scholarly journals Flow of nano-fluid over a sheet of variable thickness with non-uniform stretching (shrinking) and porous velocities

2021 ◽  
Vol 13 (4) ◽  
pp. 168781402110129
Author(s):  
Aftab Alam ◽  
Dil Nawaz Khan Marwat ◽  
Azhar Ali
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Wall Thickness ◽  
Variable Thickness ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Porous Plate ◽  
Concentration Profiles ◽  
Dimensionless Numbers ◽  
Nano Fluid

Nano-fluid flow is maintained over a non-uniform porous plate of variable thickness with non-uniform stretching (shrinking) velocity. In real engineering systems, the conduction resistance of sheets is necessarily important, whereas, in typical analysis very thin walls are undertaken. The surface thickness is ignored in the classical studies of flow, heat, and mass transfer problems. However, it the compulsory component in many physical problems, therefore, we thoroughly examined the perceptiveness of the wall thickness on the field variables and the transport of heat and nano-particle between solid surfaces and fluids. The phenomenon of variable wall thickness is extensively investigated with the combination of other boundary inputs. The variable stretching and shrinking velocities of the plate may have linear and non-linear forms and the sheet is uniformly heated whereas the nanoparticles are uniformly distributed over its surface. The diffusion of heat and nanoparticles in the fluid are governed using the boundary layer PDE’s, which satisfy certain BC’s. A set of unseen transformations is generated for solving the system of boundary value PDE’s. In view of these new variables, we obtained a system of boundary value ODE’s and it contains several dimensionless numbers (parameters). It is worthy noticeable that the problem describes and enhances the behavior of all field quantities in view of the governing parameters. All the field quantities, rates of heat and mass transfer are evaluated and effects all the parameters are seen on them and they are significantly changed with the variation of these dimensionless quantities. New results are presented in different graphs and tables and thoroughly examined. The Thermophoresis force enhances both the temperature and concentration profiles, however, the concentration distribution of nanoparticles is abruptly changed with a small variation in this force. The concentration profiles are bell-shaped on the right and behaves like a normal distribution. On the other hand, the addition of more nanoparticles into the base fluids increased (decreased) the temperature (concentration) profiles. Moreover, the two different attitudes of wall thickness are also examined on filed variables. The significant features and diversity of modeled equations are scrutinized and we recovered the previous problems of mass and heat transfer in Nano-fluid from a uniformly heated sheet of variable (uniform) thickness with variable (uniform) stretching/shrinking and injection/suction velocities. Moreover, two different numerical solutions of the modeled equations are found. These solutions are compared in a table and exactly matched with each other.

Heat and mass transfer on a stretching/shrinking and porous sheet of variable thickness with suction and injection

2021 ◽  
pp. 095440622098233
Author(s):  
Aftab Alam ◽  
Dil Nawaz Khan Marwat
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Variable Thickness ◽  
Porous Plate ◽  
Heated Plate ◽  
Dimensionless Numbers ◽  
Electrically Conducting ◽  
Steam Boilers ◽  
Plate Of Variable Thickness ◽  
Cartesian Coordinate

Heat and mass transfer in a viscous flow over a non-uniform porous plate of variable thickness is investigated in this paper. The variably heated plate is stretched/shrunk in a stagnant fluid with variable velocity and has the non-uniform species concentration. The governing partial differential equations are simplified and solved numerically. The transport of heat and mass in the flow regime is governed by a set of PDE’s satisfying certain necessary boundary conditions. The governing PDE’s are simplified by using boundary layer approximations and transformed into a set of ODE’s by invoking a set of new transformations. The system of ODE’s contains several dimensionless numbers (parameters) which demonstrates the behavior of all field quantities. All the unknown variables, rates of heat and mass transfer are evaluated and effects of the existing parameters are seen on them, whereas, they are significantly changed with the variation of these dimensionless quantities. New solutions and results are presented in graphs and tables, whereas, they are thoroughly examined and discussed. In addition to that the modeled problem and its solutions are exactly matched with the classical problems and their corresponding solutions for specific numerical values of the governing parameters involved in the current modeled problem. The engineering applications of heat and mass transfer problems are very famous in many industrial processes. Therefore, these two phenomena are widely discussed and analyzed, whereas, they are frequently utilized for the formation of metallic devices/objects while using additive manufacturing processes, cryogenics, formation of reasonable and suitable heat exchangers, falling film evaporation and the steam boilers. However, most of the engineering systems with or without magnetized and electrically conducting surfaces cannot be expressed in usual coordinates i.e. cartesian coordinate system, moreover, most of the engineering processes involve fluids of different nature and kinds, whereas, sometime they also require different physical and environmental conditions. Therefore, in such situations we need, to upgrade and modify the present modeled problem according to prevailing situations.

scholarly journals Unsteady Hydromagnetic Heat and Mass Transfer Flow of a Heat Radiating and Chemically Reactive Fluid Past a Flat Porous Plate with Ramped Wall Temperature

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
R. Nandkeolyar ◽  
M. Das ◽  
P. Sibanda
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Wall Temperature ◽  
Numerical Solutions ◽  
Porous Plate ◽  
Transfer Coefficients ◽  
Electrically Conducting ◽  
Fluid Properties ◽  
Parameter Values ◽  
Transfer Flow

Unsteady hydromagnetic free convective flow of a viscous, incompressible, electrically conducting, and heat radiating fluid past a flat plate with ramped wall temperature and suction/blowing is studied. The governing equations are first subjected to Laplace transformation and then inverted numerically usingINVLAProutine of Matlab. The numerical solutions of the fluid properties are presented graphically while the skin friction and heat and mass transfer coefficients are presented in tabular form. The results are verified by a careful comparison with results in the literature for certain parameter values.

scholarly journals A BINARY CHEMICAL REACTION ON UNSTEADY FREE CONVECTIVE BOUNDARY LAYER HEAT AND MASS TRANSFER FLOW WITH ARRHENIUS ACTIVATION ENERGY AND HEAT GENERATION/ABSORPTION

2014 ◽  
Vol 44 (1) ◽  
pp. 97-104
Author(s):  
KH. A. MALEQUE
Keyword(s):  
Activation Energy ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Numerical Solutions ◽  
Porous Plate ◽  
Local Similarity ◽  
Arrhenius Activation Energy

We investigate a local similarity solution of an unsteady natural convection heat and mass transfer boundary layer incompressible fluid flow past a moving vertical porous plate in the presence of the heat absorption and generation. The effects of chemical reaction rate which is function of temperature and Arrhenius activation energy on the velocity, temperature and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing local similarity transformation (Maleque, 2010a). Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim- Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity, temperature and concentration profiles. The corresponding skin friction coefficient, the Nusselt number and the Sherwood number are also calculated and displayed in table showing the effects of various parameters on them.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

scholarly journals Influence of Couple Stresses and Thermophoresis on Free Convective Heat and Mass Transfer of Viscoelastic Fluid.

2020 ◽  
Vol 17 ◽  
pp. 50-63
Author(s):  
N. T. M. Eldabe ◽  
Ahmed Refaie Ali ◽  
Gamil Ali Shalaby
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Viscoelastic Model ◽  
Skin Friction Coefficient ◽  
Physical Parameters ◽  
Couple Stresses ◽  
Linear Differential

A theoretical study has been developed to investigate the influence of thermophoresis and couple stresses on the steady flow of non-Newtonian fluid with free convective heat and mass transfer over a channel bounded by two permeable plates. The considered non-Newtonian fluid follows a viscoelastic model. The problem is modulated mathematically by a system of non-linear differential equations pertaining to describe the continuity, momentum, energy, and concentration. These equations involve the effects of viscous dissipation and chemical reaction. The numerical solutions of the dimensionless equations are found as a function of the physical parameters of this problem. The numerical formulas of the velocity (u), temperature Φ and concentration Θ as well as skin friction coefficient T*, Nusselt number(Nu) and Sherwood number(Sh) are computed. The physical parameter's effects of the problem on these formulas are described and illustrated graphically through some figures and tables. It is observed that any increase in the thermophoretic parameter T leads to reduce in velocity profiles as well as concentration layers. In contrast, the velocity increases with increasing the couple stresses inverse parameter.

Effect of Thermophoresis and Brownian Moment on 2D MHD Nanofluid Flow over an Elongated Sheet

2017 ◽  
Vol 377 ◽  
pp. 111-126 ◽  
Author(s):  
C. Sulochana ◽  
G.P Ashwinkumar ◽  
Naramgari Sandeep
Keyword(s):  
Mass Transfer ◽  
Heat Source ◽  
Heat And Mass Transfer ◽  
Newtonian Fluid ◽  
Numerical Solutions ◽  
Frictional Heating ◽  
Mass Transfer Rate ◽  
Dual Nature ◽  
Source Sink ◽  
The Impact

In this study, we investigated the 2D MHD flow of a dissipative Maxwell nanofluid past an elongated sheet with uneven heat source/sink, Brownian moment and thermophoresis effects. The flow governing PDEs are transmuted into nonlinear ODEs adopting the suitable similarity transmissions. Further, the RK-4 technique is employed to acquire the numerical solutions. The impact of pertinent parameters such as thermal radiation, frictional heating, irregular heat source/sink, biot number, Brownian moment and thermophoresis on the flow quantities such as velocity, thermal and concentration fields likewise friction factor, heat and mass transfer rates are bestowed with the succour of graphs and tables. Dual nature is witnessed for Newtonian and non-Newtonian fluid cases. It is noticed that the heat and mass transfer rate in Newtonian fluid larger as compared with non-Newtonian fluid.

Sign in / Sign up

Export Citation Format

Share Document