Turkey formulas

js/CookingFormula.js

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+//Global Variables for Turkey
+density = 996; // kg/m3 Assuming Density of Water 1000 kg/m3
+cp = 2810 // J/kg K for Turkey
+
+function celsiusToFarenheit(celsius) {
+farenheit = (celsius*(9/5)) + 32;
+return(farenheit)
+}
+
+function poundsToKilograms(pounds) {
+kilograms = (pounds * 0.453592);
+return(kilograms)
+}
+
+function findClosest(value,array) {
+closestDiff = null;
+closestPosition = null;
+	for (var i=0;i<array.length;i++) {
+		diff = Math.abs(value-array[i])
+		if (diff<closestDiff || closestDiff == null) {
+			closestPosition=i;
+			closestDiff = diff;
+		} 
+	}
+	return ([closestPosition,array[closestPosition]])
+}
+
+function biotSphereCoefficients (Biot) {
+Bi = [0.01, 0.02, 0.04, 0.06, 0.08, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 100, 10000]
+lambdaOne = [0.1730, 0.2445, 0.3450, 0.4217, 0.4860, 0.5423, 0.7593, 0.9208, 1.0528, 1.1656, 1.2644, 1.3525, 1.4320, 1.5044, 1.5708, 2.0288, 2.2889, 2.4556, 2.5704, 2.6537, 2.7165, 2.7654, 2.8044, 2.8363, 2.9857, 3.3072, 3.0632, 3.0788, 3.1102, 3.1416]
+alphaOne = [ 1.0030, 1.0060, 1.0120, 1.0179, 1.0239, 1.0298, 1.0592, 1.0880, 1.1164, 1.1441, 1.1713, 1.1978, 1.2236, 1.2488, 1.2732, 1.4793, 1.6227, 1.7202, 1.7870, 1.8338, 1.8673, 1.8920, 1.9106, 1.9249, 1.9781, 1.9898, 1.9942, 1.9962, 1.9990, 2 ]
+position = findClosest(Biot,Bi)[0]
+return([lambdaOne[position], alphaOne[position]])
+}
+
+
+function calculateRadius(weight) {
+//Using Ratios for a rectangular Box Turkey
+ratioLvG=1.4; //1.4, Turkey length vs shoulder girth
+ratioLvH=2; //2, Turkey length vs height from resting position
+
+length = Math.pow(weight/((1/ratioLvG)*(1/ratioLvH)*density),(1/3))
+depth = 1/(ratioLvG /length);
+height = 1/(ratioLvH /length);
+simpleRadius = length/2; //Doesn't take into account equal Volume
+
+rectangleVolume = depth*height*length*(1/3); //m^3  Multiple by 1/3 to account for triangular shape and empty Space
+complexRadius = Math.pow(rectangleVolume/((4/3)*Math.PI), 1/3); //Volume of 3D Box = 3D Sphere
+
+console.log("Simple Radius  " + simpleRadius + " Meters")
+console.log("Complex Radius  " + complexRadius + " Meters")
+}
+
+function LumpedCapacitanceMethod (radiusTotal,radiusInner tempInitial,tempInfini, t) {
+name : "Skin"
+volume = (4/3)*Math.PI*Math.pow(radiusTotal,3) - (4/3)*Math.PI*Math.pow(radiusInner,3); //3D Sphere
+surfaceArea = 4*Math.PI*Math.pow(radiusTotal,2); //3D Sphere
+heatConvection = 12; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
+thermalConduct = 0.412 // W/m K
+cp = 2810 // J/kg K
+
+mass = density * volume;
+
+charLength = volume/surfaceArea ;
+
+biotNum = heatConvection * charLength/thermalConduct
+
+console.log("The Biot Value is " + biotNum)
+
+b=(heatConvection)/(density*charLength*cp)
+console.log("The time constant b is "+ b)
+
+tempAtTime = Math.exp(-b*t)*(tempInitial-tempInfini)+tempInfini;
+console.log("The Temperature at time " + t +" seconds is " + tempAtTime)
+
+Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rate Useful for water Loss
+console.log("The Heat Flux is " + Qdot )
+}
+
+function transientSphere (rPosition,rTotal,tempInitial,tempInfini,t) {
+heatConvection = 12; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
+thermalConduct = 0.412 // W/m K
+alpha = thermalConduct/(density*cp)
+console.log("Alpha is " + alpha)
+
+Fourier = (alpha*t)/Math.pow(rTotal,2)
+console.log("Fourier is " +  Fourier)
+biotNum = heatConvection * rTotal/thermalConduct
+console.log("The Biot Value is " + biotNum)
+temp=biotSphereCoefficients(biotNum)
+lambdaOne=temp[0];
+alphaOne=temp[1];
+console.log("lambda1 is " + lambdaOne)
+console.log("A1 is " + alphaOne)
+
+//This is only valid for Fourier greater than 0.2
+sinPortion= Math.sin(lambdaOne*rPosition/rTotal)/(lambdaOne*rPosition/rTotal);
+expotentialPortion = alphaOne*(1/Math.exp(Math.pow(lambdaOne,2)*Fourier))
+tempAtTimeAndRadius=(sinPortion*expotentialPortion*(tempInitial-tempInfini))+tempInfini
+console.log("The Temperature at radius " + rPosition + " m and time " + t + "  seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
+}
+
+
+function transientSphereEgg (rPosition,tempInitial,tempInfini,t) {
+rTotal = 0.025
+heatConvection = 1200; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
+thermalConduct = 0.627 // W/m K
+alpha = 0.000000151
+console.log("Alpha is " + alpha)
+
+Fourier = alpha * t/Math.pow(rTotal,2)
+console.log("Fourier is " +  Fourier)
+biotNum = heatConvection * rTotal/thermalConduct
+
+console.log("The Biot Value is " + biotNum)
+temp=biotSphereCoefficients(biotNum)
+lambdaOne=temp[0];
+alphaOne=temp[1];
+console.log("lambda1 is " + lambdaOne)
+console.log("A1 is " + alphaOne)
+
+//This is only valid for Fourier greater than 0.2
+sinPortion= Math.sin(lambdaOne*rPosition/rTotal)/(lambdaOne*rPosition/rTotal);
+expotentialPortion = alphaOne*(1/Math.exp(Math.pow(lambdaOne,2)*Fourier))
+tempAtTimeAndRadius=(sinPortion*expotentialPortion*(tempInitial-tempInfini))+tempInfini
+console.log("The Temperature At radius " + rPosition +" m and time " + t + "  seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F" );
+}

js/Turkey.html

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+<!DOCTYPE html>
+<html>
+<head>
+<title>Turkey Formulas</title>
+<script src=CookingFormula.js></script>
+</head>
+<body>
+</body>
+</html>