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NUR AIREEN NATASYA DR SITI FARAH HARYATIE K242/39

BINTI MARZELAN BINTI MOHD KANAFIAH

SOLVING VISCOUS FLUID MODEL USING RUNGE-KUTTA

FEHLBERG FOURTH-FIFTH(RKF45) METHOD FOR HEAT

TRANSFER PROBLEM PASSING OVER STRETCHING SHEET

"Let’s dive
"Heat transfer +
into the problem viscous fluid +

we’re solving..." RKF45 = real-world

ABSTRACT PROBLEM STATEMENT challenge!"

Mathematical modeling for a stagnation This study aims to solve the mathematical model using appropriate formulation.

point over a stretching sheet in a viscous In fluid flow and heat transfer problem, numerical method is used to solve the non-

fluid subject to CBC is considered. linear ODEs

Using similarity transformations to Numerically methods struggle with computational efficiency and the ability to handle

transform the PDEs into nonlinear ODEs complex boundary conditions

Using RKF45 method in Maple software This study proposes using the RKF45 method to solve the viscous fluid model for heat

Investigated for the effects of various transfer problems involving a stretching sheet

Prandtl numbers, stretching parameters, Aims to improve the understanding of the properties of viscous f luid flow and heat

and conjugate parameters. transfer under CBC conditions, while providing more efficient and accurate numerical

solutions

METHODOLOGY

"But what are we

OBJECTIVES trying to achieve?"

To transform partial

differential equations To solve the To compare the

(PDEs) which are ODEs using the results with the

“Non-linear boundary layer RKF45 method previous

The physical viscous fluid model: ODEs ahead... equations to ordinary with the help of

Transform PDEs to nonlinear ODEs: brace numerical

The boundary layer equations: yourself!” differential equations Maple software. solution

(ODEs) using similarity

transformations

RESULTS & DISCUSSION

Boundary conditions:

Velocity Profiles

Using similarity transformations:

“Error comparison

complete.

Accuracy

confirmed.”

Temperature Profiles

CONCLUSION

The increase in the Prandtl number, Pr, and

the stretching parameter ε was found to

lead to a decrease in the temperature in the

boundary layer and the thickness of the "Success! Finally we

thermal boundary layer. found the answer !!!

The temperature within the boundary layer RECOMMENDATIONS

and the thickness of the thermal boundary
Validating the model is essential by comparing RKF45

layer increase as γ increases. solutions with analytical, experimental data, or other

The increase in the Prandtl number, Pr, and Numerical accuracy can be enhanced by numerical techniques to ensure the accuracy of the

the conjugate parameter, γ, leads to an utilizing the adaptive step size of RKF45, results.

which ensures precise calculations in areas
increase in the velocity profiles but quickly Efficiency can be achieved by investigating hybrid

where the flow changes rapidly, and using approaches, such as combining RKF45 with other

approaches the asymptotic value of one. In more precision arithmetic can help to reduce

contrast, the velocity profiles change errors. methods, such as using machine learning to optimize
calculations or connecting RKF45 with finite element

significantly when ε > 1 and ε <1. methods for complex geometries.