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In this investigation, the heat and mass transfer on unstable MHD convective flow of a non-compressible gelatinous electrical performing non-Newtonians Cassons hybrid nanoliquid past an unbounded exponential accelerated perpendicular stirring spongy surface underneath the influences of slips velocity has been discussed. H2O as well as ethyleneglycol mixtures have been taking as the fundamental Cassons fluid. The stable homogeneous magnetic domain was applied underneath the presumption of least magnetic Reynold numbers. The ramped walls temperatures as well as time changing concentrations near the surface were constructed into consideration. The initial ordered systematical chemical reacting and heat absorptions were also considering. Silver (Ag) in addition to CuO nanoparticles were spread in fundamental liquid H2O as well as ethylene-glycol combined to be produced as hybrids nanoliquid. The Laplaces transformations techniques are applied on the in-dimensional leading equations for the closed forms solution. The equations for the non-dimensionalized shear stresses, rate of temperature along with accumulation transport were also obtained. The graphical solutions are represented to scrutinized the impacts of physically parameters on the most important flow features. The computational quantities of the shear stress, rates of heat as well as mass transport near the surface were tabulate with the distinct entrenched parametrics. The resulting velocity was growing by an enhancing in heat as well as concentrations buoyancy strengths, while slips parameter has opposite outcome on this for case of ramped walls temperatures. The current problems have most appliances by magnetic material processes, electrical performing polymers mechanics, as well as purifications of molten metals with non-metallics.

Nanofluid flow has acquired various interesting dimensions with the advent of several novel approaches to studying thermophysical properties. The present work focuses on a comparative study of clear viscous and nanofluid (EG−Al2O3, EG−Zr, H2O−Al2O3, H2O−Zr) flow in a two-phase inclined channel saturated with a porous medium in the presence of thermal radiation, species diffusion, and viscous and Darcy dissipation effects. The controlling equations of the flow model were solved analytically using the regular perturbation technique. The graphical solutions are used to examine the impacts of physical parameters on the most significant flow features. Surface graphs with distinct entrenched parameters represent heat transfer rates and shear stresses on plates. The resulting heat transfer was enhanced by raising the thermal and solute buoyancy strengths, while thermal radiation had the opposite outcome. This enhancement of temperature was maximum for water–zirconium and minimum for ethylene glycol–aluminum oxide nanofluid. The concentration of the entire fluid medium is reduced by decreased mass diffusivity. The enhancement of temperature and velocity is found to be maximum in the nanofluid region and clear fluid region, respectively. This study is validated with previously published works to demonstrate its effectiveness.

This study explores the influence of an inclined magnetic field and variable viscosity on the entropy generation in steady flow of a couple stress fluid in an inclined channel. The walls of the channel are stationary and non-isothermal. The fluid flow is driven due to pressure gradient and gravitational force. Reynold’s model for temperature-dependent viscosity was used. The dimensionless, non-linear coupled equations of momentum and energy was solved, and we obtained an analytical solution for the velocity and temperature fields. The entropy generation and Bejan number were evaluated. The variation of pertinent parameters on flow quantities was discussed graphically. The rate of volume flow, skin friction coefficient, and Nusselt number at the surfaces of the channel were calculated and their variations were discussed through surface graphs. From the results, it is noticed that the entropy generation rate can be minimized by increasing the magnetic field and the temperature difference parameters. The findings of the current study in some special cases are in precise agreement with the previous investigation.

This mathematical model explains the three-dimensional flow of Casson liquid through a stretchable rotating disk. In momentum equation magnetic effect and in mass equation Arrhenius chemical reaction and activation energy effects are incorporated. The equation which represents the described flow pattern is reduced to ordinary differential equations (ODEs) by using apposite similarity transformations and then they are tackled with the RKF45 method with shooting proficiency. The impact of pertinent parameters on thermal, mass and velocity curves are deliberated graphically. Further statistical values of skin friction, Nusselt number and Sherwood number are portrayed in table format. The result outcome reveals that, increase in the values of a magnetic parameter reduces velocity gradient. The concentration profile declines for augmented values of chemical reaction rate parameter, but a contrasting trend is seen in the concentration gradient for increased values of activation energy. Further, upsurge in thermophoretic and Brownian motion parameter reduces the mass transfer.

The main aim of the present investigation is to examine the imapacts of Cattaneo-Christov double diffusions, variable properties and activation energy on Eyring-Powell non-Newtonian liquid over a non-linear stretching surafce numerically. The features of applied magnetic field and velocity slip condition is also considered in the modeling. The flow governing system of partial differential equations (PDE's) is simpliefied into a non-linear differential system through the relevant similarity transfromations and determined flow equations are resolved numerically. The distributions for flow field, temperature and species, skin-friction coefficient, rate of heat and mass transfers for the impactsundry flow variables has been reported subject to the two-dimensional (2D) plots. The comparison has been emphasized with the published outcomes through a table and found that a good agreement for the present numerical procedure. The fluid velocity is diminished for escalating slip parameter. It is revealed that that the related solutal and thermal energy fields are declined for escalating values of solutal and thermal relaxation time parameters. The dimensionless velocity is an enhancing function for the Eyring-Powell fluid parameter K. The thermal and concentration layers are improves for the variable thermal conductivity and solutal diffusivity. The current investigation has the significant features in maintain of advanced nuclear reactor systems.

An electrically conducting three-dimensional non-Newtonian Carreau fluid induced by bidirectional movement of sheet is demonstrated in this work. The aspects of viscous heating, radiation and first-order chemical reactions are executed in energy transport and mass species expressions. The new variables are defined to restructure the mathematical problem into single independent variable equations (ordinary differential equations, ODE’s). The re-framed ODE’s are exploited numerically through the utilization of MATLAB bvp4c package. The derived results of velocities, temperature and species distributions are executed graphically and interpreted physically for both shear-thinning and shear-thickening cases. Also, the numerical results for coefficients of skin friction, rate of mass transfer in terms of Sherwood number and rate of heat transfer in terms of Nusselt number are presented in tables. The influence of local Weissenberg numbers on Sherwood and Nusselt numbers for shear-thinning fluids is reversed to shear-thickening fluids. The thermal radiation parameter enhances the fluid temperature, and chemical reaction parameter decelerates the fluid concentration.

This problem discusses the magnetic field effects on the flow of Cattaneo-Christov heat flux model for MoS2 and MgO water-based nanofluid past a stretching sheet. The effects of Uniform heat source...

In this paper, we propose a mathematical model to analyze the effect of a non-uniform heat source or sink on chemically reacting magnetohydrodynamic Casson fluid flowing across a slendering sheet. A chemically reacting fluid with multiple slips has various applications in controlling heating and mass transport phenomena such as biological reactants being converted to products, biomedical signal processing and image processing to establish a dynamic area of specialization in research aspects of biomedical engineering. For these reasons multiple slips (diffusion, thermal and momentum slips) are applied in modeling the heat and mass transfer process. The non-linear ordinary differential equations (ODEs) are solved using the Runge-Kutta-Fehlberg integration method. The characteristics of the velocity, temperature and concentration boundary layers are presented for different physical parameters such as space and temperature-dependent heat source or sink parameter, porosity parameter, chemical reaction parameter, velocity slip parameter, and temperature and concentration jump parameters. Moreover, the skin friction coefficient, and the local Nusselt and Sherwood numbers have been estimated for different parameters are discussed from an engineering point of view. We found a significant increase in thickness of the thermal and concentration boundary layer when the strength of the thermophoresis parameter is increased. In contrast, the thermal boundary layer increases with increasing the Brownian motion parameter while the reverse trend holds true for the concentration field.

The present paper is on 2D Casson magnetohydrodynamic flow through exponentially shrinking surface. The set of nonlinear PDEs are established into ODEs by using R-K scheme connected by shooting methodology. Some of the physical quantities are implemented to demonstrate the effects of exponential, Eckert number, Casson and radiation parameters on temperature and velocity distributions. The constraint of Eckert numbers decelerates the rate of heat transfer in both \( \Pr = 2 \) and \( \Pr = 9 \) cases.

The current paper scrutinizes the sway of the aligned magnetic field and Kuvshinski fluid model on unsteady MHD free convective flow past a moving inclined plate in the occurrence of thermal radiation as well as radiation absorption with chemical effect and mass blowing or suction. It is implicit that the plate is entrenched in a uniform porous medium moving with a steady velocity in the flow direction and in the existence of a transverse magnetic field. Perturbation technique was employed for solving non-dimensional governing equations. Significant consequences with regard to embedded parameters are illustrated graphically for the temperature, velocity, and concentration profiles. The expression for the Skin friction coefficient is also obtained.

In this paper the effects of Diffusion thermo, radiation absorption and chemical reaction on MHD free convective heat and mass transfer flow of a nanofluid bounded by a semi-infinite flat plate are analyzed. The plate is moved with a constant velocity U0, temperature and the concentration are assumed to be fluctuating with time harmonically from a constant mean at the plate. The analytical solutions of the boundary layer equations are assumed of oscillatory type and are solved by using the small perturbation technique. Two types of nanofluids namely Cu-water nanofluid and TiO2-water nanofluid are used. The effects of various fluid flow parameters are discussed through graphs and tables. It is observed that the diffusion thermo parameter/radiation absorption parameter enhance the velocity, temperature and skin friction. This enhancement is very significant for copper nanoparticles. This is due to the high conductivity of the solid particles of Cu than those of TiO2. Also it is noticed that the solutal boundary layer thickness decreases with an increase in chemical reaction parameter. It is because chemical molecular diffusivity reduces for higher values of Kr. Keywords: MHD, Chemical reaction, Dufour effect, Nanofluid, Porous medium

Numerical study of three dimensional Carreau liquid flow with heat and mass transport features over a variable thickness sheet filled with microorganisms is analyzed. We considered the non-uniform heat sink or source and multiple slip effects. The governing non-linear partially differential expressions are developed into ordinary differential systems by using variable transformations. These expressions are solved numerically by using Runge-Kutta fourth order method connected with shooting methodology. A Parametric study is implemented to demonstrate the effects of Hartmann number, Prandtl number, Weissenberg number, Peclet number, chemical reaction and heat sink/source parameters on liquid velocity, temperature and concentration profiles. The quantities of physical interest are described within the boundary layer. From this analysis, we found that the magnetic parameter decrease the local Sherwood and local Nusselt numbers for both and cases. The constraint of chemical reaction enhances the mass transfer rate and decelerates the density of motile mass transfer rate. The space dependent and temperature dependent heat source/sink suppress the local Nusselt number.

Tuberculosis of thyroid gland is a rare entity even in countries with high prevalence of tuberculosis. The diagnosis of extra-pulmonary tuberculosis, especially in the rare sites like thyroid, pancreas, striated and cardiac muscles is difcult. Thyroid tuberculosis, if at all present, is more commonly associated with either miliary or disseminated tuberculosis or with contagious involvement from adjacent viscera and vertebral body. Hence, for an accurate diagnosis of thyroid tuberculosis, pathological examination with demonstration of acid-fast bacilli is important along with a proper clinico-radiological evaluation. Herein we report a case of 30-year-old male with swelling on the right side of neck who presented with a “solitary thyroid nodule” on ultrasound and “colloid” in ne needle aspiration cytology (FNAC) with scattered epithelioid like cells along with benign follicular epithelial cells. However, no denitive diagnosis could be given on cytology due to pauci-cellularity. Tuberculous thyroiditis was diagnosed on histopathology since the patient underwent right hemithyroidectomy for right side solitary nodule. The patient was started on Anti-tubercular therapy (ATT) and had no complications in 6 months follow up period. Although rare, thyroid tuberculosis should be kept in mind in differential diagnosis of thyroid nodules, even in patients with no history and symptoms of TB disease elsewhere specially in TB endemic areas.

Cysticercosis cellulosae is a systemic parasitic infection caused by the larval stage of pork tapeworm, taenia solium which involve humans as either a denitive or secondary host. It is a common disease in developing countries. The cases presenting as an isolated muscle mass is an extremely rare entity and demands documentation. Herein, we present a case of healthy pediatric patient who presented with unilateral cheek swelling which on ultrasound suggested a benign cystic lesion. The diagnosis was conrmed on ne needle aspiration cytology (FNAC).

Lupus vulgaris is a cutaneous form of tuberculosis that occurs in previously sensitized individuals with a strong positive delayed type of hypersensitivity to tuberculin. Classical lupus lesions are seen in head and neck region and isolated involvement of pinna is rare and therefore high index of suspicion is required for its diagnosis. We present a 39-year-old male with non-healing ulcer of pinna since a year. The diagnosis of lupus vulgaris was conrmed on histopathological evaluation along with positivity for acid fast bacilli. The patient showed well response to standard 4 drug regimen of antitubercular therapy

Investigation of entropy generation assures significantly the trustworthiness of mechanical and electronic components. Entropy generation is useful in many applications including heat exchangers, capacitors, circuit boards and resistors. In this article, we discussed the optimization of entropy generation on a radiative MHD fluid flow combined with CCHF model in two instances i.e., hybrid nanofluid(PEG − Water + ZrO2 + MgO)and mono- nanofluid(PEG − Water + ZrO2)amidst (two) revolving disks with chemical reaction. Mathematical model describing the fluid flow is resolved by using a shooting procedure together with R-K 4th order method after converting as a system of ODEs. Outcomes are displayed via plots and impacts of the pertinent parameters on physical quantities such as heat transfer rate are elucidated using a statistical tool, correlation coefficient in two cases. Primary conclusions of this study are larger stretching parameter of the lower disk ameliorates axial velocity, volumetric nanoparticle parameter alleviates radial velocity, higher thermal relaxation parameter belittles the fluid temperature, radiation and rotation parameters improve the entropy generation in the fluid flow and concentration diminishes with larger chemical reaction parameter. Further, we observed that elongating parameters of both disks are having significant positive association with surface drag force near the disks in both occasions. However, there is a significant negative association between the heat transfer rates. Rotation parameters improves the entropy generation in the fluid flow. Validation of the current study is done by comparing the present findings with the available outcomes in the literature and found an adequate agreement.

Unsteady two dimensional free convective flow of a viscous electrically conducting micropolar fluid through a highly porous medium over a semi-infinite moving vertical porous plate, in the presence...

The present study aims to analyze the radiation absorption and viscous dissipation effects on MHD free convective Casson fluid flow over a vertical permeable semi-infinite plate in the presence of first order homogeneous chemical reaction. The time-dependent wall suction is assumed to occur at the permeable surface. The non-Newtonian fluid behavior is characterized by using the Casson fluid model. The coupled non-linear ordinary differential equations (ODE’s) are solved by perturbation technique. The impact of sundry parameters on the velocity, temperature, species concentration as well as the friction factor coefficient, the rate of heat and mass transfer coefficients are computed and analyzed through graphs.

In this paper MHD rotating double diffusive and chemically reactive fluid flow past a vertical porous plate with thermal radiation and heat absorption/generation is studied. The non-dimensional governing equations involved in the present analysis are solved by using finite difference technique. The effects of various physical parameters on velocity, temperature and concentration along with skin friction, the rate of heat transfer in the form of Nusselt number and the rate of mass transfer in the form of Sherwood number are studied through the graphs and tables.

A theoretical analysis is performed for investigating the flow and heat transfer characteristics of Maxwell fluid over a stretching cylinder with Cattaneo–Christov, heat source or sink, and suction/injection. The solution to the transformed similarity equations is derived using Runge–Kutta fourth-order method along shooting technique. The present result for both the surface shear stress and the local Nusselt number is validated with the previously published results, while a very sound agreement is attained. The impacts of the distinct parameters related to this study are presented in graph and tabular form, respectively. Moreover, the local Nusselt number and surface shear stress have been computed for both the suction and injection cases. It is found that strengthening the thermal relaxation parameter value increases the heat transfer rate. The dimensional heat transfer rate is observed being rising in the injection case when compared with the suction case.

This paper reveals the physical properties of Jeffery nanofluid flow past a moving plate embedded in porous medium under the existence of radiation and thermal diffusion. The analysis is carried out in three cases of moving plate, namely stationary plate λ = 0, forth-moving plate λ = 1, back-moving plate λ = −1. Finite difference method is applied to solve the governing equations of the flow and pointed out the variations in velocity, temperature and concentration with the use of graphical presentations. The impact of several parameters on local skin friction, Nusselt number and Sherwood number is also noticed and discussed. Enhancement of velocity is observed under the impact of Jeffery parameter for the cases of stationary plate and back-moving plate, whereas reverse nature is found in the case of forth-moving plate. The velocity enhances as the values of porosity parameter increases for the case of stationary plate and forth-moving plate but a reverse nature is noticed in the case of back-moving plate.

The simultaneous interaction of viscous dissipative and thermal radiation in MHD two dimensional flows of ferro-liquid over a nonlinear moving surface is analyzed here. The slip on velocity and convective boundary condition on temperature are imposed on stretching surface. We used water as conventional base liquid which have magnetite (Fe3O4) and alumina (Al2O3) as nanoparticles. The governing mathematical expressions are converted into non-dimensional form via nonlinear type similarity variables. The resulting mathematical model is numerically solved with the help of MATLAB solver bvp4c. The roles of non-dimensional constraints on velocity and temperature are elaborated through plots. The numerical data of skin-friction coefficient and Nusselt number is presented and visualized. The validity of computed results is analyzed through comparative benchmark. Keywords: Ferro fluid, Velocity slip condition, Convective boundary condition, Viscous dissipation, Radiation

Purpose The purpose of this paper is to present an analytical study for a problem of unsteady free convection boundary layer flow past a periodically accelerated vertical plate with Newtonian heating (NH). Design/methodology/approach The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expressions for skin friction, Nusselt number and Sherwood number are also derived and discussed numerically. Findings It is observed that velocity, concentration and skin friction decrease with the increasing values of Sc whereas temperature distribution decreases in the increase in Pr in the presence of NH. Research limitations/implications This study is limited to a Newtonian fluid. This can be extended for non-Newtonian fluids. Practical implications Heat and mass transfer frequently occurs in chemically processed industries, distribution of temperature and moisture over agricultural fields, dispersion of fog and environment pollution and polymer production. Social implications Free convection flow of coupled heat and mass transfer occurs due to the temperature and concentration differences in the fluid as a result of driving forces. For example, in atmospheric flows, thermal convection resulting from heating of the earth by sunlight is affected differences in water vapor concentration. Originality/value The authors have studied heat and mass transfer effects on unsteady free convection boundary layer flow past a periodically accelerated vertical surface with NH, where the heat transfer rate from the bounding surface with a finite heat capacity is proportional to the local surface temperature, and which is usually termed as conjugate convective flow. The equations governing the flow are studied in the closed form by using the Laplace transform technique. The effects of various physical parameters are studied through graphs and the expression for skin friction also derived and discussed.

In this paper, an exact analysis is carried out for the Laplace transform solution of unsteady MHD chemically reacting elasto-viscous fluid past an infinite vertical plate through porous medium in the presence of radiation absorption and transverse applied magnetic field. The governing equations describing the flow pattern are transformed to a system of linear partial differential equations using appropriate non-dimensional quantities. The resulting transformed equations are solved analytically by using Laplace transform technique and exact solutions for velocity, temperature and concentration as well as Nusselt number and Sherwood number are obtained in terms of exponential and complementary error functions. Behaviour of emerging parameters like elasto-viscous, heat absorption, radiation absorption, magnetic field, Schmidt number, chemical reaction, thermal Grashof number, mass Grashof number, Prandtl number and time is presented graphically and discussed in detail. It was found that increasing radiation absorption parameter, velocity is decreasing for elasto-viscous fluid, but the reverse effect is found for viscous fluid in case of cooling of the plate. An increase in heat absorption, Schmidt number and chemical reaction lead to rise in the Sherwood number and Nusselt number while a reverse effect is noticed in the flow transport.

A numerical investigation is carried out on an unsteady MHD free convection flow of a well-known non-Newtonian visco elastic second order Rivlin-Erickson fluid past an impulsively started semi-infinite vertical plate in the presence of homogeneous chemical reaction, thermal radiation, thermal diffusion, radiation absorption and heat absorption with constant mass flux. The presence of viscous dissipation is also considered at the plate under the influence of uniform transverse magnetic field. The flow is governed by a coupled nonlinear system of partial differential equations which are solved numerically by using finite difference method. The effects of various physical parameters on the flow quantities viz. velocity, temperature, concentration, Skin friction, Nusselt number and Sherwood number are studied numerically. The results are discussed with the help of graphs. We observed that the velocity decreases with an increase in magnetic field parameter, Schmidt number, and Prandtl number while it increases with an increase in Grashof number, modified Grashof number, visco-elastic parameter and Soret number. Temperature increases with an increase in radiation absorption parameter, Eckert number and visco-elastic parameter while it decreases with increasing values of radiation parameter, Prandtl number and heat absorption parameter. Concentration increases with increase in Soret number while it decreases with an increase in Schmidt number and chemical reaction parameter.

Despite numerous reports on the newly discovered hybrid nanofluid, little is known on the influence of increasing Reynolds number, stretching of lower, and upper disks on the dynamics of water conveying graphene and silver between rotating disks when Lorentz force, Joule heating, suction, thermal radiation of thermal energy, and Cattaneo-Christov heat flux are highly significant. This report provides insight into such transport phenomenon with an emphasis on the increasing effects of Reynolds number, stretching of lower, and upper disks. Initially, leading equations of motion and energy are transmuted into a system of nonlinear ordinary differential equations with the aid of suitable (Von-Karman) similarity transmutations. Later, by enforcing shooting procedure (R-K 4th order based) to obtain the numerical solutions. Based on the analysis, it is worth concluding that increasing the Reynolds number improves the thermal field but reduces the tangential velocity. Entropy generation is an increasing property of stretching lower and upper disks but these are yardsticks for decreasing Bejan number.

The present study investigated the variable viscosity and multiple slips on two-dimensional magnetohydrodynamic Carreau fluids due to slendering sheet filled with microorganisms. The Carreau model is used to characterize the behavior of the fluids with shearing thickening properties using the various values of exponent of power law. The diffusion-thermo and thermos diffusion effects are taken into account. The nonlinear sets of ordinary differential equations are treated numerically by shooting technique with Runge–Kutta Fehlberg method. Different parameters like magnetic interaction parameter $$ M $$ , Weissenberg number $$ We $$ , the index of power law $$ m $$ , various multiple slip parameters like the velocity slip parameter $$ \tau_{1} $$ , the temperature jump parameter $$ \tau_{2} $$ , the concentration $$ \tau_{3} $$ , and the concentration jump parameter $$ \tau_{4} $$ are analyzed. The velocity, the skin friction, the rate of heat transport namely Nusselt number and rate of mass transport as Sherwood number are elaborated graphically and computed in tabular benchmark. The analysis found that the density of motile organism grows with the growing magnetic field parameter, diffusion-thermo number, thermo-diffusion number and Weissenberg number.

In this article we have investigated the Soret effect due to mixed convection on unsteady magneto hydrodynamic flow past a semi-infinite vertical permeable moving plate in presence of thermal radiation, heat absorption and homogenous chemical reaction, subjected to variable suction. The plate is assumed to be embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. The equations governing the flow are transformed into a system of nonlinear ordinary differential equations by using perturbation technique. Graphical results for the velocity distribution, temperature distribution and concentration distribution based on the numerical solutions are presented and discussed. We also discuss the effects of various parameters on the skin-friction coefficient and the rate of heat transfer in the form of Nusselt number and rate of mass transfer in the form of Sherwood number at the surface. Velocity distribution is observed to increase with an increase in Soret number and in the presence of permeability, where as it shows reverse effects in the case of heat absorption coefficient, magnetic parameter, radiation parameter and chemical reaction parameter.

The objective of present work is to study the thermo diffusion effect on an unsteady simultaneous convective heat and mass transfer flow of an incompressible, electrically conducting, heat generating/absorbing fluid along a semi-infinite moving porous plate embedded in a porous medium with the presence of pressure gradient, thermal radiation field and chemical reaction. It is assumed that the permeable plate is embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. It is also assumed that the free stream consists of a mean velocity, temperature and concentration over which are super imposed an exponentially varying with time. The equations of continuity, momentum, energy and diffusion, which govern the flow field, are solved by using a regular perturbation method. The behavior of the velocity, temperature, concentration, Skin-friction, rate of heat transfer and rate of mass transfer has been discussed for variations in the physical parameters. An increase in both Pr and R results a decrease in thermal boundary layer thickness. However, concentration decreases as Kr, Sc increase but it increases with an increase in both So and δ.