1. A system for optimization analysis of oblique stagnation point hybrid nanofluid flow over an elongating cylinder, comprising: • a hybrid nanofluid consisting of multiple nanoparticles suspended in a base liquid; • a modified Buongiorno model configured to account for Brownian motion and thermophoresis effects in hybrid nanofluid transport; • a heat source/sink term integrated into the governing energy equation to represent internal heat generation or absorption; • a binary chemical reaction mechanism with activation energy incorporated into the species conservation equation to model reactive diffusion; • a computational framework for converting governing conservation equations of momentum, energy, and concentration into non-dimensional form; • an optimization strategy applied to analyze velocity, temperature, and concentration distributions, as well as engineering performance indicators including skin friction, Nusselt number, and Sherwood number; wherein the system enables precise modeling and optimization of heat and mass transfer rates under combined thermal and chemical influences in oblique stagnation point flow over an elongating cylindrical geometry.

2. The system as claimed in claim 1, wherein the modified Buongiorno model simultaneously incorporates nanoparticle Brownian motion, thermophoresis, and hybrid nanofluid thermophysical properties.

3. The system as claimed in claim 1, wherein the binary chemical reaction mechanism includes activation energy effects to regulate reaction rates and concentration gradients.

4. The system as claimed in claim 1, wherein the optimization framework identifies critical operating parameters that maximize heat transfer efficiency and minimize thermal losses.

5. The system as claimed in claim 1, wherein the analysis provides scalable solutions for high-performance thermal management and reactive flow systems involving elongating cylindrical geometries.

6. A method for optimization analysis of oblique stagnation point hybrid nanofluid flow over an elongating cylinder, comprising the steps of: • preparing a hybrid nanofluid with nanoparticles suspended in a base liquid; • modeling nanoparticle transport using a modified Buongiorno framework incorporating Brownian motion and thermophoresis; • introducing heat source/sink effects into the energy equation to represent internal heat generation or absorption; • incorporating binary chemical reaction with activation energy into the species conservation equation; • transforming governing equations into non-dimensional form; • applying numerical optimization techniques to solve for velocity, temperature, and concentration distributions; • evaluating engineering performance indicators including skin friction coefficient, Nusselt number, and Sherwood number; • determining optimal parameter ranges for maximizing heat and mass transfer efficiency under combined thermal and chemical influences.

7. The method as claimed in claim 6, wherein optimization is performed to balance thermal energy generation/absorption with reactive diffusion rates.

8. The method as claimed in claim 6, wherein activation energy is used to regulate binary chemical reaction kinetics in real-time simulations.

9. The method as claimed in claim 6, wherein the analysis is applied to industrial processes including polymer extrusion, energy conversion equipment, and chemical reactors involving elongating cylindrical surfaces.

Description:FIELD OF THE INVENTION
This invention relates to optimization analysis on oblique stagnation point hybrid nanofluid flow over an elongating cylinder with heat source/ sink and binary chemical reaction and activation energy: modified buongiorno model.
BACKGROUND OF THE INVENTION
One of the problems of advanced thermal and chemical engineering processes like energy conversion equipment, polymer processing, cooling equipment, and reaction flow systems is to improve the performance of heat and mass transfer. Traditional working fluids have low thermal efficiency and in this regard hybrid nanofluids are being used as they are better in their thermophysical characteristics. In most real life scenarios, oblique stagnation point flow across elongating cylindrical surfaces occur in extrusion, boundary layer control and aerodynamic heating where curvature and stretching forces are important determinant of flow behaviour. Also, the internal heat generation or internal absorption and binary chemical reaction with activation energy will further complicate the transport mechanisms, which directly influence the temperature distribution, concentration fields, and stability of the system. Overlooking such effects is likely to lead to poor forecasts of thermal and chemical performance.
Even though the Buongiorno model gives a realistic approach by considering the Brownian motion and the effect of thermophoresis, its classical version is not enough to analyze the interaction between the thermal, chemical and geometric effects in the hybrid nanofluids. It is therefore necessary to have an analysis of the model of Buongiorno modified and optimized in order to properly model and optimize the rates of heat and mass transfer and the dynamics of the reaction. Although much has been done concerning nanofluids and stagnation point flows alone, there is limited research mainly in the hybrid format that provides a study concerning the oblique stagnating point hybrid nanofluid flow over an extending cylinder under the influence of a heat source /sink and binary chemical reaction together with activation energy. This study seeks to address this gap by creating a detailed mathematical model and optimization of the controlling parameters to bring about an insight that can be used in high-performance thermal and reactive systems.
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 current invention is the development of a superior analytical and optimization model of optimizing the heat and mass transfer in oblique stagnation point hybrid nanofluid flow of an elonging cylindrical surface under combined thermal and chemical influences. The invention is a modified version of the Buongiorno model to precisely represent the transport mechanisms of nanoparticles (Brownian motion and thermophoresis) in a hybrid nanofluid that consists of several nanoparticles suspended in a base liquid. The system involves the effect of internal heat source/sink and binary chemical reaction with activation energy, which allows realistic representation of the thermal energy generation or absorption and reactive diffusion of mass phenomena observed in the high-performance thermal and chemical processing processes.
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
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 an optimization framework for analyzing oblique stagnation point hybrid nanofluid flow over an elongating cylindrical surface under combined thermal and chemical influences. The system employs a modified Buongiorno model that incorporates nanoparticle transport mechanisms such as Brownian motion and thermophoresis, while extending its applicability to hybrid nanofluids composed of multiple nanoparticles suspended in a base liquid. To achieve realistic representation of industrial processes, the invention integrates internal heat source/sink effects into the governing energy equation, thereby modeling thermal energy generation or absorption, and introduces a binary chemical reaction mechanism with activation energy into the species conservation equation to capture reactive diffusion phenomena.
The governing conservation equations of momentum, energy, and concentration are transformed into a non-dimensional form and solved using advanced numerical optimization techniques. This framework enables detailed analysis of velocity, temperature, and concentration distributions, while simultaneously evaluating engineering performance indicators such as skin friction coefficient, Nusselt number, and Sherwood number. By identifying critical operating parameters, the invention provides optimized solutions that maximize heat and mass transfer efficiency, regulate reaction rates, and minimize thermal losses.
The novelty of the invention lies in its combined treatment of oblique stagnation point flow, elongating cylindrical geometry, hybrid nanofluid transport, heat source/sink effects, binary chemical reaction, and activation energy, all within a unified optimization model. Unlike conventional Buongiorno formulations, the modified model proposed herein offers a scalable and robust analytical tool for designing high-performance thermal management and reactive flow systems. The invention is particularly applicable to advanced engineering processes such as polymer extrusion, energy conversion equipment, cooling systems, and chemical reactors, where precise control of heat and mass transfer is critical for efficiency and stability
The current invention is the development of a superior analytical and optimization model of optimizing the heat and mass transfer in oblique stagnation point hybrid nanofluid flow of an elonging cylindrical surface under combined thermal and chemical influences. The invention is a modified version of the Buongiorno model to precisely represent the transport mechanisms of nanoparticles (Brownian motion and thermophoresis) in a hybrid nanofluid that consists of several nanoparticles suspended in a base liquid. The system involves the effect of internal heat source/sink and binary chemical reaction with activation energy, which allows realistic representation of the thermal energy generation or absorption and reactive diffusion of mass phenomena observed in the high-performance thermal and chemical processing processes.
The invention states that the governing conservation equations of momentum, energy, and species concentration are converted to a non-dimensional form and solved with an effective numerical optimization strategy to study and optimize the significant physical parameters. The suggested framework analyses both velocity, temperature, and concentration distributions as well as engineering performance indicators like skin friction, Nusselt number, and Sherwood number. The invention offers a scalable and robust solution to the design and optimization of high-performance hybrid nanofluid-based thermal management and reactive flow systems of elongating cylindrical shapes through the identification of the best operating conditions that maximize heat and mass transfer and control reaction rates and thermal losses.
The new analytical model is a combination of oblique stagnation point flow, elongating cylindrical geometry and a modified Buongiorno model that is designed to precisely model hybrid nano fluid transport processes. The proposed method is the first of its kind to take advantage of the heat source/sink effects, binary chemical reaction, and the activation energy together with parameter optimization analysis to increase the effectiveness of heat and mass transfer, which has not been collectively covered in current literature.
The best method of working the present invention involves applying the modified Buongiorno model to analyze and optimize oblique stagnation point hybrid nanofluid flow over an elongating cylindrical surface under combined thermal and chemical influences. A hybrid nanofluid is prepared by dispersing multiple types of nanoparticles in a base liquid to enhance thermophysical properties. The governing conservation equations of momentum, energy, and species concentration are formulated to include Brownian motion and thermophoresis effects, internal heat source/sink terms, and binary chemical reaction with activation energy.
These equations are transformed into a non-dimensional form and solved using robust numerical optimization techniques. The computational framework evaluates velocity, temperature, and concentration distributions, while simultaneously calculating engineering performance indicators such as skin friction coefficient, Nusselt number, and Sherwood number. Optimization analysis is performed to identify critical operating parameters that maximize heat and mass transfer efficiency, regulate reaction rates, and minimize thermal losses.
The invention is best worked by implementing this analytical framework in industrial applications such as polymer extrusion, energy conversion equipment, cooling systems, and chemical reactors where oblique stagnation point flow over cylindrical geometries is common. By integrating the modified Buongiorno model with optimization strategies, the invention provides a scalable and reliable method for designing high-performance thermal management and reactive flow systems.
This section ensures that the examiner understands how the invention is practically applied and demonstrates its industrial utility.
, Claims:1. A system for optimization analysis of oblique stagnation point hybrid nanofluid flow over an elongating cylinder, comprising:
• a hybrid nanofluid consisting of multiple nanoparticles suspended in a base liquid;
• a modified Buongiorno model configured to account for Brownian motion and thermophoresis effects in hybrid nanofluid transport;
• a heat source/sink term integrated into the governing energy equation to represent internal heat generation or absorption;
• a binary chemical reaction mechanism with activation energy incorporated into the species conservation equation to model reactive diffusion;
• a computational framework for converting governing conservation equations of momentum, energy, and concentration into non-dimensional form;
• an optimization strategy applied to analyze velocity, temperature, and concentration distributions, as well as engineering performance indicators including skin friction, Nusselt number, and Sherwood number;
wherein the system enables precise modeling and optimization of heat and mass transfer rates under combined thermal and chemical influences in oblique stagnation point flow over an elongating cylindrical geometry.
2. The system as claimed in claim 1, wherein the modified Buongiorno model simultaneously incorporates nanoparticle Brownian motion, thermophoresis, and hybrid nanofluid thermophysical properties.
3. The system as claimed in claim 1, wherein the binary chemical reaction mechanism includes activation energy effects to regulate reaction rates and concentration gradients.
4. The system as claimed in claim 1, wherein the optimization framework identifies critical operating parameters that maximize heat transfer efficiency and minimize thermal losses.
5. The system as claimed in claim 1, wherein the analysis provides scalable solutions for high-performance thermal management and reactive flow systems involving elongating cylindrical geometries.
6. A method for optimization analysis of oblique stagnation point hybrid nanofluid flow over an elongating cylinder, comprising the steps of:
• preparing a hybrid nanofluid with nanoparticles suspended in a base liquid;
• modeling nanoparticle transport using a modified Buongiorno framework incorporating Brownian motion and thermophoresis;
• introducing heat source/sink effects into the energy equation to represent internal heat generation or absorption;
• incorporating binary chemical reaction with activation energy into the species conservation equation;
• transforming governing equations into non-dimensional form;
• applying numerical optimization techniques to solve for velocity, temperature, and concentration distributions;
• evaluating engineering performance indicators including skin friction coefficient, Nusselt number, and Sherwood number;
• determining optimal parameter ranges for maximizing heat and mass transfer efficiency under combined thermal and chemical influences.
7. The method as claimed in claim 6, wherein optimization is performed to balance thermal energy generation/absorption with reactive diffusion rates.
8. The method as claimed in claim 6, wherein activation energy is used to regulate binary chemical reaction kinetics in real-time simulations.
9. The method as claimed in claim 6, wherein the analysis is applied to industrial processes including polymer extrusion, energy conversion equipment, and chemical reactors involving elongating cylindrical surfaces.