scholarly journals Ordinary Differential Equations Models for Observing the Phenomena of Temperature Changes on a Single Rectangular Plate Fin

2021 ◽  
Vol 8 (1) ◽  
pp. 89-94
Author(s):  
Arief Goeritno
Keyword(s):  
Mass Transfer ◽  
Blood Flow ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Sherwood Number ◽  
Schmidt Number ◽  
Capillary Tube ◽  
Slip Parameter ◽  
Thermal Buoyancy ◽  
Buoyancy Parameter

In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equations (ODEs). Then the solutions are obtained by Runge-Kutta method of 4thorder with shooting technique. The effects of various parameters such as Hartman number, radiation parameter, unsteadiness parameter, permeable parameter, thermal buoyancy parameter, Prandtl number, mass buoyancy parameter, velocity slip parameter, thermal slip parameter, Schmidt number on velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are depicted through graphs. Local Sherwood number enhances because of increase in Schmidt number. Moreover, some of the important results, which are discussed in the present study and have an impact on diseases like hyperthermia, stoke and moyamoya in human body.

scholarly journals Influence of Buoyant Forces on Magnetohydrodynamics (MHD) Blood Flow with an Interaction of Thermal Radiation

2021 ◽  
Vol 8 (1) ◽  
pp. 71-80
Author(s):  
Madhusudan Senapati ◽  
Sampada Kumar Parida
Keyword(s):  
Mass Transfer ◽  
Blood Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Sherwood Number ◽  
Schmidt Number ◽  
Capillary Tube ◽  
Slip Parameter ◽  
Thermal Buoyancy ◽  
Buoyancy Parameter

In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equations (ODEs). Then the solutions are obtained by Runge-Kutta method of 4thorder with shooting technique. The effects of various parameters such as Hartman number, radiation parameter, unsteadiness parameter, permeable parameter, thermal buoyancy parameter, Prandtl number, mass buoyancy parameter, velocity slip parameter, thermal slip parameter, Schmidt number on velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are depicted through graphs. Local Sherwood number enhances because of increase in Schmidt number. Moreover, some of the important results, which are discussed in the present study and have an impact on diseases like hyperthermia, stoke and moyamoya in human body.

scholarly journals The Effect of Surface Roughness on Diffusion and Chemical Reaction Controlled Limiting Currents on a Rotating Cylinder Electrode in Deaerated Solutions with and Without CO2

CORROSION ◽  
10.5006/2552 ◽  
2018 ◽  
Vol 74 (9) ◽  
pp. 971-983 ◽  
Author(s):  
M. Al-Khateeb ◽  
R. Barker ◽  
A. Neville ◽  
H.M. Thompson
Keyword(s):  
Mass Transfer ◽  
Surface Roughness ◽  
Sherwood Number ◽  
Schmidt Number ◽  
Rotating Cylinder ◽  
Operating Conditions ◽  
Limiting Current ◽  
Surface Roughening ◽  
Rotating Cylinder Electrode ◽  
Effect Of Surface

The influence of surface roughness on mass transfer on a rotating cylinder electrode apparatus is investigated experimentally for a roughness pattern consisting of grooves parallel to the direction of fluid flow. Mass transfer from four different samples, with roughness values of 0.5 μm, 6 μm, 20 μm, and 34 μm, is measured using the limiting current technique for a range of rotational speeds in NaCl solutions saturated with N2 at pH = 3 and 4. Comparison with available correlations for the Sherwood number in literature (which are independent of surface roughness and are either for specific or arbitrary roughness patterns) shows that H+ mass transfer only correlates well for particular levels of roughness and that their accuracy can be increased if a correlation is utilized which is a function of surface roughening. A new correlation for Sherwood number as a function of the Reynolds number, Schmidt number, and surface roughness is proposed which agrees well with the mass transfer observed from all of the rough surface cases considered for this particular roughness pattern. Complementary experiments in CO2 environments were used to assess the combined limiting current associated with H+ and H2CO3 reduction (with the latter occurring via the buffering effect and being associated with the slow CO2 hydration step). Although the increase in sample roughness clearly leads to an increase in the rate of H+ mass transfer, in the CO2 environments considered, surface roughness is found to have no significant influence on the limiting current contribution from H2CO3, which can therefore be determined from Vetter’s equation across this range of operating conditions.

Lie Group Analysis for a Mixed Convective Flow and Heat Mass Transfer Over a Permeable Stretching Surface with Soret and Dufour Effects

2013 ◽  
Vol 30 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Reda G. Abdel-Rahman ◽  
Ahmed M. Megahed
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Analysis ◽  
Group Method ◽  
Stretching Surface ◽  
Partial Differential ◽  
Soret And Dufour Effects

ABSTRACTThe Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

Combined Heat and Mass Transfer in Mixed Convection over a Horizontal Flat Plate

1980 ◽  
Vol 102 (3) ◽  
pp. 538-543 ◽  
Author(s):  
T. S. Chen ◽  
F. A. Strobel
Keyword(s):  
Mass Transfer ◽  
Flat Plate ◽  
Heat And Mass Transfer ◽  
Transfer Rate ◽  
Buoyancy Force ◽  
Schmidt Number ◽  
Thermal Buoyancy ◽  
Buoyancy Forces ◽  
Thermal Buoyancy Force ◽  
Species Diffusion

The combined effects of buoyancy forces from thermal and species diffusion on the heat and mass transfer characteristics are analyzed for laminar boundary layer flow over a horizontal flat plate. The analysis is restricted to processes with low concentration levels such that the interfacial velocities due to mass diffusion and the diffusion-thermo/thermo-diffusion effects can be neglected. Numerical results for friction factor, Nusselt number, and Sherwood number are presented for gases having a Prandtl number of 0.7, with Schmidt numbers ranging from 0.6 to 2.0. In general, it is found that, for the thermally assisting flow, the surface heat and mass transfer rates as well as the wall shear stress increase with increasing thermal buoyancy force. These quantities are further enhanced when the buoyancy force from species diffusion assists the thermal buoyancy force, but are reduced when the two buoyancy forces oppose each other. While a higher heat transfer rate is found to be associated with a lower Schmidt number, a higher mass transfer rate occurs at a higher Schmidt number.

scholarly journals Effect of Thermal Radiation and Chemical Reaction on MHD Flow of Blood in Stretching Permeable Vessel

2020 ◽  
Vol 25 (3) ◽  
pp. 198-211
Author(s):  
B. Zigta
Keyword(s):  
Blood Flow ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reaction ◽  
Schmidt Number ◽  
Hartmann Number ◽  
Time Dependent ◽  
Reaction Parameter ◽  
Linear Partial Differential Equations ◽  
Chemical Reaction Parameter

AbstractThis paper focuses on the theoretical analysis of blood flow in the presence of thermal radiation and chemical reaction under the influence of time dependent magnetic field intensity. Unsteady non linear partial differential equations of blood flow consider time dependent stretching velocity, the energy equation also accounts time dependent temperature of vessel wall and the concentration equation includes the time dependent blood concentration. The governing non linear partial differential equations of motion, energy and concentration are converted into ordinary differential equations using similarity transformations solved numerically by applying ode45. The effect of physical parameters, viz., the permeability parameter, unsteadiness parameter, Prandtl number, Hartmann number, thermal radiation parameter, chemical reaction parameter and Schmidt number on flow variables, viz., velocity of blood flow in vessel, temperature and concentration of blood, has been analyzed and discussed graphically. From the simulation study the following important results are obtained: velocity of blood flow increases with the increment of both permeability and unsteadiness parameter. The temperature of blood increases at the vessel wall as the Prandtl number and Hartmann number increase. Concentration of blood decreases as time dependent chemical reaction parameter and Schmidt number increases.

Convective heat transport in a heat generating MHD vertical layer saturated by a non-Newtonian nanofluid: a bidirectional study

2020 ◽  
Vol 16 (6) ◽  
pp. 1669-1689 ◽  
Author(s):  
M. Gnaneswara Reddy ◽  
P. Vijayakumari ◽  
L. Krishna ◽  
K. Ganesh Kumar ◽  
B.C Prasannakumara
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stretching Sheet ◽  
Hartmann Number ◽  
Viscosity Ratio ◽  
Nonlinear Thermal Radiation ◽  
Content Type ◽  
Thermal Buoyancy ◽  
Nonlinear Radiation ◽  
The Impact

PurposeIn this framework, the three dimensional (3D) flow of hydromagnetic Carreau nanofluid transport over a stretching sheet has been addressed by considering the impacts of nonlinear thermal radiation and convective conditions.Design/methodology/approachInfinite shear rate viscosity impacts are invoiced in the modeling. The heat and mass transport characteristics are explored by employing the effects of a magnetic field, thermal nonlinear radiation and buoyancy effects. Rudimentary governing partial differential equations (PDEs) are represented and are transformed into ordinary differential equations by the use of similarity transformation. The nonlinear ordinary differential equations (ODEs), along with the boundary conditions, are resolved with the aid of a Runge-Kutta-Fehlberg scheme (RKFS) based on the shooting technique.FindingsThe impact of sundry parameters like the viscosity ratio parameter (β*), nonlinear convection parameters due to temperature and concentration (βT, βC), mixed convection parameter (α), Hartmann number (M2), Weissenberg number (We), nonlinear radiation parameter (NR), and the Prandtl number (Pr) on the velocity, temperature and the concentration distributions are examined. Furthermore, the impacts of important variables on the skin friction, Nusselt number and the Sherwood number have been scrutinized through tables and graphical plots.Originality/valueThe velocity distribution is suppressed by greater values of the Hartmann number. The velocity components in the tangential and axial directions of the fluid are raised with the viscosity ratio parameter and the tangential slip parameter, but these components are reduced with concentration to thermal buoyancy forces ratio and stretching sheet ratio.

scholarly journals Similarity Analysis for Effects of Variable Diffusivity and Heat Generation/Absorption on Heat and Mass Transfer for a MHD Stagnation-Point Flow of a Convective Viscoelastic Fluid over a Stretching Sheet with a Slip Velocity

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
H. M. El-Hawary ◽  
Mostafa A. A. Mahmoud ◽  
Reda G. Abdel-Rahman ◽  
Abeer S. Elfeshawey
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Viscoelastic Fluid ◽  
Slip Velocity ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Local Skin

A mathematical analysis has been carried out for stagnation-point heat and mass transfer of a viscoelastic fluid over a stretching sheet with surface slip velocity, concentration dependent diffusivity, thermal convective boundary conditions, and heat source/sink. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using Lie group analysis. Numerical solutions of the resulting ordinary differential equations are obtained using shooting method. The influences of various parameters on velocity, temperature, and mass profiles have been studied. Also, the effects of various parameters on the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are given in graphics form and discussed.

Stagnation-Point Flow of a Jeffrey Nanofluid over a Stretching Surface with Induced Magnetic Field and Chemical Reaction

2015 ◽  
Vol 20 ◽  
pp. 93-111 ◽  
Author(s):  
Naramgari Sandeep ◽  
Chalavadi Sulochana ◽  
Isaac Lare Animasaun
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Stagnation Point ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Stretching Surface ◽  
Jeffrey Nanofluid

With every passing day the heat transfer enhancement in the convectional base fluids plays a major role in several industrial and engineering processes. During these process nanofluids has attained its great importance to enhance the heat transfer rate in the convectional flows. Keeping this into view, in this study we investigated the stagnation point flow, heat and mass transfer behaviour of MHD Jeffrey nanofluid over a stretching surface in the presence of induced magneticfield, non-uniform heat source or sink and chemical reaction. Using similarity technique, the governing boundary layer partial differential equations are transformed into nonlinear coupled ordinary differential equations. The ordinary differential equations are solved numerically using Runge-Kutta-Felhberg scheme. An excellent agreement of the present results has been observed with the existed literature under some special cases. The effects of various dimensionless governing parameters on velocity, induced magneticfield, temperature and nanoparticle concentration profiles are discussed and presented through graphs. Also, friction factor, local Nusselt and Sherwood numbers are computed and discussed. Dual solutions are presented for suction and injection cases. It is found that dual solutions exist only for certain range of suction or injection parameter. It is also observed that an increase in the heat and mass transfer rate for higher values of Deborah number.

Effects of Chemical Reaction and Soret Effect on Mixed Heat and Mass Transfer for Hiemenz flow through Porous Media with Heat Source

2012 ◽  
Vol 197 ◽  
pp. 712-716 ◽  
Author(s):  
S. Shateyi ◽  
S.S. Motsa
Keyword(s):  
Mass Transfer ◽  
Porous Media ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Soret Effect ◽  
Flow Through Porous Media ◽  
Hiemenz Flow ◽  
Flow Through

The effects of chemical reaction and thermal-diffusion mixed convection heat and mass transfer for Hiemenz flow through porous media has been studied. The plate is embedded in a uniform porous medium in order to allow for possible fluid wall suction or blowing and has a power-law variation of both the wall temperature and concentration. We used similarity solution to transform the system of partial differential equations, into a boundary value problem of coupled ordinary differential equations. We then solve these ordinary differential equations by a MATLAB routine bvp4c. We conducted a parametric study of all involved parameters and the results represented graphically.

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