Thermal and solutal transport by Cattaneo-Christov model for the magnetohydrodynamic Williamson fluid with joule heating and heat source/sink.

This article scrutinizes the 2-dimensional and boundary layer flow of magnetohydrodynamic Williamson fluid flowing on a stretchable surface with variable viscosity. The thermal and solutal rates are examined through the Cattaneo-Christov model with Joule heating, heat source/sink, and chemical reaction. The authors are motivated to conduct this study because of its practical and scientific significance in various processes, including polymer processing, textile industries, food industries, solar energy, biomedical science, wind turbine blades, oil spill clean-up, metal rolling, and forging. With the mentioned assumptions, the partial differential equations are achieved by using the basic governing laws, including momentum law, energy law, and concentration law. This non-linear system of equations is transmuted into ordinary differential equations by taking similarity transformations. The main novelty behind the conduction of this work is the numerical technique, namely the 'Adams-Milne (Predictor-Corrector)' method along with the Runge-Kutta technique on Matlab software, which has not previously been studied by any researcher in the literature. The analytical solution of the determined equations is not possible due to their highly non-linear nature; therefore the multistep numerical method namely the 'Adams-Milne (Predictor-Corrector)' method, along with the Runge-Kutta technique is used to determine the numerical results. The outcomes are noted due to numerous parameters for velocity, temperature, and concentration profiles. The explanation of graphical and numerical results is discussed here. The graphical impression of the Williamson parameter reveals that the velocity and temperature curves diminish for higher inputs of this parameter. The movement of fluid shows the declining behavior for the Hartmann number and viscosity parameter. The solutal and thermal findings due to Cattaneo-Christov heat and mass relaxation coefficients mark the reducing behaviour in respective field. The rise in reaction coefficient decreases the mass distribution. The analyses of comparison of results are also presented here.

Medullary Thyroid Carcinoma: A Single Institute Experience.

Medullary thyroid carcinoma is a rare tumour that is anatomically located in the thyroid gland but is functionally a neuroendocrine tumour. It is usually a disease of older age group but manifests in a young patient in familial form. It is derived from parafollicular c cells and has a predilection for lymph node metastasis. It is associated with slow growth in thyroid gland with early nodal metastasis. Serum calcitonin is useful as a preoperative marker of disease burden and prognosis. In the preoperative period serum levels of calcitonin can guide regarding the need for compartment wise lymph node dissection and the possibility of distant metastasis. It is used as a tool of surveillance in the postoperative period. The levels of serum CEA and calcitonin and their doubling time is a useful guide in the detection of early recurrence or distant metastasis. Imaging modality useful for diagnosis is USG in a majority of patients. Thus, the initial diagnosis and preoperative assessment of medullary thyroid carcinoma is similar to other forms of thyroid cancer but further management of disease differs significantly form other forms of differentiated thyroid carcinoma or even anaplastic carcinoma. Prognosis however differs according to age, gender, presence or absence of lymph node metastasis at presentation, metastatic disease at presentation and levels of biochemical markers.

Natural convection with variable fluid properties of couple stress fluid with Cattaneo-Christov model and enthalpy process.

The geometry under consideration for this flow problem, namely paraboloid surface is similar to aircraft and car bonnet, bullet shape, front shape of submarine, rockets and these types of are useful in manufacturing of formula F1 cars and airplanes. The flow of fluid over paraboloid surface has several applications in space science, industries, mechanical works and architecture. The aim of this study is to explore the Cattaneo-Christov heat and mass flux model in steady 2D couple stress fluid flow with variable thermo-physical characteristics near the parabolic surface. The effects of enthalpy and activation energy are also taken into consideration. The stretching in the layers of fluid is assumed at the surface of body. The problem is amended by using the law of conservation of momentum, energy and mass transfer. The non-linear governing partial differential equations are converted into ordinary differential equations by using self-similar form with similarity transformation. The resulting ODE's are numerically solved by bvp4c method. The conclusion indicates that the fluid moves quickly due to higher inputs of couples stress parameter and buoyancy parameter while the viscosity coefficient creates restriction in the fluid motion. The transference analysis of temperature and concentration enhances for higher impacts of thermal conduction and mass diffusivity coefficient. The thermal concentration relaxation parameters are the source of decline in the concentration and temperature of fluid. The heat transmission rate is maximum and mass transfer is minimum due to raising values of Dramkholer number. The impression of all parameters on different fields is listed in discussion section.

Theoretical analysis of non-Newtonian blood flow in a microchannel.

BACKGROUND: In this work the theoretical analysis is presented for a electroosmotic flow of Bingham nanofluid induced by applied electrostatic potential. The linearized Poisson-Boltzmann equation is considered in the presence of Electric double layer (EDL). A Bingham fluid model is employed to describe the rheological behavior of the non-Newtonian fluid. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. Flow characteristics are investigated by employing Debye-Huckel linearization principle. Such preferences have not been reported previously for non-Newtonian Bingham nanofluid to the best of author's knowledge. METHOD: The transformed equations for electroosmotic flow are solved to seek values for the nanofluid velocity, concentration and temperature along the channel length. RESULTS: The effects of key parameters like Brinkmann number, Prandtl number, Debey Huckel parameter, thermophoresis parameter, Brownian motion parameter are plotted on velocity, temperature and concentration profiles. Graphical results for the flow phenomenon are discussed briefly. CONCLUSIONS: Non-uniformity in channel as well as yield stress τ0 cause velocity declaration for both positive and negative values of U. Nanofluid temperature is found an increasing function of electro osmotic parameter κ if U is positive while it is a decreasing function if U is negative. A completely reverse response is seen in case of concentration profile. The thermophoresis parameter Nt, the Brow nian motion parameter Nb and Brinkman number Br cause an enhancement in temperature. The results are new in case of U.

Corrigendum to "Predicting entropy generation in flow of non-Newtonian flow due to a stretching sheet with chemically reactive species" [Comput. Methods Prog. Biol. 187 (2020) 105246].

This is the corrigendum to our recent published research article [1] in which the analysis of non-Newtonian fluid (Williamson model) is presented in the presence of entropy generation by a stretched surface. Total entropy rate is discussed via thermodynamics second law. The results are arranged for nonlinear ODE's through Rung Kutta integration technique with shooting method. In this communication [1] some minor typing errors are noted which is occurred during the writing and typing of momentum, energy and entropy generation. Therefore, we have rewritten the above mentioned equations in correct form in this corrigendum. Note that the updated version of manuscript does not affect the scientific and physical validity of the paper.

Theoretical investigation of peristaltic activity in MHD based blood flow of non-Newtonian material.

OBJECTIVE: The flow kinetics generated with a pulsatile wave that travel along the channel has prime relevance in various processes in physiology and industry. The aim here is to investigate such phenomenon with Bingham fluid with chemically reacting species in terms of their homogeneous and heterogeneous characteristics. METHOD: To formulate the mathematical descriptions Bingham fluid with heat and mass equations is accounted. Using the similarity solutions, the proposed leading partial differential equations of the flow phenomena transferred into the nonlinear ordinary differential equations and boundary conditions are solved analytically. Such considerations perceive prime importance in medicine and genetics where heterogeneity in a cell makes several diseases difficult to execute. RESULTS: Further the physical aspect of human tabular organs i.e., porosity in a medium is retained in the analysis. The utility of magnetic field in reference to medicine is employed. The walls are considered flexible. The whole problem is set to lubrication approach for simplification of resulting system. The attained results are tested on physical grounds by plotting graphs. CONCLUSION: It is analyzed that the Hartman number and porosity parameter reduce the velocity and temperature profiles. The elastic wall parameters E1 and E2 enhances both the velocity and temperature fields while E3 enrolls an adverse effect.

Predicting entropy generation in flow of non-Newtonian flow due to a stretching sheet with chemically reactive species.

BACKGROUND: We have studied the steady Darcy Forchheimer MHD generalized non-Newtonian flow of an incompressible non-linear stretched surface in the presence chemical reactive species. Darcy Forchheimer effect and chemically reactive species are considered under entropy generation. Entropy generation analysis has been essentially applied in engineering procedure in order to improve the theoretical and mathematical evaluation problems. METHOD: To approximate the entropy generation rate, the leading nonlinear equations are solved numerically by using Rung Kutta integration technique with shooting method. RESULTS: Next using the reproduction date, the entropy generation results are discussed by using theoretical and mathematical approaches. The numerical results acquired for different physical mechanism are exposing through graphs and tables. CONCLUSIONS: The physical effects of nanomaterials, skin friction coefficient, heat transfer, mass transfer and entropy generation have been illustrated for different values of involved parameters such as the Weissenberg number, magnetic field parameter, porous medium parameter, the Darcy parameter, the Lewis number, thermophoresis diffusion, the Brownian motion parameter, chemical reaction parameter and the Prandtl number. The numerical results acquired for different physical mechanism are exposing through graphs and tables.

Numerical simulation of electroosmosis regulated peristaltic transport of Bingham nanofluid.

The effects of slip condition and Joule heating on the peristaltic flow of Bingham nanofluid are investigated. The flow is taken in a porous channel with elastic walls. Mathematical formulation is presented under the assumption of long wavelength and small Reynolds number. The transformed equations for the flow are solved to seek values for the nanoparticles velocity, concentration and temperature along the channel length. Graphs are plotted to evaluate the behavior of various physical parameters on flow quantities in both slip and no-slip cases. The main features of the physical parameters are highlighted on the inclined non uniform channel. The results show an increment in velocity with rise in inclination and porosity while it reduces with magnetic field. Moreover, nanofluid favors the heat transfer and decline the concentration.

Homogenous-heterogeneous reactions in MHD flow of Powell-Eyring fluid over a stretching sheet with Newtonian heating.

This article addresses the effects of homogenous-heterogeneous reactions on electrically conducting boundary layer fluid flow and heat transfer characteristics over a stretching sheet with Newtonian heating are examined. Using similarity transformations, the governing equations are transformed into nonlinear ordinary differential equations. The constricted ordinary differential equations are solved computationally by shooting technique. The impact of pertinent physical parameters on the velocity, concentration and temperature profiles is discussed and explored via figures and tables. It is clear from figures that the velocity profile reduces for large values of fluid parameter B and Hartmann number H. Skin friction coefficient decreases for large values of Hartmann number H and fluid parameter B. Also, heat transfer rate monotonically enhances with conjugate parameter of Newtonian heating γ and Prandtl number Pr.

Management of chronic subdural haematoma--a review of 23 cases.

Twenty-three cases of chronic subdural hematoma were admitted and treated at the neurosurgery department of Allied Hospital, Faisalabad, from 1991 to 1993. All these patients were treated with simple burr holes and drainage. Six patients developed post-operative complications; infection in one, cerebral oedema in two, haematoma recurrence in two. There was no mortality. Follow-up revealed that 18 patients recovered completely, one still had neurological or mental deficit and four suffered epileptic seizures.

Presence of plasma proteins in spinal nerve roots. An immunohistochemical study in the rat.

The presence of plasma proteins in the spinal nerve roots of normal rats was investigated using an avidin-biotin peroxidase technique on formaldehyde-fixed, paraffin-embedded material. Sections from the roots, exposed to a rabbit-anti rat albumin antiserum showed widespread, intense immunoreactivity which filled the spaces between the nerve fibers. The reaction product usually ended at the junction between the roots and the spinal cord. The sheath enclosing the roots showed the same strong immunoreaction. There was also a marked reaction in the dorsal root ganglia and peripheral nerve. Spinal cord sections, however, showed no extracellular reactivity, but many motor neurons of the ventral horn were distinctly positive, presumably the result of a normally occurring retrograde axonal transport from the periphery. Parallel sections from the roots exposed to rabbit anti rat IgG antiserum, rabbit anti rat IgM antiserum, rabbit anti human fibrinogen antiserum and rabbit anti human fibronectin antiserum revealed no positive immunoreaction. Thus, rat spinal nerve roots normally contain material with albumin antigenic properties. This would indicate that albumin is present in the extracellular fluid of the roots in the same way as in the endoneurium of peripheral nerves. The fluid microenvironment of the roots, therefore, appears to be different from that in the CNS which lacks extracellular albumin due to the impermeability of the blood-brain barrier.

Structural changes in the rat brain after carotid infusions of hyperosmolar solutions: a light microscopic and immunohistochemical study.

A solution of mannitol or urea was infused into the carotid artery of rats to open the blood-brain barrier (BBB) and to find out if such a procedure results in brain injury. Paraformaldehyde-fixed, paraffin-embedded material was available to determine the localization and extent of albumin extravasation by immunochemistry. Other light microscopic and immunocytochemical techniques were applied on consecutive sections to find out if structural damage had occurred. The cerebral cortex, the hippocampus and the basal ganglia of the infused brain hemisphere contained within regions of albumin extravasation scattered, collapsed, acidophilic neurons. In addition, there were multifocal lesions with marked sponginess of the neuropil which contained numerous shrunken, acidophilic neurons and a perifocal astrocytic gliosis. A moderate macrophage infiltration was present in rats with 72 h survival. In conclusion, infusion of hypertonic mannitol or urea into the carotid artery of the rat may result in structural brain damage within regions showing BBB injury. The presence of acidophilic neurons and the macrophage response indicate that some of the brain changes are irreversible.

Observations on exsudation of fibronectin, fibrinogen and albumin in the brain after carotid infusion of hyperosmolar solutions. An immunohistochemical study in the rat indicating longlasting changes in the brain microenvironment and multifocal nerve cell injuries.

An immunohistochemical study was carried out on rat brain to determine if a transient opening of the blood-brain barrier (BBB), leading to extravasation of serum albumin, is also associated with exudation and cellular uptake of fibronectin and fibrinogen. Both of them might exert important biological effects provided that they pass the BBB and come into contact with cells of the brain parenchyma. Hyperosmolar solutions of urea or mannitol were infused in the carotid artery for 30 s to open the BBB and the animals were killed at various time intervals thereafter. Formaldehyde-fixed, paraffin-embedded material was used for immunohistochemical demonstration of extravasated proteins by an avidin-biotin peroxidase technique. Multifocal, often confluent areas of widely different sizes with signs of albumin extravasation were observed both in the grey and the white matter of the cerebral hemispheres exposed to the hyperosmolar solutions. Much less pronounced changes were observed in rats given an intracarotid saline infusion alone. Immunoreactive material indicating extravasation of fibronectin and fibrinogen was present in the infused cerebral hemispheres but albumin immunoreactivity was much more widespread. Reaction product was observed in vascular walls, presumably in extracellular spaces and in nerve cells. Immunoreactivity in the perikaryon of neurons formed different patterns in various cells. A granular type most probably represents accumulation of the proteins in lysosomal organelles after pinocytotic uptake into the neuron. The second so-called diffuse variety is presumably the result of a severe nerve cell injury with an uncontrolled leakage of proteins into the cytoplasm. Our results indicate that vascular walls, extracellular spaces, glial cells and neurons will be exposed to extravasated fibronectin and fibrinogen as well as to albumin and that antigenic sites in such compounds remain for a long period after the BBB opening. In addition, there are indications that carotid infusions of hyperosmolar solutions may cause nerve cell injuries in regions with BBB opening. These findings have obvious clinical and experimental significance.

Structural changes in the rat brain after carotid infusions of hyperosmolar solutions. An electron microscopic study.

Infusion of hypertonic solutions into the carotid artery is one method by which the blood-brain barrier (BBB) can be opened transiently in experimental animals. This technique has also been tried in clinical situations in which an enhanced uptake of intravenously injected chemotherapeutic drugs into the brain is desired. We have previously found that infusion of hypertonic mannitol or urea into the carotid artery of the rat, leading to a BBB opening, is associated with light microscopic signs of cellular damage in the brain parenchyma. An electron microscopic study has now been made to obtain more detailed information about the events taking place in the rat brain 1 to 72 h after an intracarotid infusion of hyperosmolar solution of mannitol. Toluidine blue-stained semithin epon sections were also available for high-resolution light microscopy of brain samples from urea-infused animals. Intravenously injected Evan's blue dye was used to confirm that BBB opening had occurred as a consequence of the carotid infusions. The infused hemispheres had numerous structural changes. The dominating light microscopic alteration was the presence of multifocal lesions in the gray or the white matter with closely packed microvacuoles causing status spongiosus. Ultrastructurally the microvacuoles corresponded to very pronounced watery swelling of astrocytic processes and to a minor degree to expansion of dendrites and axons. There was also a light or moderate perivascular astrocytic swelling. In the "spongy" lesions as well as occasionally in non-vacuolated parts of the cerebral cortex, there were collapsed electron-dense neurons with pronounced mitochondrial alterations such as severe swelling associated with rupture of christae.(ABSTRACT TRUNCATED AT 250 WORDS)