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Numerical simulation of normal and cancer cells' populations with fractional derivative under radiotherapy

Farayola MF, Shafie S, Mohd Siam F, Khan I

Comput Methods Programs Biomed, 2020 Apr;187:105202.
PMID: 31835107 DOI: 10.1016/j.cmpb.2019.105202

Background This paper presents a numerical simulation of normal and cancer cells' population dynamics during radiotherapy. The model used for the simulation was the improved cancer treatment model with radiotherapy. The model simulated the population changes during a fractionated cancer treatment process. The results gave the final populations of the cells, which provided the final volumes of the tumor and normal cells. Method The improved model was obtained by integrating the previous cancer treatment model with the Caputo fractional derivative. In addition, the cells' population decay due to radiation was accounted for by coupling the linear-quadratic model into the improved model. The simulation of the treatment process was done with numerical variables, numerical parameters, and radiation parameters. The numerical variables include the populations of the cells and the time of treatment. The numerical parameters were the model factors which included the proliferation rates of cells, competition coefficients of cells, and perturbation constant for normal cells. The radiation parameters were clinical data based on the treatment procedure. The numerical parameters were obtained from the previous literature while the numerical variables and radiation parameters, which were clinical data, were obtained from reported data of four cancer patients treated with radiotherapy. The four cancer patients had tumor volumes of 28.4 cm3, 18.8 cm3, 30.6 cm3, and 12.6 cm3 and were treated with different treatment plans and a fractionated dose of 1.8 Gy each. The initial populations of cells were obtained by using the tumor volumes. The computer simulations were done with MATLAB. Results The final volumes of the tumors, from the results of the simulations, were 5.67 cm3, 4.36 cm3, 5.74 cm3, and 6.15 cm3 while the normal cells' volumes were 28.17 cm3, 18.68 cm3, 30.34 cm3, and 12.54 cm3. The powers of the derivatives were 0.16774, 0.16557, 0.16835, and 0.16. A variance-based sensitivity analysis was done to corroborate the model with the clinical data. The result showed that the most sensitive factors were the power of the derivative and the cancer cells' proliferation rate. Conclusion The model provided information concerning the status of treatments and can also predict outcomes of other treatment plans.
Mathematical modeling of radiotherapy cancer treatment using Caputo fractional derivative

Farayola MF, Shafie S, Siam FM, Khan I

Comput Methods Programs Biomed, 2020 May;188:105306.
PMID: 31901851 DOI: 10.1016/j.cmpb.2019.105306

BACKGROUND: This paper presents a mathematical model that simulates a radiotherapy cancer treatment process. The model takes into consideration two important radiobiological factors, which are repair and repopulation of cells. The model was used to simulate the fractionated treatment process of six patients. The results gave the population changes in the cells and the final volumes of the normal and cancer cells.
METHOD: The model was formulated by integrating the Caputo fractional derivative with the previous cancer treatment model. Thereafter, the linear-quadratic with the repopulation model was coupled into the model to account for the cells' population decay due to radiation. The treatment process was then simulated with numerical variables, numerical parameters, and radiation parameters. The numerical parameters which included the proliferation coefficients of the cells, competition coefficients of the cells, and the perturbation constant of the normal cells were obtained from previous literature. The radiation and numerical parameters were obtained from reported clinical data of six patients treated with radiotherapy. The patients had tumor volumes of 24.1cm3, 17.4cm3, 28.4cm3, 18.8cm3, 30.6cm3, and 12.6cm3 with fractionated doses of 2 Gy for the first two patients and 1.8 Gy for the other four. The initial tumor volumes were used to obtain initial populations of cells after which the treatment process was simulated in MATLAB. Subsequently, a global sensitivity analysis was done to corroborate the model with clinical data. Finally, 96 radiation protocols were simulated by using the biologically effective dose formula. These protocols were used to obtain a regression equation connecting the value of the Caputo fractional derivative with the fractionated dose.
RESULTS: The final tumor volumes, from the results of the simulations, were 3.58cm3, 8.61cm3, 5.68cm3, 4.36cm3, 5.75cm3, and 6.12cm3, while those of the normal cells were 23.87cm3, 17.29cm3, 28.17cm3, 18.68cm3, 30.33cm3, and 12.55cm3. The sensitivity analysis showed that the most sensitive model factors were the value of the Caputo fractional derivative and the proliferation coefficient of the cancer cells. Lastly, the obtained regression equation accounted for 99.14% of the prediction.
CONCLUSION: The model can simulate a cancer treatment process and predict the results of other radiation protocols.
Fulltext Impacts of gold nanoparticles on MHD mixed convection Poiseuille flow of nanofluid passing through a porous medium in the presence of thermal radiation, thermal diffusion and chemical reaction

Aman S, Khan I, Ismail Z, Salleh MZ

Neural Comput Appl, 2018;30(3):789-797.
PMID: 30100679 DOI: 10.1007/s00521-016-2688-7

Impacts of gold nanoparticles on MHD Poiseuille flow of nanofluid in a porous medium are studied. Mixed convection is induced due to external pressure gradient and buoyancy force. Additional effects of thermal radiation, chemical reaction and thermal diffusion are also considered. Gold nanoparticles of cylindrical shape are considered in kerosene oil taken as conventional base fluid. However, for comparison, four other types of nanoparticles (silver, copper, alumina and magnetite) are also considered. The problem is modeled in terms of partial differential equations with suitable boundary conditions and then computed by perturbation technique. Exact expressions for velocity and temperature are obtained. Graphical results are mapped in order to tackle the physics of the embedded parameters. This study mainly focuses on gold nanoparticles; however, for the sake of comparison, four other types of nanoparticles namely silver, copper, alumina and magnetite are analyzed for the heat transfer rate. The obtained results show that metals have higher rate of heat transfer than metal oxides. Gold nanoparticles have the highest rate of heat transfer followed by alumina and magnetite. Porosity and magnetic field have opposite effects on velocity.
Fulltext Doctors' knowledge of hypertension guidelines recommendations reflected in their practice

Ahmad N, Khan AH, Khan I, Khan A, Atif M

Int J Hypertens, 2018;2018:8524063.
PMID: 29721335 DOI: 10.1155/2018/8524063

Aim: To evaluate doctors' knowledge, attitude, and practices and predictors of adherence to Malaysian hypertension guidelines (CPG 2008).
Methods: Twenty-six doctors involved in hypertension management at Penang General Hospital were enrolled in a cross-sectional study. Doctors' knowledge and attitudes towards guidelines were evaluated through a self-administered questionnaire. Their practices were evaluated by noting their prescriptions written to 520 established hypertensive outpatients (20 prescriptions/doctor). SPSS 17 was used for data analysis.
Results: Nineteen doctors (73.07%) had adequate knowledge of guidelines. Specialists and consultants had significantly better knowledge about guidelines' recommendations. Doctors were positive towards guidelines with mean attitude score of 23.15 ± 1.34 points on a 30-point scale. The median number of guidelines compliant prescriptions was 13 (range 5-20). Statistically significant correlation (rs = 0.635, P < 0.001) was observed between doctors' knowledge and practice scores. A total of 349 (67.1%) prescriptions written were guidelines compliant. In multivariate analysis hypertension clinic (OR = 0.398, P = 0.008), left ventricular hypertrophy (OR = 0.091, P = 0.001) and heart failure (OR = 1.923, P = 0.039) were significantly associated with guidelines adherence.
Conclusion: Doctors' knowledge of guidelines is reflected in their practice. The gap between guidelines recommendations and practice was seen in the pharmacotherapy of uncomplicated hypertension and hypertension with left ventricular hypertrophy, renal disease, and diabetes mellitus.
Study site: Cardiology, nephrology, diabetic, and hypertension clinics of Hospital Pulau Pinang, Malaysia
Fulltext Exact solutions for unsteady free convection flow over an oscillating plate due to non-coaxial rotation

Mohamad AQ, Khan I, Ismail Z, Shafie S

Springerplus, 2016;5(1):2090.
PMID: 28018798 DOI: 10.1186/s40064-016-3748-2

BACKGROUND: Non-coaxial rotation has wide applications in engineering devices, e.g. in food processing such as mixer machines and stirrers with a two-axis kneader, in cooling turbine blades, jet engines, pumps and vacuum cleaners, in designing thermal syphon tubes, and in geophysical flows. Therefore, this study aims to investigate unsteady free convection flow of viscous fluid due to non-coaxial rotation and fluid at infinity over an oscillating vertical plate with constant wall temperature.
METHODS: The governing equations are modelled by a sudden coincidence of the axes of a disk and the fluid at infinity rotating with uniform angular velocity, together with initial and boundary conditions. Some suitable non-dimensional variables are introduced. The Laplace transform method is used to obtain the exact solutions of the corresponding non-dimensional momentum and energy equations with conditions. Solutions of the velocity for cosine and sine oscillations as well as for temperature fields are obtained and displayed graphically for different values of time (t ), the Grashof number (Gr), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]). Skin friction and the Nusselt number are also evaluated.
RESULTS: The exact solutions are obtained and in limiting cases, the present solutions are found to be identical to the published results. Further, the obtained exact solutions also validated by comparing with results obtained by using Gaver-Stehfest algorithm.
CONCLUSION: The interested physical property such as velocity, temperature, skin friction and Nusselt number are affected by the embedded parameters time (t), the Grashof number (Gr), the Prandtl number ([Formula: see text]), and the phase angle ([Formula: see text]).
Fulltext Uniform magnetic force impact on water based nanofluid thermal behavior in a porous enclosure with ellipse shaped obstacle

Sheikholeslami M, Shah Z, Shafee A, Khan I, Tlili I

Sci Rep, 2019 02 04;9(1):1196.
PMID: 30718893 DOI: 10.1038/s41598-018-37964-y

In the present research, aluminum oxide- water (Al2O3-H2O) nanofluid free convection due to magnetic forces through a permeable cubic domain with ellipse shaped obstacle has been reported. Lattice Boltzmann approach is involved to depict the impacts of magnetic, buoyancy forces and permeability on nanoparticles migration. To predict properties of Al2O3- water nanofluid, Brownian motion impact has been involved. Outcomes revels that considering higher magnetic forces results in greater conduction mechanism. Permeability can enhance the temperature gradient.
Fulltext Bacterial polysaccharides-A big source for prebiotics and therapeutics

Khan R, Shah MD, Shah L, Lee PC, Khan I

Front Nutr, 2022;9:1031935.
PMID: 36407542 DOI: 10.3389/fnut.2022.1031935

Bacterial polysaccharides are unique due to their higher purity, hydrophilic nature, and a finer three-dimensional fibrous structure. Primarily, these polymers provide protection, support, and energy to the microorganism, however, more recently several auxiliary properties of these biopolymers have been unmasked. Microbial polysaccharides have shown therapeutic abilities against various illnesses, augmented the healing abilities of the herbal and Western medicines, improved overall health of the host, and have exerted positive impact on the growth of gut dwelling beneficial bacteria. Specifically, the review is discussing the mechanism through which bacterial polysaccharides exert anti-inflammatory, antioxidant, anti-cancer, and anti-microbial properties. In addition, they are holding promising application in the 3D printing. The review is also discussing a perspective about the metagenome-based screening of polysaccharides, their integration with other cutting-edge tools, and synthetic microbiome base intervention of polysaccharides as a strategy for prebiotic intervention. This review has collected interesting information about the bacterial polysaccharides from Google Scholar, PubMed, Scopus, and Web of Science databases. Up to our knowledge, this is the first of its kind review article that is summarizing therapeutic, prebiotics, and commercial application of bacterial polysaccharides.
Fulltext Natural convection heat transfer in an oscillating vertical cylinder

Khan I, Ali Shah N, Tassaddiq A, Mustapha N, Kechil SA

PLoS One, 2018;13(1):e0188656.
PMID: 29304161 DOI: 10.1371/journal.pone.0188656

This paper studies the heat transfer analysis caused due to free convection in a vertically oscillating cylinder. Exact solutions are determined by applying the Laplace and finite Hankel transforms. Expressions for temperature distribution and velocity field corresponding to cosine and sine oscillations are obtained. The solutions that have been obtained for velocity are presented in the forms of transient and post-transient solutions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. Numerical computations and graphical illustrations are used in order to study the effects of Prandtl and Grashof numbers on velocity and temperature for various times. The transient solutions for both cosine and sine oscillations are also computed in tables. It is found that, the transient solutions are of considerable interest up to the times t = 15 for cosine oscillations and t = 1.75 for sine oscillations. After these moments, the transient solutions can be neglected and, the fluid moves according with the post-transient solutions.
Fulltext Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives

Sheikh NA, Ching DLC, Khan I, Sakidin HB

Sci Rep, 2022 Aug 18;12(1):14117.
PMID: 35982149 DOI: 10.1038/s41598-022-18110-1

The flow of fluid through porous media is of great importance in industry and other physical situations, Darcy's law is one of the most useful laws to describe such situation, however, the flows through a dense swarm of particles or through a very high porous media cannot be elaborated by this law. To overcome this difficulty, Brinkman proposed a new idea of Brinkman-type fluid in highly porous media. In this study, the Brinkman-type fluid flow is analyzed with hybrid nanoparticles (a hybridized mixture of clay and alumina), suspended in water taken as a base fluid under the effect of an applied magnetic field. The fluid motion is taken inside a vertical channel with heated walls. Free convection is induced due to buoyancy. The momentum and energy equations are written in dimensionless form using the non-dimensional variables. The energy equation is modified to fractional differential equations using the generalized Fourier's law and the Caputo fractional derivatives. The fractional model is solved using the Laplace and Fourier transformation. Variations in velocity and temperature are shown for various fractional parameter values, as well as charts for the classical model. For the volume fractions of nanoparticles, the temperature distribution increases, with maximum values of hybrid nanoparticles with the highest specified volume fractions. Moreover, due to hybrid nanoparticles, the rate of heat transfer is intensified.
Fulltext Author Correction: Enhancement in heat transfer due to hybrid nanoparticles in MHD flow of Brinkman-type fluids using Caputo fractional derivatives

Sheikh NA, Ching DLC, Khan I, Sakidin HB

Sci Rep, 2022 Dec 16;12(1):21772.
PMID: 36526701 DOI: 10.1038/s41598-022-26239-2
A new implicit high-order iterative scheme for the numerical simulation of the two-dimensional time fractional Cable equation

Khan MA, Alias N, Khan I, Salama FM, Eldin SM

Sci Rep, 2023 Jan 27;13(1):1549.
PMID: 36707653 DOI: 10.1038/s41598-023-28741-7

In this article, we developed a new higher-order implicit finite difference iterative scheme (FDIS) for the solution of the two dimension (2-D) time fractional Cable equation (FCE). In the new proposed FDIS, the time fractional and space derivatives are discretized using the Caputo fractional derivative and fourth-order implicit scheme, respectively. Moreover, the proposed scheme theoretical analysis (convergence and stability) is also discussed using the Fourier analysis method. Finally, some numerical test problems are presented to show the effectiveness of the proposed method.
Alpha terpineol directs bone marrow mesenchymal stem cells toward neuronal lineage through regulation of wnt signaling pathway

Ishaque A, Salim A, Simjee SU, Khan I, Adli DSH

Cell Biochem Funct, 2023 Mar;41(2):223-233.
PMID: 36651266 DOI: 10.1002/cbf.3775

Central nervous system anomalies give rise to neuropathological consequences with immense damage to the neuronal tissues. Cell based therapeutics have the potential to manage several neuropathologies whereby the differentiated cells are explored for neuronal regeneration. The current study analyzes the effect of a bioactive compound, alpha terpineol (AT) on the differentiation of rat bone marrow derived mesenchymal stem cells (BM-MSCs) toward neuronal lineage, and explores regulation of differentiation process through the study of Wnt pathway mediators. BM-MSCs were cultured and characterized based on their surface markers and tri-lineage differentiation. Safe dose of AT as optimized by 3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium bromide assay, was used for the treatment of MSCs. Treated cells were analyzed for the neuronal, astroglial and germ layer transition markers at the gene and protein levels, by quantitative polymerase chain reaction and immunocytochemistry, respectively. Temporal expression of Wnt pathway genes was assessed during the course of neuronal differentiation. AT treated group showed significant upregulation of neuron specific (NSE, MAP2, Tau, Nestin, and NefL) and astroglial (GFAP) genes with positive expression of late neuronal markers. Germ layer transition analysis showed the overexpression of ectodermal markers (NCAM, Nestin, and Pax6), whereas endodermal (AFP, MixL1, and Sox17), and mesodermal (Mesp1 and T Brachyury) markers were also found to be upregulated. Wnt signaling pathway was activated during the initial phase (30 min) of differentiation, which later was downregulated at 1, 3, and 5 h. AT efficiently induces neuronal differentiation of BM-MSCs by regulating Wnt signaling. Overexpression of both early and late neuronal markers indicate their neuro-progenitor state and thus can be utilized as a promising approach in cellular therapeutics to treat various neurodegenerative ailments. In addition, exploration of the molecular pathways may be helpful to understand the mechanism of cell-based neuronal regeneration.
Fulltext Short term energy consumption forecasting using neural basis expansion analysis for interpretable time series

Shaikh AK, Nazir A, Khan I, Shah AS

Sci Rep, 2022 Dec 29;12(1):22562.
PMID: 36581655 DOI: 10.1038/s41598-022-26499-y

Smart grids and smart homes are getting people's attention in the modern era of smart cities. The advancements of smart technologies and smart grids have created challenges related to energy efficiency and production according to the future demand of clients. Machine learning, specifically neural network-based methods, remained successful in energy consumption prediction, but still, there are gaps due to uncertainty in the data and limitations of the algorithms. Research published in the literature has used small datasets and profiles of primarily single users; therefore, models have difficulties when applied to large datasets with profiles of different customers. Thus, a smart grid environment requires a model that handles consumption data from thousands of customers. The proposed model enhances the newly introduced method of Neural Basis Expansion Analysis for interpretable Time Series (N-BEATS) with a big dataset of energy consumption of 169 customers. Further, to validate the results of the proposed model, a performance comparison has been carried out with the Long Short Term Memory (LSTM), Blocked LSTM, Gated Recurrent Units (GRU), Blocked GRU and Temporal Convolutional Network (TCN). The proposed interpretable model improves the prediction accuracy on the big dataset containing energy consumption profiles of multiple customers. Incorporating covariates into the model improved accuracy by learning past and future energy consumption patterns. Based on a large dataset, the proposed model performed better for daily, weekly, and monthly energy consumption predictions. The forecasting accuracy of the N-BEATS interpretable model for 1-day-ahead energy consumption with "day as covariates" remained better than the 1, 2, 3, and 4-week scenarios.
Effect of lawsone-preconditioned mesenchymal stem cells on the regeneration of pancreatic β cells in Type 1 diabetic rats

Masnoon J, Ishaque A, Khan I, Salim A, Kabir N

Cell Biochem Funct, 2023 Oct;41(7):833-844.
PMID: 37814478 DOI: 10.1002/cbf.3833

Diabetes is one of the major health issues globally. Type 1 diabetes mellitus develops due to the destruction of pancreatic β cells. Mesenchymal stem cells (MSCs) having remarkable self-renewal and differentiation potential, can regenerate β cells. MSCs preconditioned with bioactive small molecules possess enhanced biological features and therapeutic potential under in vivo environment. Interestingly, compounds of naphthoquinone class possess antidiabetic and anti-inflammatory properties, and can be explored as potential candidates for preconditioning MSCs. This study analyzed the effect of lawsone-preconditioned human umbilical cord MSCs (hUMSCs) on the regeneration of β cells in the streptozotocin (STZ)-induced Type 1 diabetes (T1D) rats. hUMSCs were isolated and characterized for the presence of surface markers. MSCs were preconditioned with optimized concentration of lawsone. T1D rat model was established by injecting 50 mg/kg of STZ intraperitoneally. Untreated and lawsone-preconditioned hUMSCs were transplanted into the diabetic rats via tail vein. Fasting blood sugar and body weight were monitored regularly for 4 weeks. Pancreas was harvested and β cell regeneration was evaluated by hematoxylin and eosin staining, and gene expression analysis. Immunohistochemistry was also done to assess the insulin expression. Lawsone-preconditioned hUMSCs showed better anti-hyperglycemic effect in comparison with untreated hUMSCs. Histological analysis presented the regeneration of islets of Langerhans with upregulated expression of βcell genes and reduced expression of inflammatory markers. Immunohistochemistry revealed strong insulin expression in the preconditioned hUMSCs compared with the untreated hUMSCs. It is concluded from the present study that lawsone-preconditioned hMSCs were able to exhibit pronounced anti-hyperglycemic effect in vivo compared with hUMSCs alone.
Linking job crafting, innovation performance, and career satisfaction: The mediating role of work engagement

Rafiq M, Farrukh M, Attiq S, Shahzad F, Khan I

Work, 2023;75(3):877-886.
PMID: 36683474 DOI: 10.3233/WOR-211363

BACKGROUND: The demand for innovation and satisfaction is increasing rapidly due to technological advancement and the fast-changing business environment.
OBJECTIVE: The purpose of this article is to investigate how job crafting augments work outputs (i.e., innovation performance and career satisfaction) through work engagement.
METHODS: Data were collected from 477 workers working in the Pakistan manufacturing sector. A structural equation modeling technique was used to investigate the mediation model.
RESULTS: Job crafting has a direct and indirect association with innovation performance and career satisfaction - via employees' work engagement. Additionally, the mediating impact was stronger for innovation performance than for career satisfaction. The findings advocate that managers should pay attention to employees' job crafting to improve employees' work engagement in manufacturing organizations. To improve employees' innovation performance and career satisfaction via work engagement, it is important to improve organization-wide job crafting in traditional manufacturing organizations. Strategic and managerial actions related to job crafting might boost employees' engagement in the organization that environments provide incessantly better outcomes.
CONCLUSION: By linking job crafting and work engagement to their attitude towards career satisfaction and innovation performance in Pakistani manufacturing firms, this study adds a new dimension to the study of Pakistani manufacturing employees and typically to the best practices in career debates. This knowledge is important and unique because it accentuates that in addition to work engagement, which focuses primarily on employee growth in the organization, job crafting should also be given equal importance to advance manufacturing employees' outcomes.
Fulltext Efficacy comparison of oseltamivir alone and oseltamivir-antibiotic combination for early resolution of symptoms of severe influenza-A and influenza-B hospitalized patients

Ishaqui AA, Khan AH, Sulaiman SA, Alsultan M, Khan I

Saudi Med J, 2020 Sep;41(9):1015-1021.
PMID: 32893285 DOI: 10.15537/smj.2020.9.25249

OBJECTIVES: To assess the comparative efficacy of oseltamivir alone and oseltamivir-antibiotic therapy for early relief of symptoms associated with severe influenza-A (non-H1N1) and influenza-B infection hospitalized patients.
METHODS: In this retrospective multicenter study conducted from 2016-2019, enrolled patients were divided into 2 treatment groups. Group 1 patients were started on Antiviral drug (oseltamivir) alone therapy. Group 2 patients were initiated on Antiviral drug (oseltamivir) in combination with Antibiotic therapy. Using acute respiratory illness scoring, symptom severity score was assessed daily for 8 symptoms namely, fever, fatigue, headache, cough, sore throat, wheezing, muscle ache and nasal congestion. For each symptom the severity was scored from scale 0-3. Results: Overall mean ARI severity score was statistically significantly lower (p less than 0.05) on day 2 (14.65-vs-13.68), day 3 (12.95-vs-11.67) and day 4 (10.31-vs-9.12 ) for influenza-A (non-H1N1) while day 3 (12.52-vs-11.87) and day 4 (11.21-vs-10.18) for influenza-B patients for patients who were initiated on oseltamivir-antibiotic combination therapy. Fever, cough and nasal congestion showed statistically significant improvement within 4 days of initiation of combination treatment. Fatigue, sore throat and muscle ache improvement pattern was same for both treatment protocols.
CONCLUSION: Oseltamivir-antibiotic combination treatment showed early resolution of some symptoms with cumulatively reduced mean symptom severity score in severe influenza infection hospitalized patients.
Fulltext Unveiling the Performance of Cu-Water Nanofluid Flow with Melting Heat Transfer, MHD, and Thermal Radiation over a Stretching/Shrinking Sheet

Hyder A, Lim YJ, Khan I, Shafie S

ACS Omega, 2023 Aug 15;8(32):29424-29436.
PMID: 37599919 DOI: 10.1021/acsomega.3c02949

The use of melting heat transfer (MHT) and nanofluids for electronics cooling and energy storage efficiency has gained the attention of numerous researchers. This study investigates the effects of MHD, mixed convection, thermal radiation, stretching, and shrinking on the heat transfer characteristics of a Cu-water-based nanofluid over a stretching/shrinking sheet with MHT effects. The governing equations are transformed into nonlinear ordinary differential equations and solved numerically using the Keller Box method. To the best of our knowledge, this comprehensive analysis, encompassing all of these factors, including the utilization of a robust numerical method, in a single study, has not been previously reported in the literature. Our findings demonstrate that an increase in the melting parameter leads to an enhanced rate of heat transfer, while an increase in the stretching/shrinking parameter results in a decrease in the rate of heat transfer. Additionally, we present a comprehensive analysis of the influences of all of the mentioned driving parameters. The results are presented through graphical and tabulated representations and compared with existing literature.
Fulltext Shape effect on MHD flow of time fractional Ferro-Brinkman type nanofluid with ramped heating

Saqib M, Khan I, Shafie S, Mohamad AQ

Sci Rep, 2021 Feb 12;11(1):3725.
PMID: 33580116 DOI: 10.1038/s41598-020-78421-z

The colloidal suspension of nanometer-sized particles of Fe3O4 in traditional base fluids is referred to as Ferro-nanofluids. These fluids have many technological applications such as cell separation, drug delivery, magnetic resonance imaging, heat dissipation, damping, and dynamic sealing. Due to the massive applications of Ferro-nanofluids, the main objective of this study is to consider the MHD flow of water-based Ferro-nanofluid in the presence of thermal radiation, heat generation, and nanoparticle shape effect. The Caputo-Fabrizio time-fractional Brinkman type fluid model is utilized to demonstrate the proposed flow phenomenon with oscillating and ramped heating boundary conditions. The Laplace transform method is used to solve the model for both ramped and isothermal heating for exact solutions. The ramped and isothermal solutions are simultaneously plotted in the various figures to study the influence of pertinent flow parameters. The results revealed that the fractional parameter has a great impact on both temperature and velocity fields. In the case of ramped heating, both temperature and velocity fields decreasing with increasing fractional parameter. However, in the isothermal case, this trend reverses near the plate and gradually, ramped, and isothermal heating became alike away from the plate for the fractional parameter. Finally, the solutions for temperature and velocity fields are reduced to classical form and validated with already published results.
Fulltext Dual similarity solutions of MHD stagnation point flow of Casson fluid with effect of thermal radiation and viscous dissipation: stability analysis

Lund LA, Omar Z, Khan I, Baleanu D, Nisar KS

Sci Rep, 2020 Sep 21;10(1):15405.
PMID: 32958775 DOI: 10.1038/s41598-020-72266-2

In this paper, the rate of heat transfer of the steady MHD stagnation point flow of Casson fluid on the shrinking/stretching surface has been investigated with the effect of thermal radiation and viscous dissipation. The governing partial differential equations are first transformed into the ordinary (similarity) differential equations. The obtained system of equations is converted from boundary value problems (BVPs) to initial value problems (IVPs) with the help of the shooting method which then solved by the RK method with help of maple software. Furthermore, the three-stage Labatto III-A method is applied to perform stability analysis with the help of a bvp4c solver in MATLAB. Current outcomes contradict numerically with published results and found inastounding agreements. The results reveal that there exist dual solutions in both shrinking and stretching surfaces. Furthermore, the temperature increases when thermal radiation, Eckert number, and magnetic number are increased. Signs of the smallest eigenvalue reveal that only the first solution is stable and can be realizable physically.
Fulltext Heat transfer analysis of MHD thin film flow of an unsteady second grade fluid past a vertical oscillating belt

Gul T, Islam S, Shah RA, Khan I, Khalid A, Shafie S

PLoS One, 2014;9(11):e103843.
PMID: 25383797 DOI: 10.1371/journal.pone.0103843

This article aims to study the thin film layer flowing on a vertical oscillating belt. The flow is considered to satisfy the constitutive equation of unsteady second grade fluid. The governing equation for velocity and temperature fields with subjected initial and boundary conditions are solved by two analytical techniques namely Adomian Decomposition Method (ADM) and Optimal Homotopy Asymptotic Method (OHAM). The comparisons of ADM and OHAM solutions for velocity and temperature fields are shown numerically and graphically for both the lift and drainage problems. It is found that both these solutions are identical. In order to understand the physical behavior of the embedded parameters such as Stock number, frequency parameter, magnetic parameter, Brinkman number and Prandtl number, the analytical results are plotted graphically and discussed.

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