Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity

Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In...
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Autor*in:	Khader, M. M. [verfasserIn] Babatin, M. M. Megahed, Ahmed M.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2023

Schlagwörter:	Williamson nanofluid Aligned magnetic field Exponential stretching Slip velocity Vieta-Lucas polynomials Spectral collocation method Optimization technique

Anmerkung:	© The Author(s) 2023

Übergeordnetes Werk:	Enthalten in: Journal of nonlinear mathematical physics - Abingdon, Oxon : Taylor & Francis, 1994, 30(2023), 3 vom: 09. Juni, Seite 1134-1152
Übergeordnetes Werk:	volume:30 ; year:2023 ; number:3 ; day:09 ; month:06 ; pages:1134-1152

Links:	Volltext

DOI / URN:	10.1007/s44198-023-00115-7

Katalog-ID:	SPR05314502X

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245	1	0	\|a Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
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520			\|a Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here.
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allfields	10.1007/s44198-023-00115-7 doi (DE-627)SPR05314502X (SPR)s44198-023-00115-7-e DE-627 ger DE-627 rakwb eng Khader, M. M. verfasserin aut Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213 Babatin, M. M. aut Megahed, Ahmed M. aut Enthalten in Journal of nonlinear mathematical physics Abingdon, Oxon : Taylor & Francis, 1994 30(2023), 3 vom: 09. Juni, Seite 1134-1152 (DE-627)325293635 (DE-600)2034956-7 1776-0852 nnns volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152 https://dx.doi.org/10.1007/s44198-023-00115-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 30 2023 3 09 06 1134-1152
spelling	10.1007/s44198-023-00115-7 doi (DE-627)SPR05314502X (SPR)s44198-023-00115-7-e DE-627 ger DE-627 rakwb eng Khader, M. M. verfasserin aut Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213 Babatin, M. M. aut Megahed, Ahmed M. aut Enthalten in Journal of nonlinear mathematical physics Abingdon, Oxon : Taylor & Francis, 1994 30(2023), 3 vom: 09. Juni, Seite 1134-1152 (DE-627)325293635 (DE-600)2034956-7 1776-0852 nnns volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152 https://dx.doi.org/10.1007/s44198-023-00115-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 30 2023 3 09 06 1134-1152
allfields_unstemmed	10.1007/s44198-023-00115-7 doi (DE-627)SPR05314502X (SPR)s44198-023-00115-7-e DE-627 ger DE-627 rakwb eng Khader, M. M. verfasserin aut Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213 Babatin, M. M. aut Megahed, Ahmed M. aut Enthalten in Journal of nonlinear mathematical physics Abingdon, Oxon : Taylor & Francis, 1994 30(2023), 3 vom: 09. Juni, Seite 1134-1152 (DE-627)325293635 (DE-600)2034956-7 1776-0852 nnns volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152 https://dx.doi.org/10.1007/s44198-023-00115-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 30 2023 3 09 06 1134-1152
allfieldsGer	10.1007/s44198-023-00115-7 doi (DE-627)SPR05314502X (SPR)s44198-023-00115-7-e DE-627 ger DE-627 rakwb eng Khader, M. M. verfasserin aut Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213 Babatin, M. M. aut Megahed, Ahmed M. aut Enthalten in Journal of nonlinear mathematical physics Abingdon, Oxon : Taylor & Francis, 1994 30(2023), 3 vom: 09. Juni, Seite 1134-1152 (DE-627)325293635 (DE-600)2034956-7 1776-0852 nnns volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152 https://dx.doi.org/10.1007/s44198-023-00115-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 30 2023 3 09 06 1134-1152
allfieldsSound	10.1007/s44198-023-00115-7 doi (DE-627)SPR05314502X (SPR)s44198-023-00115-7-e DE-627 ger DE-627 rakwb eng Khader, M. M. verfasserin aut Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2023 Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213 Babatin, M. M. aut Megahed, Ahmed M. aut Enthalten in Journal of nonlinear mathematical physics Abingdon, Oxon : Taylor & Francis, 1994 30(2023), 3 vom: 09. Juni, Seite 1134-1152 (DE-627)325293635 (DE-600)2034956-7 1776-0852 nnns volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152 https://dx.doi.org/10.1007/s44198-023-00115-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_2088 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 30 2023 3 09 06 1134-1152
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source	Enthalten in Journal of nonlinear mathematical physics 30(2023), 3 vom: 09. Juni, Seite 1134-1152 volume:30 year:2023 number:3 day:09 month:06 pages:1134-1152
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topic_facet	Williamson nanofluid Aligned magnetic field Exponential stretching Slip velocity Vieta-Lucas polynomials Spectral collocation method Optimization technique
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author	Khader, M. M.
spellingShingle	Khader, M. M. misc Williamson nanofluid misc Aligned magnetic field misc Exponential stretching misc Slip velocity misc Vieta-Lucas polynomials misc Spectral collocation method misc Optimization technique Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
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topic_title	Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity Williamson nanofluid (dpeaa)DE-He213 Aligned magnetic field (dpeaa)DE-He213 Exponential stretching (dpeaa)DE-He213 Slip velocity (dpeaa)DE-He213 Vieta-Lucas polynomials (dpeaa)DE-He213 Spectral collocation method (dpeaa)DE-He213 Optimization technique (dpeaa)DE-He213
topic	misc Williamson nanofluid misc Aligned magnetic field misc Exponential stretching misc Slip velocity misc Vieta-Lucas polynomials misc Spectral collocation method misc Optimization technique
topic_unstemmed	misc Williamson nanofluid misc Aligned magnetic field misc Exponential stretching misc Slip velocity misc Vieta-Lucas polynomials misc Spectral collocation method misc Optimization technique
topic_browse	misc Williamson nanofluid misc Aligned magnetic field misc Exponential stretching misc Slip velocity misc Vieta-Lucas polynomials misc Spectral collocation method misc Optimization technique
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title	Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
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title_full	Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
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title_sort	numerical simulation by using the spectral collocation method for williamson nanofluid flow over an exponentially stretching sheet with slip velocity
title_auth	Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
abstract	Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. © The Author(s) 2023
abstractGer	Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. © The Author(s) 2023
abstract_unstemmed	Abstract The current research examines the rate of heat and mass transfer in MHD non-Newtonian Williamson nanofluid flow across an exponentially permeable stretched surface sensitive to heat generation/absorption and mass suction. The influences of Brownian motion and thermophoresis are included. In addition, the stretched surface is subjected to an angled outside magnetic field. This study incorporates the variable viscosity, viscous dissipation, and slip velocity. The fundamental rules of motion and heat transmission have been constructed mathematically to fit the current flow problem. By using appropriate self-similarity transformations, the supplied system of PDEs is transformed into a nonlinear system of ODEs. Here, we use the spectral collocation method with the help of Vieta-Lucas polynomials approximation. This procedure converts the present model to a system of algebraic equations which is developed as a constrained optimization problem, which is then optimized to get the solution and the unknown coefficients. Calculations are made for the skin friction, wall temperature gradient, and wall concentration gradient. By comparing our findings in some special cases to those in the literature, a review of the literature confirms the results described here. © The Author(s) 2023
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title_short	Numerical Simulation by Using the Spectral Collocation Method for Williamson Nanofluid Flow Over an Exponentially Stretching Sheet with Slip Velocity
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