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Purpose This paper aims to study the magnetohydrodynamic (MHD) wall jet of a hybrid nanofluid flow over a moving surface with a thermally convective surface, wall moving with suction/injection. Design/methodology/approach On using appropriate similarity transformations, the governing equations that describe the model are converted into a system of nonlinear ordinary differential equations. These equations are solved both analytically and numerically using standard two-point boundary-value problem solvers and Chebyshev pseudospectral differentiation matrix method, respectively. Findings These results show that the HNF is heating/cooling with growth of the positive/negative values of the parameter measuring the velocity of the moving surface. The temperature distributions increase, where the thermal boundary layer gets thicker, as the magnetic field strengthens and with an increase in the absolute value of the Biot number. Originality/value The current findings for the HNFs are new and original. They generalize successfully the problems investigated previously by different researchers for the cases of fluids and also nanofluids.

Purpose This work aims to investigates exact solutions of the classical Glauert’s laminar wall jet mass and heat transfer under wall suction, wall contraction or dilation, and two thermal transport boundary conditions; prescribed constant surface temperature and prescribed constant surface flux in nanofluidic environment. Design/methodology/approach The flow system arranged in terms of partial dif- ferential equations is non-dimensionalized with suitable dimensionless transformation variables, and this new set of equations is reduced into ordinary differential equations via a set of similarity transformations, where they are treated analytically for closed form solutions. Findings Exact solutions of nanofluid flow for velocity distributions, momentum flux, wall shear stress and heat transfer boundary layers for commonly studied nanoparticles; namely copper, alumina, silver, and titanium oxide are presented. The flow behavior of alumina and titanium oxide is identical, and a similar behavior is seen for copper and silver, making two pairs of identical traits. The mathematical expressions as well as visual analysis of wall shear drag and temperature gradient which are of practical interest are analyzed. It is shown that wall stretching or shrinking, wall transpiration and velocity slip together influences the jet flow mechanism and extends the original Glauert’s jet solutions. The exact solutions for the two temperature boundary layer conditions and temperature gradients are analyzed analytically. It is found that the effect of nanopar- ticles concentration on thermal boundary layer is intense, causing temperature uplift, whereas the wall transpiration causes a decrease in thermal layers. Originality/value The analysis carried out in nanofluid environment is genuinely new and unique, as our work generalizes the Glauert’s classical regular wall jet fluid problem.

Purpose The purpose of this paper is to study the steady biomagnetic hybrid nanofluid (HNF) of oxytactic microorganisms taking place over a thin needle with a magnetic field using the modified Buongiorno’s nanoliquid model. Design/methodology/approach On applying the appropriate similarity transformations, the governing partial differential equations were transformed into a set of ordinary differential equations. These equations have been then solved numerically using Runge–Kutta–Fehlberg method of fourth–fifth order programming in MAPLE software. Features of the velocity profiles, temperature distribution, reduced skin friction coefficient, reduced Nusselt number and microorganisms’ flux, for different values of the governing parameters were analyzed and discussed. Findings It was observed that as the needle thickness and solid volume fraction increase, the temperature rises, but the velocity field decreases. For a higher Peclet number, the motile microorganism curve increases, and for a higher Schmidt number, the concentration curve rises. Originality/value On applying the modified Buongiorno’s model, the present results are original and new for the study of HNF flow and heat transfer past a permeable thin needle.

Hybrid nanofluid wall jet problem of Glauert type has been investigated under effects of the thermal radiation, suction parameter, moving parameter, slip velocity and temperature jumps. Via similarity variables governing equations are converted to system of ODEs. Then, resulted equations are solved exactly for velocity and temperature field in the view of gamma and hypergeometric functions. Further, to confirm the similarity solutions, a relationship between the free stream velocity, slip parameter along with suction parameter, moving parameter and solid volume fractions were introduced. In addition, we discussed the physical existence of the slip parameter and asymptotic behavior in a relation with the moving and suction parameters. Further, the obtained outputs are matched with the previous works. It is seen that adding the copper nanoparticles to the nanofluid titanium dioxide/water has effective part in the velocity behavior. Moreover, they warm the hybrid nanofluid on increasing the thermal radiation parameter. However, effects of suction and temperature jump parameters lead to cooling the hybrid nanofluid temperature. Furthermore, for enlarging the wall velocity, the hybrid nanofluid is much better rather than the classical nanofluid. The current analysis has important applications; such as liquid crystal solidification and polymer process.

The model presented in this paper deals with the investigation of the unsteady laminar flow past a stretchable disk. The nanofluids Al2O3/H2O and Cu/H2O are considered for the analysis where the thermal characteristics and flow behavior of these nanofluids are compared. In addition, the system is subjected to the suction force that has significant impacts on velocity of the nanofluid flow. Further, the nanoparticle solid volume fraction is another important parameter that is discussed which has a prominent role on both profiles of the nanofluid. Furthermore, the investigated mathematical model is framed using PDEs that are transformed to ODEs using suitable transformations. The system of equations obtained in this regard is solved by employing the RKF-45 numerical method where the results are obtained in the form of graphs. Various nanofluids flow parameters arise in the study and the impact of all these parameters has been analyzed and interpreted. Some of the major outcomes are that the higher values of nanoparticle solid volume fraction enhance the temperature while it decreases velocity of the flow. The comparison of flow of the two nanofluids concluded that alumina–water nanofluid has a better velocity while the copper–water nanofluid has a better thermal conductivity.

The current work employs the single wall and multiwall carbon nanotube models to investigate the effect of suction and injection over a Marangoni boundary layer flow on magnetohydrodynamics (MHD) Casson fluid and thermal radiation on a permeable surface. The nonlinear partial differential equations (PDEs) produced by the governing equations for the prescribed flow are translated using the proper similarity transformations into a system of nonlinear ordinary differential equations (ODEs). The consequential nonlinear equation is solved analytically by using incomplete Gamma function. The effects of suction and injection over velocity profile and temperature distribution are presented graphically. It was found that the heat transfer rate increased due to increases in the volume fraction. In addition, the applied magnetics energy, on the other hand, causes it to decrease. Further, single wall carbon nanoliquid has a higher temperature than multiwall nanoliquid. The problem under consideration has a wide range of commercial and scientific applications in various industries like aviation and medicine field. The impacts of MHD and suction/injection on the flow and heat transfer properties of the fluid are examined under the influence of radiation, and the solution of each profile is shown in the form of figures along with the outcomes of the interface velocity and heat transfer rate at the surface.

Lateral pelvic lymph nodes (LPLN) are a major site for local recurrence following curative resection for low locally advanced rectal cancer. Ongoing advances in imaging techniques have improved predicting LPLN metastasis (LPLNM) during pre-operative staging. However, there is ongoing debate on optimal management of this subgroup of patients with variation between guidance of different societies. In Japan, LPLNM is considered as local disease and addressed by lateral pelvic node dissection (LPLND) in addition to total mesorectal excision (TME). However, in the west, LPLNM is considered as metastatic disease and those patients are offered neoadjuvant chemoradiotherapy (nCRT) followed by TME surgery. The potential surgical risks and morbidity associated with LPLND as well as the uncertainty of the oncological outcome have raised the concern that patients with locally advanced low rectal cancer with LPLNM could be over or under-treated. A comprehensive review of literature was performed, summarizing the current evidence on available modalities for predicting LPLNM, the role of LPLND in the management of advanced low rectal cancer and the available surgical approaches with their impact on surgical and oncological outcomes. LPLND is associated with increased operative time, blood loss and post-operative morbidity. The potential benefits for local disease control and survival still awaits high quality studies. There has been increasing number of reports of the use minimally invasive approaches in LPLND in an attempt to reduce post-operative complications. There is need for high quality evidence to define the role of LPLND in management of patients with advanced low rectal cancer.

In this work, Bodewadt flow over a stretchable rotating disc is executed by considering three types of hybrid nanoliquids. In addition, heat transport nature is analysed by incorporating the effect...

The classical Merkin and Needham’s wall-jet problem was studied for copper-titanium dioxide/water hybrid nanofluid with the effects of suction/injection and thermal energy. The governing equations were converted into non-linear ordinary differential equations by using proper similarity transformations. These equations were then solved analytically for the hybrid nanofluid flow and temperature distribution in hypergeometric function. Therefore, we have obtained expressions for both the reduced skin friction coefficient and reduced Nusselt number. It was found that the upper-branch and lower-branch solutions are possible only for suction. Further in the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. Moreover, it was shown that copper-nanoparticle volume fraction plays a very important role in variation of the velocity. Furthermore, adding nanoparticles of copper to the nanofluid titanium dioxide/water cools/warms the resulting hybrid nanofluid on increasing some of the involved parameters.

PurposeThe purpose of this paper is to study flow of the Marangoni boundary layer pasta surface embedded in a porous medium saturated by a hybrid nanofluid in the presence of a magnetic field and thermal radiation.Design/methodology/approachThe governing model was converted into ordinary differential equations applying proper similarity transformations. Therefore, Laplace transform was used to exactly solve the resulted equations. Hence, the influence of the velocity profile and temperature distribution was investigated under impacts of the involved parameters.FindingsIn the case of regular fluid, i.e. the solid volume fractions are zeros, the current results are in a very good agreement with those in the literature. It was found that the velocity decreases (increases) on increasing the parameters of copper-nanoparticles volume fraction, magnetic field and suction (permeability and injection). Further, the temperature increases (decreases) with an increase of the copper-nanoparticles volume fraction, magnetic field, injection and radiation (permeability and suction).Originality/valueThe current results of the Marangoni boundary layer problem for hybrid nanofluids are new, original and extend the previous problems investigated by many authors for the case of regular/nano fluids.

PurposeThe purpose of this paper is to discuss the 3D micropolar hybrid (Ag-CuO/H2O) nanofluid past rapid moving surface, where porous medium has been considered.Design/methodology/approachThe model of problem was represented by highly partial differential equations which were deduced by using suitable approximations (boundary layer). Then, the governing model was converted into five combined ordinary differential equations applying proper similarity transformations. Therefore, the eminent iterative Runge–Kutta–Fehlberg method (RKF45) has been applied to solve the resulting equations.FindingsHigher values of vortex viscosity, spin gradient viscosity and micro-inertia density parameters are reduced in horizontal direction, whereas opposite behaviour is noticed for vertical direction.Originality/valueThe work has not been done in the area of hybrid micropolar nanofluid. Hence, this article culminates to probe how to improve the thermal conduction and fluid flow in 3D boundary layer flow of micropolar mixture of nanoparticles driven by rapidly moving plate with convective boundary condition.

The steady magnetohydrodynamic stagnation point flow and heat transfer over a stretching/shrinking surface in a hybrid nanofluid with partial slip and viscous dissipation were theoretically/numerically studied. The governing equations of the problem were turned into ODEs by using appropriate transformations. The plots of most important parameters were presented for both surfaces. It was found that on increasing the magnetic parameter, the hybrid nanofluid is better as a heater rather than nanofluid, however, it is better as a cooler on rising Eckert number, the stretching and slip parameters. For shrinking sheet, critical regions of unique/dual solution have been introduced. Further, stability of the unique/dual solution was studied where three regions of stability were noticed. It was deduced that the velocity and temperature are sensitively available close to the terminated line in the dual solution region. It was also proved that their behavior is absolutely different over the three regions of stability.

Despite low-quality and conflicting evidence, the Association of Coloproctology of Great Britain and Ireland recommends the routine use of antibiotics in the treatment of uncomplicated acute diverticulitis. Recent studies have shown that treatment without antibiotics did not prolong recovery. Some new guidelines currently recommend selective use of antibiotics.The purpose of this study was to compare the safety, effectiveness, and outcomes in treating uncomplicated acute diverticulitis without antibiotics with treatment with antibiotics.PubMed, Embase, Clinicaltrials.gov, and the Cochrane Library were searched with the key words antibiotics and diverticulitis.All studies published in English on treating uncomplicated acute diverticulitis without antibiotics and containing20 individuals were included.Treatment without antibiotics versus treatment with antibiotics were compared.The primary outcome was the percentage of patients requiring additional treatment or intervention to settle during the initial episode. The secondary outcomes were duration of hospital stay, rate of readmission or deferred admission, need for surgical or radiological intervention, recurrence, and complication.Search yielded 1164 studies. Nine studies were eligible and included in the meta-analysis, composed of 2505 patients, including 1663 treated without antibiotics and 842 treated with an antibiotic. The no-antibiotics group had a significantly shorter hospital stay (mean difference = -0.68; p = 0.04). There was no significant difference in the percentage of patients requiring additional treatment or intervention to settle during the initial episode (5.3% vs 3.6%; risk ratio = 1.48; p = 0.28), rate of readmission or deferred admission (risk ratio = 1.17; p = 0.26), need for surgical or radiological intervention (risk ratio = 0.61; p = 0.34), recurrence (risk ratio = 0.83; p = 0.21), and complications (risk ratio = 0.70-1.18; p = 0.67-0.91).Only a limited number of studies were available, and they were of variable qualities.Treatment of uncomplicated acute diverticulitis without antibiotics is associated with a significantly shorter hospital stay. There is no significant difference in the percentage of patients requiring additional treatment or intervention to settle in the initial episode, rate of readmission or deferred admission, need for surgical or radiological intervention, recurrence, or complications.

Introduction The ‘watch and wait’ approach has recently emerged as an alternative approach for managing patients with complete clinical response in rectal cancer. However, less is understood whether the intervention is associated with a favourable outcome among patients who require salvage therapy following local recurrence. Materials and methods A comprehensive systematic search was performed using EMBASE, PubMed, MEDLINE, Journals@Ovid as well as hand searches; published between 2004 and 2018, to identify studies where outcomes of patients undergoing watch and wait were compared with conventional surgery. Study quality was assessed using the Newcastle–Ottawa assessment scale. The main outcome was relative risks for overall and disease specific mortality in salvage therapy. Results Nine eligible studies were included in the meta-analysis. Of 248 patients who followed the watch and wait strategy, 10.5% had salvage therapy for recurrent disease. No statistical heterogeneity was found in the results. The relative risk of overall mortality in the salvage therapy group was 2.42 (95% confidence interval 0.96–6.13) compared with the group who had conventional surgery, but this was not statistically significant (P > 0.05). The relative risk of disease specific mortality in salvage therapy was 2.63 (95% confidence interval 0.81–8.53). Conclusion Our findings demonstrated that there was no significant difference in overall and disease specific mortality in patients who had salvage treatment following recurrence of disease in the watch and wait group compared with the standard treatment group. However, future research into the oncological safety of salvage treatment is needed.

Purpose The purpose of this study is to present both effective analytic and numerical solutions to MHD flow and heat transfer past a permeable stretching/shrinking sheet in a hybrid nanofluid with suction/injection and convective boundary conditions. Water (base fluid) nanoparticles of alumina and copper were considered as a hybrid nanofluid. Design/methodology/approach Proper-similarity variables were applied to transform the system of partial differential equations into a system of ordinary (similarity) differential equations. Exact analytical solutions were then presented for the dimensionless stream and temperature functions. Further, the authors introduce a very nice analytic and numerical solutions for both small and large values of the magnetic parameter. Findings It was found that no/unique/two equal/dual physical solutions exist for the investigated boundary value problem. The physically realizable practice of these solutions depends on the range of the governing parameters. For a stretching/shrinking sheet, it was deduced that a hybrid nanofluid works as a cooler on increasing some of the investigated parameters. Moreover, in the case of a shrinking sheet, the first solutions of hybrid nanofluid are stable and physically realizable rather than the nanofluid, while those of the second solutions are not for both hybrid nanofluid and nanofluid. Originality/value The present results for the hybrid nanofluids are new and original, as they successfully extend (generalize) the problems previously considered by different authors for the case of nanofluids.

Purpose This paper aims to investigate the impacts of the gold nanoparticles on the peristaltic flow and heat transfer of blood in the presence of heat source. This element has been chosen because on comparing with the other common nanoparticles, gold nanoparticles are preferred due to their unique properties in absorbing the temperature when a heat source exists. Design/methodology/approach On simplifying the governing equations under the assumption of long-wavelength and low-Reynolds number approximations, the resulted system has been solved by applying the homotopy perturbation method. Then, detailed physical discussion has been introduced through several plots while focusing on the consequences of the current results on the treatment of cancer. Findings The present results revealed that the heat source has a great effect on the blood velocity, blood temperature and concentration of the gold nanoparticles within the artery/vein cavity when represented as asymmetric channel. Moreover, the accuracy of the current solutions was validated through several plots of the remainder error for each studied phenomenon. Originality/value The current idea gives some light on the attempts of using the gold nanoparticles in the treatment of cancer and therefore may lead to possible applications for diagnosis/therapy of the human cancer. To the best of authors’ knowledge, this is novel, very efficient and applicable.

Boundary layer flow of an electrically conducting fluid past a stretching/shrinking sheet inserted in graphene–water nanofluid was investigated. The detailed exact analytical solutions for the flow and heat have been extracted. A theoretical analysis was implemented to explore the regions of non–existence and existence of unique and dual solutions by providing the critical values. In addition, the asymptotic formulas for large first/second slips valid for a stretching/shrinking type, has been deduced. The profiles and distributions of the stream function, velocity, temperature, reduced skin friction coefficient and reduced Nusselt number were examined and discussed via the obtained closed forms. With no restrictions, it was proved that the unique solutions were detected for the flow of all considered parameters over the stretching sheet. However, to obtain the dimensionless temperature solutions, a very sensitive condition on the heat source/sink parameter has to be considered. Whilst in the case of flow over the shrinking sheet, solutions turn out to be unique or dual for some combinations of the parameters. Moreover, two sensitive conditions have to be simultaneously achieved to get the dual solutions depending mainly on the magnetic and thermal radiation parameters. Further, even in the weakness of magnetic field, the dual solutions were obtained for both suction and injection cases. Furthermore, it was proved in detail that the first solutions of the stream function and temperature are stable and physically realizable, whereas those of the second ones are highly–unstable. This means that, while two solutions exist mathematically, only the first one is to be physically considered. It was also concluded that graphene nanoparticles can be used as a heater on increasing the solid volume fraction, injection, thermal radiation and Eckert number. On the other hand, they act as a cooler with an increase of magnetic field, suction, first velocity slip, second velocity slip and heat source/sink. Additionally, the asymptotic formulas and behavior of the stream function and temperature for both sheets were introduced.

The peristaltic flow of velocity second slip boundary conditions and inclined magnetic field of Jeffrey fluid by means of heat and mass transfer in asymmetric channel was inspected in the present study. Leading equations described the existing flow were then simplified under lubrication approach. Therefore, exact solutions of stream function, concentration and temperature were deduced. Further, the numerical solutions of pressure rise and pressure gradient were computed using Mathematica software. Furthermore, the effect of the second slip parameter was argued via graphs. It has been depicted that this kind of slip is mandatory and very imperative to foresee the physical model. On the other hand, false results will be obtained.

Exact theoretical solutions were obtained for the peristaltic transport of viscous nanofluid in an asymmetric channel in presence of the convective conditions. Therefore, on comparing the present results with those published approximate ones by using the homotopy perturbation method (HPM), great remarkable differences and contradictions have been detected. It was also shown that the published approximate solutions does not satisfy the boundary conditions of the studied problem. In addition, it was mentioned that the current work have many advantages over those obtained by using the HPM and, hence, reveals firmly that the researchers have to be very careful on using the homotopy perturbation method to solve the governing equations of a peristalsis flow, otherwise, a spurious physical sight is to be obtained.

This paper studies the boundary layer flow and heat transfer characteristics past a permeable isothermal stretching/shrinking surface using both nanofluid and hybrid nanofluid flows (called modified Buongiorno nonliquid model). Using appropriate similarity variables, the PDEs are transformed into ODEs to be solved numerically using the function bvp4c from MATLAB. It was found that the solutions of the resulting system have two branches, upper and lower branch solutions, in a certain range of the suction, stretching/shrinking and hybrid nanofluids parameters. Both the analytic and numerical results are obtained for the skin friction coefficient, local Nusselt number, and velocity and temperature distributions, for several values of the governing parameters. It results in the governing parameters considerably affecting the flow and heat transfer characteristics.

In the current work, we investigated effects of the velocity slip for the flow and heat transfer of four nanofluids over a non-linear stretching sheet taking into account the thermal radiation and magnetic field in presence of the effective electrical conductivity. The governing partial differential equations were transformed into a set of nonlinear ordinary differential equation using similarity transformations before being solved numerically by the Chebyshev pseudospectral differentiation matrix (ChPDM). It was found that the investigated parameters affect remarkably on the nanofluid stream function for the whole investigated nanoparticles. In addition, velocity and skin friction profiles of the four investigated nanofluids decreases and increases, respectively, with the increase of the magnetic parameter, first-order and second-order velocity slips. Further, the flow velocity, surface shear stress and temperature are strongly influenced on applying the velocity slip model, where lower values of the second-order imply higher surface heat flux and thereby making the fluid warmer.

In this research, the author investigated two-dimensional incompressible, laminar and steady boundary-layer flow past a stretching/shrinking sheet which is in a water-based nanofluid containing metallic and nonmetallic nanoparticles; namely, silver, copper, alumina and titania. Theoretical exact solutions for the dimensionless stream function and dimensionless temperature were obtained. Hence, a detailed analysis of the existence of those solutions was effectively deduced for the stretching/shrinking sheet conditionally in order with the values of permeability, magnetic and suction/injection parameters. Via many tables and graphs, the effects of various physical parameters included in dimensionless profiles for the stream function, velocity and temperature were studied. These parameters include the solid volume fraction, magnetic, permeability, radiation, surface convection, stretching/shrinking sheet, reduced skin friction coefficient and reduced Nusselt number. On comparing the present results with those in the literature, a very good agreement was obtained in some special cases for different values of the investigated parameters. In addition, it was shown that the effective electrical conductivity considerably and remarkably affects the nanofluids' flow and, hence, it is mandatory to take this into account and not to ignore it as in some recent papers, especially with its presence in the solutions' conditions, otherwise, a spurious physical sight is to be obtained. It was therefore indicated that the included parameters have to be re-investigated and we must not depend on the published results that dropped this term. Further, the critical values and curves for obtaining one solution (dual solutions) were successfully secured for a stretching sheet (shrinking sheet). For a stretching/shrinking sheet, profiles of the velocity decrease as the solid volume fraction increases in the region (0, 0.2], then, they increase as this parameter increases when its value lies in the region (0.2, 0.4].