The variable salinity in stored reservoirs connected by a long channel attracts the attention of scientists worldwide,having applications in environmental and geophysical engineering.This study explores the impact of ...The variable salinity in stored reservoirs connected by a long channel attracts the attention of scientists worldwide,having applications in environmental and geophysical engineering.This study explores the impact of Navier slip conditions on exchange flows within a long channel connecting two large reservoirs of differing salinity.These horizontal density gradients drive the flow.We modify the recent one-dimensional theory,developed to avoid runaway stratification,to account for the presence of uniform slip walls.By adjusting the parameters of the horizontal density gradient based on the slip factor,we resolve analytically various flow regimes ranging from high diffusion to transitional high advection.These regimes are governed by physical parameters like channel aspect ratio,slip factor,Schmidt number,and gravitational Reynolds number.Our solutions align perfectly with ones in the no-slip limit.More importantly,under the conditions of no net flow across the channel and high Schmidt number(where stratification is concentrated near the channel’s mid-layer),we derive a closed-form solution for the slip parameter,aspect ratio,and gravitational Reynolds number that describes the interface’s behavior as a sharp interface separating two distinct zones.This interface,arising from hydrostatic wall gradients,ultimately detaches the low-and high-density regimes throughout the channel when the gravitational Reynolds number is inversely proportional to the aspect ratio for a fixed slip parameter.This phenomenon,observed previously in 2D numerical simulations with no-slip walls in the literature,is thus confirmed by our theoretical results.Our findings further demonstrate that wall slip leads to distinct and diverse flow regimes.展开更多
The physical problem of the thin film flow of a micropolar fluid over a dynamic and inclined substrate under the influence of gravitational and thermal forces in the presence of nanoparticles is formulated.Five differ...The physical problem of the thin film flow of a micropolar fluid over a dynamic and inclined substrate under the influence of gravitational and thermal forces in the presence of nanoparticles is formulated.Five different types of nanoparticle samples are accounted for in this current study,namely gold Au,silver Ag,molybdenum disulfide MoS_(2),aluminum oxide Al_(2)O_(3),and silicon dioxide SiO_(2).Blood,a micropolar fluid,serves as the common base fluid.An exact closed-form solution for this problem is derived for the first time in the literature.The results are particularly validated against those for the Newtonian fluid and show excellent agreement.It was found that increasing values of the spin boundary condition and micropolarity lead to a reduction in both the thermal and momentum boundary layers.A quantitative decay in the Nusselt number for a micropolar fluid,as compared to a Newtonian one for all the tested nanoparticles,is anticipated.Gold and silver nanoparticles(i)intensify in the flow parameter as the concentration of nanoparticles increases(ii)yield a higher thermal transfer rate,whereas molybdenum disulfide,aluminum oxide,and silicon dioxide exhibit a converse attitude for both Newtonian and micropolar fluids.The reduction in film thickness for fluid comprising gold particles,as compared to the rest of the nanoparticles,is remarkable.展开更多
A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications.It was shown in the latter through various comparative physical mode...A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications.It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual(squared)error.A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach,especially regarding the root-finding problems via the homotopy analysis method.Examples are provided to further justify this.Moreover,it is conjectured that every nonlinear differential equation can be considered as a root-finding problem by plugging a parameter in it from a physical viewpoint.Two examples from the boundary and initial and value problems are provided to verify this assertion.Hence,besides the advantages as deciphered in the previous publications,the feasibility of the ratio approach over the traditional residual approach is made clearer in this paper.展开更多
The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparam...The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value ofthis parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is alsoprevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification ofthe ADM incorporating all the boundaries into the formulation. With the presented squared residual error analysis,there is no need to check out the results against the numerical ones, as usually has to be done in the traditional ADMstudies to convince the readers that the results are indeed converged to the realistic solutions. Physical examplesselected from the recent application of ADM demonstrate the validity, accuracy and power of the presented novelapproach in this paper. Hence, the highly nonlinear equations arising from engineering applications can be safelytreated by the outlined method for which the classical ADM may fail or be slow to converge.展开更多
An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper.The standard Adomian Decomposition Method(ADM)is modified via introducing a functional term invol...An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper.The standard Adomian Decomposition Method(ADM)is modified via introducing a functional term involving both a variable and a parameter.A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L^(2) norm.Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate,more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models.Better performance of the method is further evidenced against some compared commonly used numerical techniques.展开更多
The present paper is concerned with two novel approximate analytic solutions of the undamped Duffing equation. Instead of the traditional perturbation or asymptotic methods, a homotopy technique is employed, which doe...The present paper is concerned with two novel approximate analytic solutions of the undamped Duffing equation. Instead of the traditional perturbation or asymptotic methods, a homotopy technique is employed, which does not require a small perturbation parameter or a large parameter for an asymptotic expansion. It is shown that proper choices of an auxiliary linear operator and also an initial approximation during the implementation of the homotopy analysis method can yield uniformly valid and accurate solutions. The obtained explicit analytical expressions for the solution predict the displacement, frequency and period of the oscillations much more accurate than the previously known asymptotic or perturbation formulas.展开更多
文摘The variable salinity in stored reservoirs connected by a long channel attracts the attention of scientists worldwide,having applications in environmental and geophysical engineering.This study explores the impact of Navier slip conditions on exchange flows within a long channel connecting two large reservoirs of differing salinity.These horizontal density gradients drive the flow.We modify the recent one-dimensional theory,developed to avoid runaway stratification,to account for the presence of uniform slip walls.By adjusting the parameters of the horizontal density gradient based on the slip factor,we resolve analytically various flow regimes ranging from high diffusion to transitional high advection.These regimes are governed by physical parameters like channel aspect ratio,slip factor,Schmidt number,and gravitational Reynolds number.Our solutions align perfectly with ones in the no-slip limit.More importantly,under the conditions of no net flow across the channel and high Schmidt number(where stratification is concentrated near the channel’s mid-layer),we derive a closed-form solution for the slip parameter,aspect ratio,and gravitational Reynolds number that describes the interface’s behavior as a sharp interface separating two distinct zones.This interface,arising from hydrostatic wall gradients,ultimately detaches the low-and high-density regimes throughout the channel when the gravitational Reynolds number is inversely proportional to the aspect ratio for a fixed slip parameter.This phenomenon,observed previously in 2D numerical simulations with no-slip walls in the literature,is thus confirmed by our theoretical results.Our findings further demonstrate that wall slip leads to distinct and diverse flow regimes.
基金The authors did not receive any funding support from any source.It is self-financed solely.
文摘The physical problem of the thin film flow of a micropolar fluid over a dynamic and inclined substrate under the influence of gravitational and thermal forces in the presence of nanoparticles is formulated.Five different types of nanoparticle samples are accounted for in this current study,namely gold Au,silver Ag,molybdenum disulfide MoS_(2),aluminum oxide Al_(2)O_(3),and silicon dioxide SiO_(2).Blood,a micropolar fluid,serves as the common base fluid.An exact closed-form solution for this problem is derived for the first time in the literature.The results are particularly validated against those for the Newtonian fluid and show excellent agreement.It was found that increasing values of the spin boundary condition and micropolarity lead to a reduction in both the thermal and momentum boundary layers.A quantitative decay in the Nusselt number for a micropolar fluid,as compared to a Newtonian one for all the tested nanoparticles,is anticipated.Gold and silver nanoparticles(i)intensify in the flow parameter as the concentration of nanoparticles increases(ii)yield a higher thermal transfer rate,whereas molybdenum disulfide,aluminum oxide,and silicon dioxide exhibit a converse attitude for both Newtonian and micropolar fluids.The reduction in film thickness for fluid comprising gold particles,as compared to the rest of the nanoparticles,is remarkable.
文摘A ratio approach based on the simple ratio test associated with the terms of homotopy series was proposed by the author in the previous publications.It was shown in the latter through various comparative physical models that the ratio approach of identifying the range of the convergence control parameter and also an optimal value for it in the homotopy analysis method is a promising alternative to the classically used h-level curves or to the minimizing the residual(squared)error.A mathematical analysis is targeted here to prove the equivalence of both the ratio approach and the traditional residual approach,especially regarding the root-finding problems via the homotopy analysis method.Examples are provided to further justify this.Moreover,it is conjectured that every nonlinear differential equation can be considered as a root-finding problem by plugging a parameter in it from a physical viewpoint.Two examples from the boundary and initial and value problems are provided to verify this assertion.Hence,besides the advantages as deciphered in the previous publications,the feasibility of the ratio approach over the traditional residual approach is made clearer in this paper.
文摘The present paper is devoted to the convergence control and accelerating the traditional Decomposition Methodof Adomian (ADM). By means of perturbing the initial or early terms of the Adomian iterates by adding aparameterized term, containing an embedded parameter, new modified ADM is constructed. The optimal value ofthis parameter is later determined via squared residual minimizing the error. The failure of the classical ADM is alsoprevented by a suitable value of the embedded parameter, particularly beneficial for the Duan–Rach modification ofthe ADM incorporating all the boundaries into the formulation. With the presented squared residual error analysis,there is no need to check out the results against the numerical ones, as usually has to be done in the traditional ADMstudies to convince the readers that the results are indeed converged to the realistic solutions. Physical examplesselected from the recent application of ADM demonstrate the validity, accuracy and power of the presented novelapproach in this paper. Hence, the highly nonlinear equations arising from engineering applications can be safelytreated by the outlined method for which the classical ADM may fail or be slow to converge.
文摘An effective solution method of fractional ordinary and partial differential equations is proposed in the present paper.The standard Adomian Decomposition Method(ADM)is modified via introducing a functional term involving both a variable and a parameter.A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L^(2) norm.Numerical experiments on sample problems of open literature prove that the presented algorithm is quite accurate,more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical models.Better performance of the method is further evidenced against some compared commonly used numerical techniques.
文摘The present paper is concerned with two novel approximate analytic solutions of the undamped Duffing equation. Instead of the traditional perturbation or asymptotic methods, a homotopy technique is employed, which does not require a small perturbation parameter or a large parameter for an asymptotic expansion. It is shown that proper choices of an auxiliary linear operator and also an initial approximation during the implementation of the homotopy analysis method can yield uniformly valid and accurate solutions. The obtained explicit analytical expressions for the solution predict the displacement, frequency and period of the oscillations much more accurate than the previously known asymptotic or perturbation formulas.
