates

2013 ◽  
Vol 18 (3) ◽  
pp. 779-791 ◽  
Author(s):  
K.V. Prasad ◽  
K. Vajravelu ◽  
I. Pop
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Power Law ◽  
Numerical Solutions ◽  
Skin Friction Coefficient ◽  
Temperature Fields ◽  
Shrinking Sheet ◽  
Arbitrary Power ◽  
Keller Box Method ◽  
Flow And Heat Transfer

Abstract The boundary layer flow and heat transfer of a viscous fluid over a nonlinear permeable shrinking sheet in a thermally stratified environment is considered. The sheet is assumed to shrink in its own plane with an arbitrary power-law velocity proportional to the distance from the stagnation point. The governing differential equations are first transformed into ordinary differential equations by introducing a new similarity transformation. This is different from the transform commonly used in the literature in that it permits numerical solutions even for asymptotically large values of the power-law index, m. The coupled non-linear boundary value problem is solved numerically by an implicit finite difference scheme known as the Keller- Box method. Numerical computations are performed for a wide variety of power-law parameters (1 < m < 100,000) so as to capture the effects of the thermally stratified environment on the velocity and temperature fields. The numerical solutions are presented through a number of graphs and tables. Numerical results for the skin-friction coefficient and the Nusselt number are tabulated for various values of the pertinent parameters.

scholarly journals The NANOFLUID FLOW BETWEEN PARALLEL PLATES AND HEAT TRANSFER IN PRESENCE OF CHEMICAL REACTION AND POROUS MATRIX

2020 ◽  
Vol 50 (4) ◽  
pp. 283-289
Author(s):  
S. Jena ◽  
S. R. Mishra ◽  
P.K. Pattnaik ◽  
Ram Prakash Sharma
Keyword(s):  
Heat Transfer ◽  
Heat Source ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Porous Matrix ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Similarity Transformations ◽  
Fourth Order Method ◽  
Source Sink

This paper deals with nanofluid flow between parallel plates and heat transfer through porous media with heat source /sink. The governing equations are transformed into self-similar ordinary differential equations by adopting similarity transformations and then the converted equations are solved numerically by Runge-Kutta fourth order method. Special emphasis has been given to the parameters of physical interest which include Prandtl number, magnetic parameter, porous matrix, chemical reaction parameter and heat source parameter. The results obtained for velocity, temperature and concentration are shown in graphs. The comparison of the special case of this present results with the existing numerical solutions in the literature shows excellent agreement.

scholarly journals Analysis of Chemical Reaction on MHD Micropolar Fluid Flow over a Shrinking Sheet near Stagnation Point with Nanoparticles and External Heat

2021 ◽  
Vol 39 (1) ◽  
pp. 262-268
Author(s):  
Krishnandan Verma ◽  
Debozani Borgohain ◽  
Bishwaram Sharma
Keyword(s):  
Stagnation Point ◽  
Chemical Reaction ◽  
Micropolar Fluid ◽  
Numerical Data ◽  
Mhd Flow ◽  
Heat Transfer Process ◽  
External Heat ◽  
Shrinking Sheet ◽  
Similarity Transformations ◽  
Micropolar Nanofluid

The present study investigates numerically MHD flow near the stagnation point of micropolar fluid through a shrinking sheet containing nanoparticles under the influence of chemical reaction and external heat. The study is an attempt to investigate the flow behaviour of micropolar nanofluid because of its importance in heat transfer process in industries as well as cooling systems. The governing equations are converted to nonlinear ordinary differential equations by implementing similarity transformations. Numerical results are investigated in the form of figures and tables by using MATLAB built in solver bvp4c for various dimensionless parameters. The impacts of external heat parameter on temperature and chemical reaction factor on concentration of the nanofluid are illustrated in the form of graphs. It is observed that the temperature of the nanofluid and nanoparticle volume distributions increase when Biot number attain larger values. Rise in Thermophoretic parameter increases the nanoparticles concentration in the boundary layer. Numerical data are presented for Nusselt number and Sherwood number.

scholarly journals Stability analysis of heat transfer in nanomaterial flow of boundary layer towards a shrinking surface: Hybrid nanofluid versus nanofluid

2021 ◽  
Author(s):  
Aqeel ur Rehman ◽  
Zaheer Abbas
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stable Solution ◽  
Mhd Flow ◽  
Least Square Method ◽  
Dual Solutions ◽  
Least Square ◽  
Shrinking Sheet ◽  
Hybrid Nanofluid

Many boundary value problems (BVPs) have dual solutions in some cases containing one stable solution (upper branch) while other unstable (lower branch). In this paper, MHD flow and heat transfer past a shrinking sheet is studied for three distinct fluids: kerosene hybrid nanofluid, kerosene nanofluid, and kerosene nanofluid. The partial differential equations (PDEs) are turned into ordinary differential equations (ODEs) using an appropriate transformation and then dual solutions are obtained analytically by employing the Least Square method (LSM). Moreover, stability analysis is implemented on the time-dependent case by calculating the least eigenvalues using Matlab routine bvp4c. It is noticed that negative eigenvalue is related to unstable solution i.e., it provides initial progress of disturbance and positive eigenvalue is related to stable solution i.e., the disturbance in solution decline initially. The impacts of various parameters, skin friction coefficient, and local Nusselt number for dual solutions are presented graphically. It is also noted that the results obtained for hybrid nanofluids are better than ordinary nanofluids.

Radiation and heat source effects on MHD flow over a permeable stretching sheet through porous stratum with chemical reaction

2018 ◽  
Vol 14 (5) ◽  
pp. 1101-1114 ◽  
Author(s):  
K. Suneetha ◽  
S.M. Ibrahim ◽  
G.V. Ramana Reddy
Keyword(s):  
Porous Medium ◽  
Differential Equations ◽  
Heat Source ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Mhd Flow ◽  
Working Fluid ◽  
Content Type ◽  
Source Effects ◽  
Similarity Transformations

Purpose The purpose of this paper is to investigate the steady 2D buoyancy effects on MHD flow over a permeable stretching sheet through porous medium in the presence of suction/injection. Design/methodology/approach Similarity transformations are employed to transform the governing partial differential equations into ordinary differential equations. The transformed equations are then solved numerically by a shooting technique. Findings The working fluid is examined for several sundry parameters graphically and in tabular form. It is observed that with an increase in magnetic field and permeability of porous parameter, velocity profile decreases while temperature and concentration enhances. Stretching sheet parameter reduces velocity, temperature and concentration, whereas it increases skin friction factor, Nusselt number and Sherwood number. Originality/value Till now no numerical studies are reported on the effects of heat source and thermal radiation on MHD flow over a permeable stretching sheet embedded in porous medium in the presence of chemical reaction.

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