Analisis dan Pengolahan Data
- Persamaan
Matriks menjadi
Dengan eliminasi Gauss kita dapat menemukan persamaannya menjadi :
- Curve fitting
Berikut merupakan coding javascript :
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Curve Fitting dengan Plotly.js</title>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<style>
body {
font-family: Arial, sans-serif;
display: flex;
justify-content: center;
align-items: center;
height: 100vh;
margin: 0;
background-color: #f4f4f4;
}
#curveFitPlot {
width: 800px;
height: 600px;
background-color: white;
box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
border-radius: 8px;
}
</style>
</head>
<body>
<div id="curveFitPlot"></div>
<script>
// Data dari file CSV
const x = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]; // Posisi (m)
const T = [337.778, 351.284, 357.243, 359.911, 360.687, 359.911, 357.243, 351.284, 337.778]; // Temperatur (K)
// Fungsi untuk curve fitting (polinomial derajat 2)
function polynomial(x, a, b, c) {
return a * x * x + b * x + c;
}
// Menggunakan metode least squares untuk curve fitting
function curveFit(x, y) {
const n = x.length;
let sumX = 0, sumX2 = 0, sumX3 = 0, sumX4 = 0;
let sumY = 0, sumXY = 0, sumX2Y = 0;
for (let i = 0; i < n; i++) {
sumX += x[i];
sumX2 += x[i] * x[i];
sumX3 += x[i] * x[i] * x[i];
sumX4 += x[i] * x[i] * x[i] * x[i];
sumY += y[i];
sumXY += x[i] * y[i];
sumX2Y += x[i] * x[i] * y[i];
}
const A = [
[n, sumX, sumX2],
[sumX, sumX2, sumX3],
[sumX2, sumX3, sumX4]
];
const B = [sumY, sumXY, sumX2Y];
// Menyelesaikan sistem persamaan linear
const coefficients = solveLinearSystem(A, B);
return coefficients;
}
// Fungsi untuk menyelesaikan sistem persamaan linear
function solveLinearSystem(A, B) {
const n = A.length;
for (let i = 0; i < n; i++) {
// Pivoting
let maxRow = i;
for (let j = i + 1; j < n; j++) {
if (Math.abs(A[j][i]) > Math.abs(A[maxRow][i])) {
maxRow = j;
}
}
[A[i], A[maxRow]] = [A[maxRow], A[i]];
[B[i], B[maxRow]] = [B[maxRow], B[i]];
// Eliminasi
for (let j = i + 1; j < n; j++) {
const factor = A[j][i] / A[i][i];
B[j] -= factor * B[i];
for (let k = i; k < n; k++) {
A[j][k] -= factor * A[i][k];
}
}
}
// Substitusi mundur
const X = new Array(n);
for (let i = n - 1; i >= 0; i--) {
X[i] = B[i] / A[i][i];
for (let j = i - 1; j >= 0; j--) {
B[j] -= A[j][i] * X[i];
}
}
return X;
}
// Melakukan curve fitting
const coefficients = curveFit(x, T);
const [a, b, c] = coefficients;
// Menghasilkan data hasil curve fitting
const xFit = [];
const TFit = [];
for (let i = 0; i <= 1; i += 0.01) {
xFit.push(i);
TFit.push(polynomial(i, a, b, c));
}
// Data untuk Plotly
const data = [
{
x: x,
y: T,
mode: 'markers',
name: 'Data Asli',
marker: { color: 'blue' }
},
{
x: xFit,
y: TFit,
mode: 'lines',
name: 'Curve Fitting',
line: { color: 'red' }
}
];
// Layout plot
const layout = {
title: 'Curve Fitting Data Temperatur',
xaxis: { title: 'Posisi x (m)' },
yaxis: { title: 'Temperatur (K)' },
margin: { t: 40, b: 40, l: 50, r: 50 }
};
// Render plot
Plotly.newPlot('curveFitPlot', data, layout);
// Menampilkan persamaan hasil curve fitting
console.log(`Persamaan Curve Fitting: T(x) = ${a.toFixed(2)}xยฒ + ${b.toFixed(2)}x + ${c.toFixed(2)}`);
</script>
</body>
</html>
- Persamaan flux panas
Dengan menggunakan turunan pertama terhadap x dari persamaan sebelumnya :
kita mendapatkan persamaan fluks panasnya yaitu :
- Menghitung daya
- Persebaran daya
Energi panas (W)
- Sisi Atas = 0
- Sisi Bawah = 0
- Sisi Kiri = -18.31 W
- Sisi Kanan = 18.31 W
- Total = 36.62
<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<title>Kontur 2D Temperatur</title>
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<style>
body {
font-family: Arial, sans-serif;
display: flex;
justify-content: center;
align-items: center;
height: 100vh;
margin: 0;
background-color: #f4f4f4;
}
#contourPlot {
width: 800px;
height: 600px;
background-color: white;
box-shadow: 0 4px 8px rgba(0, 0, 0, 0.1);
border-radius: 8px;
}
</style>
</head>
<body>
<div id="contourPlot"></div>
<script>
// Data dari file CSV
const x = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]; // Posisi (m)
const T = [337.778, 351.284, 357.243, 359.911, 360.687, 359.911, 357.243, 351.284, 337.778]; // Temperatur (K)
// Membuat grid 2D
const y = [0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0]; // Sumbu y (diasumsikan dari 0 hingga 1)
const T_grid = [];
for (let i = 0; i < y.length; i++) {
T_grid.push(T); // Mengulang data temperatur pada sumbu y
}
// Data untuk Plotly
const data = {
x: x,
y: y,
z: T_grid,
type: 'contour',
colorscale: 'Viridis', // Skala warna
contours: {
coloring: 'heatmap' // Warna kontur
},
colorbar: {
title: 'Temperatur (K)' // Judul colorbar
}
};
// Layout plot
const layout = {
title: 'Kontur 2D Temperatur',
xaxis: {
title: 'Posisi x (m)'
},
yaxis: {
title: 'Posisi y (m)'
},
margin: {
t: 40, // Margin atas
b: 40, // Margin bawah
l: 50, // Margin kiri
r: 50 // Margin kanan
}
};
// Render plot
Plotly.newPlot('contourPlot', [data], layout);
</script>
</body>
</html>