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More fooling around with the equations. Not much progress. Focusing now on lumpedCapacitance in a simple capacity.

formula
Scott Mobley 11 years ago
parent
commit
bf3bc66a48
  1. 38
      js/CookingFormula.js

38
js/CookingFormula.js

@ -1,6 +1,11 @@ @@ -1,6 +1,11 @@
//Useful Websites
//http://math.stackexchange.com/questions/406082/numerical-method-to-solve-a-trigonometric-cotangent-function-transient-heat
//Global Variables for Turkey
density = 996; // kg/m3 Assuming Density of Water 1000 kg/m3
cp = 2810 // J/kg K for Turkey
heatConvection = 12; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
thermalConduct = 0.412 // W/m K
function celsiusToFarenheit(celsius) {
farenheit = (celsius*(9/5)) + 32;
@ -51,13 +56,10 @@ console.log("Simple Radius " + simpleRadius + " Meters") @@ -51,13 +56,10 @@ console.log("Simple Radius " + simpleRadius + " Meters")
console.log("Complex Radius " + complexRadius + " Meters")
}
function LumpedCapacitanceMethod (radiusTotal,radiusInner,tempInitial,tempInfini, t) {
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;
@ -77,9 +79,14 @@ Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rat @@ -77,9 +79,14 @@ Qdot = -1*heatConvection*surfaceArea*(tempAtTime-tempInfini) //Heat Transfer Rat
console.log("The Heat Flux is " + Qdot )
}
function advancedLumpedCapacitanceMethod() {
}
function transientSphereOneTerm (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)
@ -129,7 +136,7 @@ console.log("The Temperature At radius " + rPosition +" m and time " + t + " se @@ -129,7 +136,7 @@ console.log("The Temperature At radius " + rPosition +" m and time " + t + " se
function findAllRoots (Biot) {
limit = 11; //Terms to Compute too
limit = 150; //Terms to Compute too
storage = [];
for (var k=0; k<=limit; k++) {
minK = (k+0.5)*Math.PI;
@ -139,14 +146,14 @@ storage = []; @@ -139,14 +146,14 @@ storage = [];
storage.push(answer);
}
}
console.log(storage)
//console.log(storage)
return(storage)
}
function bisectionMethod(min,max,Biot) {
errorTolerance = (1/Math.pow(10,8))
result = 100 // some large value to ensure the calculation goes through.
errorTolerance = (1/Math.pow(10,9))
result = Infinity // some large value to ensure the calculation goes through.
negativeTest =lambdaFormula(min, Biot)*lambdaFormula(max, Biot)
if (negativeTest <=0 ) {
while (Math.abs(result) > errorTolerance) {
@ -178,12 +185,9 @@ return(result) @@ -178,12 +185,9 @@ return(result)
function transientSphereSeries (rPosition,rTotal,tempInitial,tempInfini,t) {
heatConvection = 6000; // W/m2 K Some Reasonable estimate for natural Convection. Change as needed. 5-25
thermalConduct = 20 // W/m K
//alpha = thermalConduct/(density*cp)
alpha = 6.66 * (1/Math.pow(10,6))
console.log("Alpha is " + alpha)
sum=0;
alpha = thermalConduct/(density*cp)
console.log("Alpha is " + alpha)
Fourier = (alpha*t)/Math.pow(rTotal,2)
console.log("Fourier is " + Fourier)
@ -200,5 +204,7 @@ lambdaTerms = findAllRoots(biotNum) @@ -200,5 +204,7 @@ lambdaTerms = findAllRoots(biotNum)
sum = frontCoefficientPortion*exponentialPortion*sinPortion + sum
}
tempAtTimeAndRadius=(sum*(tempInitial-tempInfini))+tempInfini
return(tempAtTimeAndRadius)
console.log("The Temperature at radius " + rPosition + " m and time " + t + " seconds is " + tempAtTimeAndRadius + " C or " + celsiusToFarenheit(tempAtTimeAndRadius) + " F");
}
}

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