1. A method for enhancing heat transfer in hybrid nanofluid flow over a convectively heated extending surface, comprising: • subjecting an EG-MoS2-SiO2 hybrid nanofluid to an inclined magnetic field; • applying a non-uniform heat source to the fluid domain; • accounting for viscous dissipation and Joule heating effects; and • optimizing flow and thermal boundary layer characteristics through parametric control of nanoparticle concentration, magnetic inclination, suction velocity, Eckert number, Biot number, and radiative heat flux.

2. The method of claim 1, wherein the concentration of nanoparticles is increased up to 40% to improve thermal boundary layer thickness and momentum transfer.

3. The method of claim 1, wherein the inclined magnetic field is varied at different angles to regulate momentum distribution and thermal control of the hybrid nanofluid.

4. The method of claim 1, wherein the non-uniform heat source intensity is adjusted to achieve optimized thermal conductivity and heat transfer efficiency.

5. The method of claim 1, wherein viscous dissipation and Joule heating are simultaneously incorporated to provide realistic thermodynamic transport modeling.

6. The method of claim 1, wherein the governing nonlinear momentum and energy equations are solved using a Runge-Kutta method coupled with a shooting technique to obtain accurate boundary value solutions.

7. The method of claim 1, wherein suction velocity is controlled to stabilize flow behavior and enhance cooling efficiency.

8. The method of claim 1, wherein radiative heat flux is integrated into the model to simulate realistic thermal radiation effects in hybrid nanofluid systems.

9. A computational system for analyzing hybrid EG-MoS2-SiO2 nanofluid flow, comprising: • a mathematical model configured to simulate inclined magnetic field effects, non-uniform heating, viscous dissipation, Joule heating, and radiation; • a numerical solver employing Runge-Kutta and shooting techniques; and • a parametric analysis module for evaluating nanoparticle concentration, magnetic inclination, Biot number, Eckert number, suction velocity, and radiative flux.

10. The system of claim 9, wherein hybrid nanofluids demonstrate superior thermal and momentum characteristics compared to conventional nanofluids, thereby enabling applications in cooling systems, energy storage devices, and material processing.

Description:FIELD OF THE INVENTION
This invention relates to influence of inclined magnetic field, non-uniform source of heat on hybrid eg-mos2-sio2 radiative nano fluid flow with viscous and joule dissipation in convectively heated extending surface.
BACKGROUND OF THE INVENTION
The combination of non-uniform heat sources and viscous dissipation brings a lot of complexity in the study of the hybrid nanofluid flow over an elongating surface, which remains relevant and an issue of increasing interest in thermal engineering. These effects play a significant role in improving the heat transfer efficiency in highly developed projects like cooling systems, energy storage devices, as well as material processing, where a highly organized thermal control is needed. This paper examines how a non-uniform heat source interacting with a sloping magnetic field affects the nature of flow and heat transfer in a radiative EG-MoS2-SiO2 hybrid nanofluid over a convectively-heated elongating surface taking into consideration the effects of Joule heating, as well as viscous dissipation. The equations of motion of a hybrid nanofluid as a nonlinear system are developed and analytically addressed with the Runge-Kutta method in combination with the shooting technique and the findings are compared to the available literature
The effects of the concentration of the nanoparticles, the inclination angle of the magnetic field, non-uniformity of the intensity of heat source, the Eckert number, the thermal Biot number, the suction velocity and the linear radiative heat flux on the flow behavior in the vicinity of the stretching surface are studied through a thorough parametric analysis. The findings reveal that the inclination of the magnetic field and homogenous suction have a great effect on the momentum and thermal control of the fluid. When the concentration of nanoparticles is increased to 40 percent, it increases the thermal boundary layer thickness as a result of high viscous dissipation, radiative heat flux, and thermal Biot number. In general, hybrid nanofluids exhibit better thermal and momentum characteristics than conventional nanofluids, and thus their use in a high-performance heat transfer objective is possible.
SUMMARY OF THE INVENTION
This summary is provided to introduce a selection of concepts, in a simplified format, that are further described in the detailed description of the invention.
This summary is neither intended to identify key or essential inventive concepts of the invention and nor is it intended for determining the scope of the invention.
The offered invention is associated with the development of a sophisticated thermal-fluid dynamic model of heat transfer analysis and optimization in terms of hybrid nanofluids on a growing surface. The invention explicitly discusses the interaction of non uniform source of heat, viscous dissipation, Joule heating and magnetic field in radiative hybrid nanofluid flow. It also proposes a general mathematical and computing model that describes the dynamics of an EG-MoS2-SiO2 hybrid nanofluid under the influence of an inclined magnetic field and convective surface heating. This model is especially structured to embrace realistic thermodynamic transport processes of interest when using thermal engineering to very fine precision.
The invention presents a comprehensive thermal-fluid dynamic model for analyzing hybrid EG-MoS2-SiO2 nanofluid flow over a convectively heated extending surface under the influence of an inclined magnetic field, non-uniform heat sources, viscous dissipation, and Joule heating. By integrating these physical effects into a unified framework, the invention enables precise prediction of heat transfer and momentum behavior. The governing nonlinear equations are solved using the Runge-Kutta method coupled with the shooting technique, and a parametric study is conducted to evaluate the impact of nanoparticle concentration, magnetic inclination, suction velocity, Eckert number, Biot number, and radiative heat flux. Results demonstrate that hybrid nanofluids outperform conventional nanofluids in enhancing thermal boundary layer thickness and momentum transfer, making them highly suitable for advanced cooling systems, energy storage devices, and material processing applications. The novelty lies in the simultaneous incorporation of inclined magnetic fields, non-uniform heating, and combined viscous-Joule dissipation effects, offering a more realistic and optimized solution for high-performance thermal engineering.
To further clarify advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof, which is illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting of its scope. The invention will be described and explained with additional specificity and detail with the accompanying drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
The illustrated embodiments of the subject matter will be understood by reference to the drawings, wherein like parts are designated by like numerals throughout. The following description is intended only by way of example, and simply illustrates certain selected embodiments of devices, systems, and methods that are consistent with the subject matter as claimed herein, wherein:
FIGURE 1: FLOW CHART
FIGURE 2: ANALYZING HEAT TRANSFER IN HYBRID NANOFLUID FLOW OVER ELONGATING SURFACE
The figures depict embodiments of the present subject matter for the purposes of illustration only. A person skilled in the art will easily recognize from the following description that alternative embodiments of the structures and methods illustrated herein may be employed without departing from the principles of the disclosure described herein.
DETAILED DESCRIPTION OF THE INVENTION
The detailed description of various exemplary embodiments of the disclosure is described herein with reference to the accompanying drawings. It should be noted that the embodiments are described herein in such details as to clearly communicate the disclosure. However, the amount of details provided herein is not intended to limit the anticipated variations of embodiments; on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the scope of the present disclosure as defined by the appended claims.
It is also to be understood that various arrangements may be devised that, although not explicitly described or shown herein, embody the principles of the present disclosure. Moreover, all statements herein reciting principles, aspects, and embodiments of the present disclosure, as well as specific examples, are intended to encompass equivalents thereof.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms “a",” “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises,” “comprising,” “includes” and/or “including,” when used herein, specify the presence of stated features, integers, steps, operations, elements and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components and/or groups thereof.
It should also be noted that in some alternative implementations, the functions/acts noted may occur out of the order noted in the figures. For example, two figures shown in succession may, in fact, be executed concurrently or may sometimes be executed in the reverse order, depending upon the functionality/acts involved.
In addition, the descriptions of "first", "second", “third”, and the like in the present invention are used for the purpose of description only, and are not to be construed as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Thus, features defining "first" and "second" may include at least one of the features, either explicitly or implicitly.
Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which example embodiments belong. It will be further understood that terms, e.g., those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The present invention relates to a novel method and computational framework for analyzing and optimizing heat transfer in hybrid EG-MoS2-SiO2 nanofluid flow over a convectively heated extending surface. The invention integrates the combined effects of an inclined magnetic field, non-uniform heat source, viscous dissipation, and Joule heating into a single analytical model, thereby enabling a more realistic prediction of thermal-fluid dynamics. The claims encompass both the process of subjecting hybrid nanofluids to parametric variations—such as nanoparticle concentration, magnetic inclination, suction velocity, Eckert number, Biot number, and radiative heat flux—and the computational system that employs the Runge-Kutta method coupled with the shooting technique to solve nonlinear governing equations. By incorporating these parameters, the invention demonstrates that hybrid nanofluids exhibit superior thermal boundary layer thickness and momentum transfer compared to conventional nanofluids, making them highly suitable for applications in cooling systems, energy storage devices, and material processing. The invention further claims the ability to regulate flow behavior and heat transfer efficiency through controlled variation of magnetic field angles, nanoparticle concentration up to 40%, and suction velocity, thereby offering a comprehensive solution for advanced thermal engineering applications.
Best Method of Performing the Invention
The best method of carrying out the invention involves the following steps:
- Preparation of Hybrid Nanofluid
- Formulate an EG-MoS2-SiO2 hybrid nanofluid with nanoparticle concentration optimized up to 40%.
- Ensure uniform dispersion of nanoparticles to achieve stable thermophysical properties.
- Application of Inclined Magnetic Field
- Subject the nanofluid flow to a controlled inclined magnetic field, with adjustable angles to regulate momentum distribution.
- Magnetic inclination is varied systematically to study its effect on flow stability and heat transfer.
- Introduction of Non-Uniform Heat Source
- Apply a spatially varying heat source along the extending surface to simulate realistic thermal gradients.
- Control the intensity of the heat source to optimize thermal conductivity and boundary layer thickness.
- Incorporation of Viscous Dissipation and Joule Heating
- Model viscous dissipation and Joule heating effects simultaneously to capture realistic thermodynamic transport processes.
- Integrate these effects into the governing nonlinear momentum and energy equations.
- Numerical Solution
- Employ the Runge-Kutta method in combination with the shooting technique to solve the boundary value problem.
- Conduct parametric analysis to evaluate the influence of nanoparticle concentration, magnetic inclination, Biot number, Eckert number, suction velocity, and radiative flux.
- Optimization and Validation
- Compare results with existing literature to validate accuracy.
- Optimize parameters for maximum heat transfer efficiency and momentum control.
This method ensures that the invention achieves its objective of providing a comprehensive, realistic, and high-precision model for hybrid nanofluid heat transfer systems, thereby enabling practical applications in advanced cooling technologies, energy storage, and material processing.
The offered invention is associated with the development of a sophisticated thermal-fluid dynamic model of heat transfer analysis and optimization in terms of hybrid nanofluids on a growing surface. The invention explicitly discusses the interaction of non uniform source of heat, viscous dissipation, Joule heating and magnetic field in radiative hybrid nanofluid flow. It also proposes a general mathematical and computing model that describes the dynamics of an EG-MoS2-SiO2 hybrid nanofluid under the influence of an inclined magnetic field and convective surface heating. This model is especially structured to embrace realistic thermodynamic transport processes of interest when using thermal engineering to very fine precision.
In the suggested system, the governing nonlinear momentum and energy equations of hybrid nanofluid dynamics are developed by considering major physical processes that include inclination of magnetic field, non-uniform heating of the interior, thermal radiation, viscous dissipation and suction. The invention uses a powerful numerical approach solution of the Runge-Kutta method coupled with the shooting technique to solve the accurate solution of the boundary value problem. A parametric analysis is done to determine the effect of the concentration of the nanoparticles, magnetic inclination of the nanoparticles, Eckert number, Biot number, radiative heat flux and suction velocity on the flow behavior, friction factor and heat transfer rate. It is revealed by the invention that hybrid nanofluids are much superior to the conventional nanofluids in improving the thermal boundary layer thickness and momentum transfer, hence providing an efficient solution in the optimization of heat transfer systems in cooling technology, energy storage devices, and material processing.
The suggested invention will introduce a new analytical, computational system that is unique and integrating an inclined magnetic field, non-uniform heat source, thermal radiation, and joint viscous-Joule dissipation effects in the study of hybrid EG-MoS2-SiO2 nanofluid flow on a convectively heated elongating surface thus allowing a more realistic and comprehensive prediction of the heat and momentum transfer behavior in way not before explored.
, Claims:1. A method for enhancing heat transfer in hybrid nanofluid flow over a convectively heated extending surface, comprising:
• subjecting an EG-MoS2-SiO2 hybrid nanofluid to an inclined magnetic field;
• applying a non-uniform heat source to the fluid domain;
• accounting for viscous dissipation and Joule heating effects; and
• optimizing flow and thermal boundary layer characteristics through parametric control of nanoparticle concentration, magnetic inclination, suction velocity, Eckert number, Biot number, and radiative heat flux.
2. The method of claim 1, wherein the concentration of nanoparticles is increased up to 40% to improve thermal boundary layer thickness and momentum transfer.
3. The method of claim 1, wherein the inclined magnetic field is varied at different angles to regulate momentum distribution and thermal control of the hybrid nanofluid.
4. The method of claim 1, wherein the non-uniform heat source intensity is adjusted to achieve optimized thermal conductivity and heat transfer efficiency.
5. The method of claim 1, wherein viscous dissipation and Joule heating are simultaneously incorporated to provide realistic thermodynamic transport modeling.
6. The method of claim 1, wherein the governing nonlinear momentum and energy equations are solved using a Runge-Kutta method coupled with a shooting technique to obtain accurate boundary value solutions.
7. The method of claim 1, wherein suction velocity is controlled to stabilize flow behavior and enhance cooling efficiency.
8. The method of claim 1, wherein radiative heat flux is integrated into the model to simulate realistic thermal radiation effects in hybrid nanofluid systems.
9. A computational system for analyzing hybrid EG-MoS2-SiO2 nanofluid flow, comprising:
• a mathematical model configured to simulate inclined magnetic field effects, non-uniform heating, viscous dissipation, Joule heating, and radiation;
• a numerical solver employing Runge-Kutta and shooting techniques; and
• a parametric analysis module for evaluating nanoparticle concentration, magnetic inclination, Biot number, Eckert number, suction velocity, and radiative flux.
10. The system of claim 9, wherein hybrid nanofluids demonstrate superior thermal and momentum characteristics compared to conventional nanofluids, thereby enabling applications in cooling systems, energy storage devices, and material processing.