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

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.

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

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2020-0043 ◽

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.

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Numerical study of thermal radiation and mass transfer effects on free convection flow over a moving vertical porous plate using cubic B-spline collocation method

Journal of the Egyptian Mathematical Society ◽

10.1186/s42787-019-0035-8 ◽

2019 ◽

Vol 27 (1) ◽

Author(s):

M. Abu zeid ◽

Khalid K. Ali ◽

M. A. Shaalan ◽

K. R. Raslan

Keyword(s):

Mass Transfer ◽

Differential Equations ◽

Free Convection ◽

Thermal Radiation ◽

Porous Plate ◽

Convection Flow ◽

Spline Collocation ◽

Free Convection Flow ◽

B Spline ◽

Vertical Porous Plate

Abstract In this paper, we present a numerical method based on cubic B-spline function for studying the effects of thermal radiation and mass transfer on free convection flow over a moving vertical porous plate. Similarity transformations reduced the governing partial differential equations of the fluid flow to a system of nonlinear ordinary differential equations which are solved numerically using a cubic B-spline collocation method. The effects of various physical parameters on the velocity, temperature, and concentration distributions are shown graphically, and the numerical values of physical quantities like skin friction, Nusselt number, and Sherwood number for various parameters are presented in tabular form and discussed.

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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 ◽

Cited By ~ 4

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.

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

Journal of Heat Transfer ◽

10.1115/1.3244337 ◽

1980 ◽

Vol 102 (3) ◽

pp. 538-543 ◽

Cited By ~ 11

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.

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Effects of Exothermic/Endothermic Chemical Reactions with Arrhenius Activation Energy on MHD Free Convection and Mass Transfer Flow in Presence of Thermal Radiation

Journal of Thermodynamics ◽

10.1155/2013/692516 ◽

2013 ◽

Vol 2013 ◽

pp. 1-11 ◽

Cited By ~ 39

Author(s):

Kh. Abdul Maleque

Keyword(s):

Activation Energy ◽

Mass Transfer ◽

Differential Equations ◽

Thermal Radiation ◽

Chemical Reactions ◽

Numerical Solutions ◽

Porous Plate ◽

Local Similarity ◽

Shooting Methods ◽

Arrhenius Activation Energy

A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with 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 locally similarity transformation (Maleque (2010)). Numerical solutions to the reduced nonlinear 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 obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow () and shows excellent agreement with Bestman (1990), hence encouragement for the use of the present computations.

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Effect of Thermal Radiation, Chemical Reaction and Viscous Dissipation on MHD Flow

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2018-0043 ◽

2018 ◽

Vol 23 (3) ◽

pp. 787-801

Author(s):

B. Zigta

Keyword(s):

Kinetic Energy ◽

Differential Equations ◽

Thermal Radiation ◽

Viscous Dissipation ◽

Chemical Reaction ◽

Energy Equation ◽

Eckert Number ◽

Radiation Chemical ◽

Thermal Buoyancy ◽

Molecular Diffusivity

Abstract This study examines the effect of thermal radiation, chemical reaction and viscous dissipation on a magnetohydro- dynamic flow in between a pair of infinite vertical Couette channel walls. The momentum equation accounts the effects of both the thermal and the concentration buoyancy forces of the flow. The energy equation addresses the effects of the thermal radiation and viscous dissipation of the flow. Also, the concentration equation includes the effects of molecular diffusivity and chemical reaction parameters. The gray colored fluid considered in this study is a non-scattering medium and has the property of absorbing and emitting radiation. The Roseland approximation is used to describe the radiative heat flux in the energy equation. The velocity of flow transforms kinetic energy into heat energy. The increment of the velocity due to internal energy results in heating up of the fluid and consequently it causes increment of the thermal buoyancy force. The Eckert number being the ratio of the kinetic energy of the flow to the temperature difference of the channel walls is directly proportional to the thermal energy dissipation. It can be observed that increasing the Eckert number results in increasing velocity. A uniform magnetic field is applied perpendicular to the channel walls. The temperature of the moving wall is high enough due to the presence of thermal radiation. The solution of the governing equations is obtained using regular perturbation techniques. These techniques help to convert partial differential equations to a set of ordinary differential equations in dimensionless form and thus they are solved analytically. The following results are obtained: from the simulation study it is observed that the flow pattern of the fluid is affected due to the influence of the thermal radiation, the chemical reaction and viscous dissipation. The increment in the Hartmann number results in the increment of the Lorentz force but a decrement in velocity of the flow. An increment in the radiative parameter results in a decrement in temperature. An increment in the Prandtl number results in a decrement in thermal diffusivity. An increment in both the chemical reaction parameter and molecular diffusivity results in a decrement in concentration.

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Thermal radiation and magnetic field effects on unsteady mixed convection flow and mass transfer over a porous stretching surface with heat generation

International Journal of Applied Mechanics and Engineering ◽

10.2478/ijame-2013-0071 ◽

2013 ◽

Vol 18 (4) ◽

pp. 1151-1164 ◽

Cited By ~ 1

Author(s):

G.V.R. Reddy ◽

B.A. Reddy ◽

N.B. Reddy

Keyword(s):

Mass Transfer ◽

Differential Equations ◽

Mixed Convection ◽

Thermal Radiation ◽

Heat Generation ◽

Convection Flow ◽

Physical Parameters ◽

Mixed Convection Flow ◽

Stretching Surface ◽

Porous Stretching Surface

Abstract The effects of thermal radiation and mass transfer on an unsteady hydromagnetic boundary layer mixed convection flow along a vertical porous stretching surface with heat generation are studied. The fluid is assumed to be viscous and incompressible. The governing partial differential equations are transformed into a system of ordinary differential equations using similarity variables. Numerical solutions of these equations are obtained by using the Runge-Kutta fourth order method along with the shooting technique. Velocity, temperature, concentration, the skin-friction coefficient, Nusselt number and Sherwood number for variations in the governing thermo physical parameters are computed, analyzed and discussed.

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Heat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluids

Journal of Applied Mathematics ◽

10.1155/2020/1890972 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13 ◽

Cited By ~ 2

Author(s):

Tesfaye Kebede ◽

Eshetu Haile ◽

Gurju Awgichew ◽

Tadesse Walelign

Keyword(s):

Magnetic Field ◽

Boundary Layer ◽

Mass Transfer ◽

Differential Equations ◽

Boundary Conditions ◽

Thermal Radiation ◽

Heat And Mass Transfer ◽

Chemical Reaction ◽

Stretching Sheet ◽

Analytic Approximation

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

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Convection heat and mass transfer in a hydromagnetic Carreau fluid past a vertical porous plate in presence of thermal radiation and thermal diffusion

Thermal Science ◽

10.2298/tsci101026060o ◽

2011 ◽

Vol 15 (suppl. 2) ◽

pp. 241-252 ◽

Cited By ~ 31

Author(s):

Ishola Olajuwon

Keyword(s):

Mass Transfer ◽

Differential Equations ◽

Thermal Radiation ◽

Heat And Mass Transfer ◽

Thermal Diffusion ◽

Porous Plate ◽

Convection Heat ◽

Carreau Fluid ◽

Vertical Porous Plate ◽

Linear Partial Differential Equations

The paper presents the numerical investigation of the convection heat and mass transfer in a hydromagnetic Carreau fluid past a vertical porous plate in presence of thermal radiation and thermal diffusion. The non-linear partial differential equations governing the flow are transformed into ordinary differential equations using the usual similarity method and the resulting similarity equations are solved numerically using Runge-Kutta shooting method. The results are presented as velocity, temperature and concentration profiles for different values of parameters entering into the problem. The effects of suction, magnetic field, thermal radiation and thermal diffusion on the skin friction, rate of heat transfer and mass transfer are presented numerically in tabular form.

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