The thermal energy transfer characteristics during hybrid nanofluid migration are studied in the presence of a variable magnetic field, heat source, and radiation. The flow is governed by the conservation laws of mass, momentum, and energy, whereas it is modeled by the coupled set of nonlinear partial differential equations (PDEs). Suitable similarity transformations are employed to convert the developed set of PDEs to a nonlinear system of coupled ordinary differential equations (ODEs). The simplified system of ODEs is solved by using the well-established analytical procedure of homotopy analysis method (HAM). The effects of varying the strength of the physical parameters on the thermal energy transfer during hybrid nanofluid motion between two plates in which one of the plate is porous, rotating, as well as stretching are investigated through tables and two-dimensional graphs. The porosity is modeled through the Koo–Kleinstreuer model (KKL) correlation. The analysis reveals that the skin friction and Nusselt number augment with the increasing strength of the magnetic field and nanomaterials’ concentrations. The gradient in the fluid velocity has a dual dependence on the strength of the applied magnetic field and Grashof number and drops with the higher values of the unsteadiness parameter. The fluid velocity constricts with the enhancing magnetic field due to higher Lorentz forces, and it also drops with the increasing rotation rate. The enhancing buoyancy associated with higher Grashof number values augments the fluid velocity. The fluid’s temperature rises with the augmenting nanomaterial concentrations, Eckert number, nonsteadiness, heat source strength, and radiation parameter, while it drops with the higher Grashof number and Prandtl number. The applied technique of the HAM shows good convergence over a wide range of the convergent parameter. This work has potential applications in the development of efficient thermal energy transfer systems.
In this paper, a new class of functions denoted by
Ψ
ν
is introduced which we use to prove new interesting fixed point results in controlled metric type spaces. Also, we present examples to illustrate our work.
<abstract><p>In this article, a new fractional mathematical model is presented to investigate the contagion of the human immunodeficiency virus (HIV). This model is constructed via recent improved fractional differential and integral operators. Other operators like Caputo, Riemann-Liouville, Katugampola, Jarad and Hadamard are being extended and generalized by these improved fractional differential and integral operators. Banach's and Leray-Schauder nonlinear alternative fixed point theorems are utilized to examine the existence and uniqueness results of the proposed fractional HIV model. Moreover, different kinds of Ulam stability for the fractional HIV model are established. It is simple to recognize that the extracted results can be reduced to some results acquired in multiple works of literature.</p></abstract>
In this article we make an improvement in the Banach contraction using a controlled function in controlled metric like spaces, which generalizes many results in the literature. Moreover, we present an application on Fredholm type integral equation.
We introduce the notion of generalized parametric metric spaces along with the study of its various properties. Further, we prove some new fixed point theorems for $(\alpha ,\psi )$
(
α
,
ψ
)
-rational-type contractive mappings in generalized parametric metric spaces. As a consequence, we deduce fixed point theorems for $(\alpha , \psi )$
(
α
,
ψ
)
-rational-type contractive mappings in partially ordered rectangular generalized fuzzy metric spaces.
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