In the current article, the focus of the study is the rate of heat transfer in three-dimensional coordinates. The cone-disk apparatus is assumed with rotating disk and stationary cone or may be taken with a stationary disk and rotating cone, or both of them co-rotating, or counter-rotating, along single-wall carbon nanotubes (SWCNTs) and multiple wall carbon nanotubes (MWCNTs) of water-based. By the definition of well-known thermal physical possessions of CNTs heat transfer enhancement at both the cone-disk surfaces is investigated. Further magnetism (MHD) is enforced perpendicular to the flow of nanofluid between the cone and the disk surface. The conical gap section is considered moderate for the better result of heat transfer. The modeled equations for the nonlinear problem are solved through an analytical approach Homotopy analysis method (HAM). On behalf of graphical outcomes of velocity, concentration, and temperature profiles the HAM BVPh 2.0 package has been used. Moreover numerical values of skin friction, Nusselt number are calculated through the effect of SWCNTs and MWCNTs at both the cone and disk surface with a moderate apex angle. On behalf of the concentration equation, the Sherwood number is also deliberate in the present analysis.
The melting procedure with a direct contact of phase change material is taken into account to consider the porous medium in the presence of a uniform and transverse magnetic field. A permeable rotating disk is taken as a heater in the melting progression of solid phase change material. The three-dimensional melting layer takes place due to the accruing of the temperature difference among the porous disk and solid material. Movement is subject to the effect of pressure loading (counting the weight of solid), direct relation with solid and rotation due to centrifugal force. The removal of melting is controlled due to the joint exertions of the porous media, wall permeability and resistive force generated due to the applied magnetic field. The motion of the melting layer is assumed unsteady and governed the nonlinear similarity equations. Furthermore, magnetic field, porosity, external load and wall suction enhance melting and heat transfer rates at the thin melts film thickness. The melting rate, momentum and thermal boundary layers are estimated under the impact of Stefan number, magnetic field, porosity parameter and unsteadiness parameter. The Eckert number enhances the thermal boundary layer, and consequently the larger amount of melting received. The governing PDEs is highly nonlinear; thus for the solution we use analytical method of HAM and BVPh 2.0 package. The important outputs of the thickness of the thin layer during melting process in the presence and absence of wall suction are mainly focused.
In mathematical models, parameters are one of the most important input factors that affect the model outputs. In this work, the effects of parameters in complementing their interaction effects on nanofluids' output variables in converging and diverging channels have been studied. The mathematical model is solved numerically by using Matlab's built-in solver bvp4c. Global sensitivity analysis (Sobol's method) quantifies the effects of input parameters and their interactions on model outputs. The results showed that the channel opening (α) is the most influential model parameter for the velocity profile. Simultaneously, Eckert number (Ec) becomes the most influential parameter for temperature distribution in diverging and converging channels. The least sensitive parameters and interaction effects of involved parameters are identified on velocity and temperature profiles in converging and diverging channels.
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