Optimal control strategies for toxoplasmosis disease transmission dynamics via harmonic mean-type incident rate.

Toxoplasma infection in humans is considered due to direct contact with infected cats. Toxoplasma infection (an endemic disease) has the potential to affect various organs and systems (brain, eyes, heart, lungs, liver, and lymph nodes). Bilinear incidence rate and constant population (birth rate is equal to death rate) are used in the literature to explain the dynamics of Toxoplasmosis disease transmission in humans and cats. The goal of this study is to consider the mathematical model of Toxoplasma disease with harmonic mean type incident rate and also consider that the population of humans and cats is not equal (birth rate and the death rate are not equal). In examining Toxoplasma transmission dynamics in humans and cats, harmonic mean incidence rates are better than bilinear incidence rates. The disease dynamics are first schematically illustrated, and then the law of mass action is applied to obtain nonlinear ordinary differential equations (ODEs). Analysis of the boundedness, positivity, and equilibrium points of the system has been analyzed. The reproduction number is calculated using the next-generation matrix technique. The stability of disease-free and endemic equilibrium are analyzed. Sensitivity analysis is also done for reproduction number. Numerical simulation shows that the infection is spread in the population when the contact rate ß h and ß c increases while the infection is reduced when the recovery rate δ h increases. This study investigates the impact of various optimal control strategies, such as vaccinations for the control of disease and the awareness of disease awareness, on the management of disease.

Morpometric and molecular characterization of Surguli goat through CO1 gene in district Kohat.

The present study was designed with the aim to study morphometric characterization as well as phylogeny and diversity of the local Surguli goat at their breeding tract district Kohat through mitochondrial DNA region, i.e., Cytochrome C Oxidase Subunit One (CO1) gene. Morphometric data and blood samples were collected from thirty (30) pure goats. Morphometric analysis showed that sex had significant effect (p < 0.05) on body weight, body length, hearth girth and horn length while no significant effect (p > 0.05) was observed for other characteristics. The results also indicated that age had significant effect (p < 0.05) on height at rump, ear length, horn length and tail length while no significant effect (p > 0.05) was observed for other characteristics. The phylogenetic analysis through CO1 nucleotide sequences within nucleotide range 1-767 showed nine polymorphic sites segregating into eight haplotypes. The mean intraspecific diversity and mean interspecific diversity were calculated as 0.23 and 2.36%, respectively. Phylogenetic tree revealed that Capra Ibex and native Surguli goat have common ancestors. The morphometric and molecular results obtained from the present study can be exploited as a selection tool for breeding and overall improvement.

Morphological, Biochemical, and Molecular Characterization of Exotic Brassica Germplasm.

Oilseed rape (Brassica napus L.) is an important oilseed crop. We examined the diversity of germplasm expressed at three distinct levels (i.e., morphological, biochemical, and DNA levels). In this study, 150 B. napus L. accessions with three check varieties were provided by Bioresources Conservation Institute. The germplasm was grown in field conditions for data collection of 15 quantitative and nine qualitative agro-morphological traits. The result indicated that for 15 quantitative agro-morphological traits, the highest coefficient of variation was recorded for plant height and days to flowering initiation. For nine qualitative traits, most of the accessions have a spatulate leaf, brown color seeds, yellow flowers, and erect silique attitude. The best adoptable genetically diverse exotic Brassica germplasms were selected, i.e., accessions 24178, 24881, 24199, 24214, 24242, and 24192. Based on biochemical analysis for high oil content and high oleic acid content, chakwal sarsoon and accession 24192 were selected. For high oleic and linoleic acids, accession 24181 performed best, for low erucic acid accessions 24177 and 24195. Based on molecular (SSR) markers, the top 50 selected genotypes were evaluated with 30 SSR markers. The 47 genotypes with three check varieties were clustered in six major groups; the coefficient of similarity ranged between 0.18 and 1.00. Based on SSR data, the germplasms accession 24178 and Abasin were the most diverse genotypes. These genotypes have the capacity and could be used in future breeding programs. High genetic variations were investigated through the SSR among the studied genotypes of Brassica napus L. The present study also concluded that SSR is a better technique for intraspecific genetic diversity. Other modern techniques should be applied such as SNIP for the investigation of a high level of genetic diversity among crop plants in the future.

Impact of nanoparticles on vegetable oil as a cutting fluid with fractional ramped analysis.

Better electrical insulation and thermal properties of vegetable oil with nanoparticles are crucial for its uses as a replacement for conventional previous lubricants used in heavy and light industries for cutting and machining. In this study, a magnetohydrodynamic (MHD) flow of a Brinkman-type nanofluid is used to investigate an infinite vertical plate with chemical reaction, heat radiation, and MHD flow. In order to improve the machining and cutting powers of regular vegetable oil, four distinct types of nanoparticles were selected to be the base fluid. The problem is modeled by coupled system partial differential equations (PDEs), and the results are generalized by the Caputo-Fabrizio fractional differential operator for the exponential non-singular kernel. In order to prepare nanofluids, four different types of nanoparticles, namely graphene oxide (GO), molybdenum disulfide (MoS2), titanium dioxide (TiO2), and aluminum oxide (Al2O3) are suspended separately in vegetable oil. The results of skin friction, the Nusselt number, and the Sherwood number are computed in various tables. It is found that GO nanoparticles, (followed by MoS2, TiO2, and Al2O3) are the materials that can heat transfer at the maximum rate. The heat transfer rate for GO is found to be the greatest with an enhancement up to 19.83% when 4% of nanoparticles are dispersed, followed by molybdenum disulfide at 16.96%, titanium dioxide at 16.25%, and alumina at 15.80%.

A time fractional model of a Maxwell nanofluid through a channel flow with applications in grease.

Several scientists are interested in recent developments in nanotechnology and nanoscience. Grease is an essential component of many machines and engines because it helps keep them cool by reducing friction between their various elements. In sealed life applications including centralized lubrication systems, electrical motors, bearings, logging and mining machinery, truck wheel hubs, construction, landscaping, and gearboxes, greases are also utilized. Nanoparticles are added to convectional grease to improve its cooling and lubricating properties. More specifically, the current study goal is to investigate open channel flow while taking grease into account as a Maxwell fluid with MoS2 nanoparticles suspended in it. The Caputo-Fabrizio time-fractional derivative is used to convert the issue from a linked classical order PDE to a local fractional model. To determine the precise solutions for the velocity, temperature, and concentration distributions, two integral transform techniques the finite Fourier sine and the Laplace transform technique are jointly utilized. The resultant answers are physically explored and displayed using various graphs. It is important to note that the fractional model, which offers a variety of integral curves, more accurately depicts the flow behavior than the classical model. Skin friction, the Nusselt number, and the Sherwood number are engineering-related numbers that are quantitatively determined and displayed in tabular form. It is determined that adding MoS2 nanoparticles to grease causes a 19.1146% increase in heat transmission and a 2.5122% decrease in mass transfer. The results obtained in this work are compared with published literature for the accuracy purpose.

Dynamics of two-step reversible enzymatic reaction under fractional derivative with Mittag-Leffler Kernel.

Chemical kinetics is a branch of chemistry that is founded on understanding chemical reaction rates. Chemical kinetics relates many aspects of cosmology, geology, and even in some cases of, psychology. There is a need for mathematical modelling of these chemical reactions. Therefore, the present research is based on chemical kinetics-based modelling and dynamics of enzyme processes. This research looks at the two-step substrate-enzyme reversible response. In the two step-reversible reactions, substrate combines with enzymes which is further converted into products with two steps. The model is displayed through the flow chart, which is then transformed into ODEs. The Atangana-Baleanu time-fractional operator and the Mittag-Leffler kernel are used to convert the original set of highly nonlinear coupled integer order ordinary differential equations into a fractional-order model. Additionally, it is shown that the solution to the investigated fractional model is unique, limited, and may be represented by its response velocity. A numerical scheme, also known as the Atangana-Toufik method, based on Newton polynomial interpolation technique via MATLAB software, is adopted to find the graphical results. The dynamics of reaction against different reaction rates are presented through various figures. It is observed that the forward reaction rates increase the reaction speed while backward reaction rates reduce it.

Molecular identification and differential proteomics of drug resistant Salmonella Typhi.

This study aimed to elucidate differentially expressed proteins in drug resistant Salmonella Typhi. Among 100 samples, S. typhi were identified in 43 samples. In drug susceptibility profile, 95.3% (41/43), 80% (35/43) and 70% (30/43) resistances were observed against Nalidixic acid, Ampicillin, and Chloramphenicol respectively. No resistance was observed against Imipenum and Azithromycin while only 11% (5/43) isolates were found resistant to Ceftriaxone. Mass spectrometric differential analysis resulted in 23 up-regulated proteins in drug resistant isolates. Proteins found up-regulated are involved in virulence (vipB, galU, tufA, and lpp1), translation (rpsF, rpsG, rplJ, and rplR), antibiotic resistance (zwf, phoP, and ompX), cell metabolism (metK, ftsZ, pepD, and secB), stress response (ridA, rbfA, and dps), housekeeping (gapA and eno) and hypothetical proteins including ydfZ, t1802, and yajQ. These proteins are of diverse nature and functions but highly interconnected. Further characterization may be helpful for elucidation of new biomarker proteins and therapeutic drug targets.

Detection of A2A2 genotype of beta casein protein (CSN2) gene in local, exotic and cross bred cattle in Pakistan.

Genetic variants of bovine Beta-casein protein (CSN2) gene especially A1 and A2 are the most important variants in dairy cattle. A1 milk protein is considered as risk factor for different disease and milk intolerance which release Beta-Casomorphin-7 during digestion which is a bioactive opioid but not released from A2 milk protein. This opioid is responsible for several human health problems like Coronary Heart disease, type 1 diabetics, milk intolerance and other neurological disorders. In present study, 360 blood sample were collected from Lohani, Achai, jersey, Holstein Friesian, Achai x jersey, Friesian x Sahiwal and Sahiwal x Friesian from different region of Khyber Pakhtunkhwa (KP) province. The polymerase chain reaction (PCR) amplicons were sequenced for the identification of polymorphism in exon 7 of Beta-casein protein (CSN2) gene. Sequencing analysis explored CSN2 genotype in exon 7 using the Genomic sequence from GenBank (X.71104) g.8101 C > A at codon 67. The allelic and genotypic frequencies of CSN2 gene were analyzed and observed that Holstein Friesian cattle exhibited A1A2 33%, A1A1 50% and A2A2 17%, Jersey cattle show 68% A1A1, 18% A1A2 and 14% A2A2, Sahiwal x Friesian 56% A1A1, 26% A1A2 and 18% A2A2, Jersey × Achai 78% A2A2, 15% A1A2 and 7% A1A1, Achai 100% A2A2 Lohani 100% A2A2. This is a preliminary study, conducted with meager resources, therefore, it is very difficult to make conclusion that which particular breed possess harmful alleles and which breed possess useful alleles of beta-casein gene. Therefore, a comprehensive molecular work is needed to be performed with greater number of samples sequencing.

Methicillin-Resistant Staphylococcus Aureus And Its Antibiotic Sensitivity Pattern In Patients With Vesiculobullous Disorders.

BACKGROUND: Vesiculobullous disorders are among the leading causes of admission to dermatology. These are characterized by distinct mucocutaneous involvement and by the development of vesicles and bullae (i.e. blisters). Methicillin-resistant Staphylococcus aureus (MRSA) is a group of gram-positive bacteria distinct from other strains of Staph aureus. As the susceptibility of bacteria to antibiotics varies from region to region and from time to time, this study will determine the pattern of antimicrobial susceptibility of MRSA isolates to the commonly prescribed antibiotics in our population. The objective is to determine the frequency of methicillin-resistant Staphylococcus aureus and its antibiotic sensitivity pattern in patients with vesiculobullous disorders admitted to the Dermatology unit of Lady Reading Hospital (LRH), Peshawar. It was Cross-sectional and carried out in study Department of Dermatology, Lady Reading Hospital, Peshawar from Oct 23, 2020, to Apr 22, 2021. METHODS: This study was carried out over 132 patients. After consent, Swabs of pus from the Vesiculobullous disorders were taken from all the patients and sent to a laboratory for culture. Staphylococcus aureus (MRSA) was labelled as Staphylococcus aureus bacteria by Kirby-Bauer disc diffusion method using oxacillin (1 µ gm.) disc on Mueller-Hinton agar (HiMedia Labs, Mumbai) with 24 hours incubation at 35 °C. RESULTS: In this study, 132 patients were observed. The average age was 44.44 years ±13.74 SD. Male to female ratio was 1.30:1. There were 44(33.33%) patients who showed Methicillin Resistant Staphylococcus aureus (MRSA) in vesiculobullous disorders patients. CONCLUSIONS: In our population, the frequency of staphylococcus aureus bacteria in vesiculobullous disorders is high so it will be considered while treating such patients.

Comparison Of Efficacy Of Topical Adapalene Plus Oral Azithromycin And Topical Adapalene Plus Oral Doxycycline In Treatment Of Acne Vulgaris.

BACKGROUND: Acne vulgaris is a commonly diagnosed dermatological condition characterised by pilosebaceous unit blockage or inflammation. It may manifest as inflammatory, non-inflammatory, or a combination of the two. The acne vulgaris mostly the face of individual and chest and back of individual is also affected sometime. The aim of my research is to compare the effectiveness of topical adapalene plus oral azithromycin versus topical adapalene plus oral doxycycline in treating acne. Acne is one of most common reason compelling a patient to see dermatological advice. Our goal is to find the most effective antibiotic to produce the best outcomes with the fewest possible unwanted effect (side effects) and a maximum level of patient satisfaction. METHODS: From May 1 to October 31, 2019, a randomised control trial was performed at Dermatology department MTI Lady Reading Hospital Peshawar. Using the lottery form, all of the patients were split into 2 groups. For 12 weeks, patients in Group A were given oral doxycycline 100 mg once daily and topical adapalene, while patients in Group B were given oral azithromycin 250 mg on alternating days and topical adapalene. All patients were followed at the end of 12 weeks after start of therapy to determine the efficacy in term of clearance of at least 60% of the number of lesions from baseline. RESULTS: In Group A, 22 (59.45%) patients expressed positive results whereas in Group B, only 9 (24.32%) patients expressed positive results. p value (0.0021.). CONCLUSIONS: My data suggest that oral doxycycline 100mg in combination with adapalene gave better results as compared to oral azithromycin which was also found well-tolerated option for treatment of acne on face.

MHD flow of time-fractional Casson nanofluid using generalized Fourier and Fick's laws over an inclined channel with applications of gold nanoparticles.

Gold nanoparticles are commonly used as a tracer in laboratories. They are biocompatible and can transport heat energy to tumor cells via a variety of clinical techniques. As cancer cells are tiny, properly sized nanoparticles were introduced into the circulation for invasion. As a result, gold nanoparticles are highly effective. Therefore, the current research investigates the magnetohydrodynamic free convection flow of Casson nanofluid in an inclined channel. The blood is considered as a base fluid, and gold nanoparticles are assumed to be uniformly dispersed in it. The above flow regime is formulated in terms of partial differential equations. The system of derived equations with imposed boundary conditions is non-dimensionalized using appropriate dimensionless variables. Fourier's and Fick's laws are used to fractionalize the classical dimensionless model. The Laplace and Fourier sine transformations with a new transformation are used for the closed-form solutions of the considered problem. Finally, the results are expressed in terms of a specific function known as the Mittag-Leffler function. Various figures and tables present the effect of various physical parameters on the achieved results. Graphical results conclude that the fractional Casson fluid model described a more realistic aspect of the fluid velocity profile, temperature, and concentration profile than the classical Casson fluid model. The heat transfer rate and Sherwood number are calculated and presented in tabular form. It is worth noting that increasing the volume percentage of gold nanoparticles from 0 to 0.04 percent resulted in an increase of up to 3.825% in the heat transfer rate.

Free convection flow of second grade dusty fluid between two parallel plates using Fick's and Fourier's laws: a fractional model.

The paper aims to investigate the channel flow of second grade visco-elastic fluid generated due to an oscillating wall. The effect of heat and mass transfer has been taken into account. The phenomenon has been modelled in terms of PDEs. The constitutive equations are fractionalized by using the definition of the Caputo fractional operator with Fick's and Fourier's Laws. The system of fractional PDEs is non-dimensionalized by using appropriate dimensionless variables. The closed-form solutions of thermal and concentration boundary layers are obtained by using the Laplace and finite Fourier-Sine transforms, while the momentum equation is solved by a numerical approach by Zakian using [Formula: see text]. Furthermore, the parametric influence of various embedded physical parameters on momentum, temperature, and concentration distributions is depicted through various graphs. It is observed that the fractional approach is more convenient and realistic as compared to the classical approach. It is worth noting that the increasing values of [Formula: see text], [Formula: see text] and [Formula: see text] retard the boundary layer profile. For instance, this behaviour of [Formula: see text] is significant where boundary control is necessary. That is, in the case of resonance, the physical solution may be obtained by adding the effect of MHD. The Reynolds number is useful in characterising the transport properties of a fluid or a particle travelling through a fluid. The Reynolds number is one of the main controlling parameters in all viscous flow. It determines whether the fluid flow is laminar or turbulent. The evolution of the rate of heat, mass transfer, and skin friction on the left plate with various physical parameters are presented in tables. These quantities are of high interest for engineers. Keeping in mind the effect of various parameters on these engineering quantities, they make their feasibility reports.

Time fractional analysis of channel flow of couple stress Casson fluid using Fick's and Fourier's Laws.

This study aim to examine the channel flow of a couple stress Casson fluid. The flow is generated due to the motion of the plate at [Formula: see text], while the plate at [Formula: see text] is at rest. This physical phenomenon is derived in terms of partial differential equations. The subjected governing PDE's are non-dimensionalized with the help of dimensionless variables. The dimensionless classical model is generalized by transforming it to the time fractional model using Fick's and Fourier's Laws. The general fractional model is solved by applying the Laplace and Fourier integral transformation. Furthermore, the parametric influence of various physical parameters like Casson parameter, couple stress parameter, Grashof number, Schmidt number and Prandtl number on velocity, temperature, and concentration distributions is shown graphically and discussed. The heat transfer rate, skin friction, and Sherwood number are calculated and presented in tabular form. It is worth noting that the increasing values of the couple stress parameter [Formula: see text] deaccelerate the velocity of Couple stress Casson fluid.

Fractional model of MHD blood flow in a cylindrical tube containing magnetic particles.

In recent years, the use of magnetic particles for biomedicine and clinical therapies has gained considerable attention. Unique features of magnetic particles have made it possible to apply them in medical techniques. These techniques not only provide minimal invasive diagnostic tools but also transport medicine within the cell. In recent years, MRI, drug supply to infected tissue, Hyperthermia are more enhanced by the use of magnetic particles. The present study aims to observe heat and mass transport through blood flow containing magnetic particles in a cylindrical tube. Furthermore, the magnetic field is applied vertically to blood flow direction. The Caputo time fractional derivative is used to model the problem. The obtained partial fractional derivatives are solved using Laplace transform and finite Hankel transform. Furthermore, the effect of various physical parameters of our interest has also been observed through various graphs. It has been noticed that the motion of blood and magnetic particles is decelerated when the particle mass parameter and the magnetic parameter are increased. These findings are important for medicine delivery and blood pressure regulation.

Mitochondrial phylogenetic and diversity analysis in Azi-Kheli buffalo.

NOVELTY STATEMENT: The present study was conducted for the first time in Pakistan to investigate Cytochrome C Oxidase Subunit 1 (CO1) gene and full-length Displacement Loop (D-loop) region of mitochondrial DNA in Azi-Kheli buffalo breed native to northern hilly areas of Khyber Pakhtunkhwa Province of Pakistan. The present study was designed to investigate phylogeny and diversity in Azi-Kheli buffalo, through two mitochondrial DNA regions, i.e., Cytochrome C Oxidase Subunit-I (CO1) and Displacement Loop (D-loop) region. Thirty (30) blood samples were taken from Azi-Kheli pure breed animals from original breeding tract, i.e., Khwazakhela, Swat. Polymerase chain reactions using gene-specific primers were carried out for amplifying 709-bp region of CO1 gene and 1159-bp region of D-Loop for identification, phylogeny, and diversity in Azi-Kheli buffalo, respectively. The sequences of CO1 gene revealed four (04) haplotypes, whereas D-loop sequences revealed five (05) haplotypes. Mean interspecific diversity with related species was 2.56%, and mean intraspecific diversity within Azi-Kheli buffalo was 0.25%, estimated via Kimura-2 parameter. Phylogenetic tree (maximum likelihood) revealed clustering of Azi-Kheli haplotypes with river buffalo and is distinct from swamp buffalo and other related species of genus Bubalus. Mean haplotype and nucleotide diversity of D-loop were Hd = 0.9601 ± SD = 0.096 and π = 0.01208 ± SD = 0.00182, respectively. Phylogenetic tree (neighbor-joining) revealed two main clades, i.e., river buffalo and swamp buffalo clade. The haplotypes of Azi-Kheli clustered with haplotypes of different river buffalo breeds at different positions. The current study suggests that Azi-Kheli has common origin with other river buffalo breeds; hence, it is river buffalo which harbors high genetic diversity.

Exploring the therapeutic potential of Hibiscus rosa sinensis synthesized cobalt oxide (Co3O4-NPs) and magnesium oxide nanoparticles (MgO-NPs).

Herein, we present a green, economic and ecofriendly protocol for synthesis of cobalt oxide (Co3O4-NPs) and magnesium oxide nanoparticles (MgO-NPs) for multifaceted biomedical applications. In the study, a simple aqueous leaf extract of Hibiscus rosa sinensis, was employed for the facile one pot synthesis of Co3O4-NPs and MgO-NPs. The well characterized NPs were explored for multiple biomedical applications including bactericidal activity against urinary tract infection (UTI) isolates, leishmaniasis, larvicidal, antidiabetic antioxidant and biocompatibility studies. Our results showed that both the NPs were highly active against multidrug resistant UTI isolates as compared to traditional antibiotics and induced significant zone of inhibition against Proteus Vulgaris, Pseudomonas Aurigenosa and E.coli. The NPs, in particular Co3O4-NPs also showed significant larvicidal activity against the Aedes Aegypti, the mosquitoes involve in the transmission of Dengue fever. Similarly, excellent leishmanicidal activity was also observed against both the promastigote and amastigote forms of the parasite. Furthermore, the particles also exhibited considerable antidiabetic activity by inhibiting α-amylase and α-glucosidase enzymes. The biosynthesized NPs were found to be excellent antioxidant and biocompatible nanomaterials. Owing to ecofriendly synthesis, non-toxic and biocompatible nature, the Hibiscus rosa sinensis synthesized Co3O4-NPs and MgO-NPs can be exploited as potential candidates for multiple biomedical applications.

Quasilinearization numerical technique for dual slip MHD Newtonian fluid flow with entropy generation in thermally dissipating flow above a thin needle.

In the present article, we investigate the dual slip effect namely the velocity slip and thermal slip conditions on MHD flow past a thin needle. The entropy generation for the incompressible fluids that's water and acetone that flowing above the thin needle is discussed. The energy dissipating term and the magnetic effect is included in the axial direction. The leading partial differential equations are transformed to ODE by an appropriate similarity transformation and solved using a numerical technique that is the Quasilinearization method. The terms for the rate of entropy generation, the Bejan number, and the irreversibility distribution ratio are discussed. Each dimensionless number is shown with velocity slip and also with the magnetic parameter is presented in graphical form. In the result, we conclude that the entropy generation rate is increasing with the increase in thermal slip parameter also some increasing effect is found as the size of the needle increases.

Sensitivity analysis and optimal control of COVID-19 dynamics based on SEIQR model.

It is of great curiosity to observe the effects of prevention methods and the magnitudes of the outbreak including epidemic prediction, at the onset of an epidemic. To deal with COVID-19 Pandemic, an SEIQR model has been designed. Analytical study of the model consists of the calculation of the basic reproduction number and the constant level of disease absent and disease present equilibrium. The model also explores number of cases and the predicted outcomes are in line with the cases registered. By parameters calibration, new cases in Pakistan are also predicted. The number of patients at the current level and the permanent level of COVID-19 cases are also calculated analytically and through simulations. The future situation has also been discussed, which could happen if precautionary restrictions are adopted.

Couette flow of viscoelastic dusty fluid in a rotating frame along with the heat transfer.

Viscoelastic fluid is an advanced fluid which exhibits both elastic and viscous properties. Whereas rotation of viscoelastic fluid is a very complex phenomenon and has an immense amount of applications in engineering and product making industries. Due to various applications in real life researchers are working to understand the rheology of viscoelastic fluids. Viscoelastic dusty fluids are used in gas cooling systems. In nuclear reactors, dusty fluids are used to lower the temperature of the system. Such fluids are also used in centrifugal separators, which separate solid particles from the liquid state, etc. Therefore, in the present study, viscoelastic dusty fluid is analyzed. More precisely free convective Couette flow under the influence of the transversely applied uniform magnetic field in a rotating frame is considered. The subject fluid is driven by the sine oscillations of the upper plate along with the effect of free convection. Due to rotation, the fluid and dust particles have complex velocities which is the sum of primary velocity and secondary velocity. The flow regime is modeled in terms of partial differential equations. To non-dimensionalize the system of governing equations, dimensionless variables have been derived through Buckingham-Pi theorem. The system of partial differential equations is solved through assumed periodic solutions (Poincare-Light Hill Technique). The expressions for skin friction (shear stresses at [Formula: see text]) and Nusselt number (the rate of heat transfer) are also calculated. Moreover, parametric influence on Nusselt number, and velocity profile of the fluid and the dust particles, is discussed. It is observed that increase in rotation parameter η causes retardation in the velocity of dust particles and the fluid. This is due to the fact that the increase in η enhances the Coriolis forces that are in fact inertial forces, causing a retardation in the velocity of the fluid phase and the dust phase.

Effects of MHD and porosity on entropy generation in two incompressible Newtonian fluids over a thin needle in a parallel free stream.

This article is devoted to studying Magnetohydrodynamic (MHD)'s combined effect and porosity on the entropy generation in two incompressible Newtonian fluids over a thin needle moving in a parallel stream. Two Newtonian fluids (air and water) are taken into consideration in this study. The viscous dissipation term is involved in the energy equation. The assumption is that the free stream velocity is in the direction of the positive x-axis-(axial direction). The thin needle moves in the same or opposite direction of free stream velocity. The reduced similar governing equations are solved numerically with the help of shooting and the fourth-order Runge-Kutta method. The expressions for dimensionless volumetric entropy generation rate and Bejan number are obtained through using similarity transformations. The effects of the magnetic parameter, porosity parameter, Eckert number, Bejan number, irreversibility parameter, Nusselt number, and skin friction are discussed graphically in detail for and taken as Newtonian fluids. The results are compared with published work and are found in excellent agreement.