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C is for Cookie (Not Specific Heat)

Modeling Cookie Cooling with MatLab. C is for Cookie (Not Specific Heat). Ken Langley and Robert Klaus. Prepared for ME 340: Heat Transfer Winter Semester 2010. Introduction. What makes the perfect cookie? Soft, warm, chewy center Outside that is firm enough to pick up

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C is for Cookie (Not Specific Heat)

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  1. Modeling Cookie Cooling with MatLab C is for Cookie(Not Specific Heat) Ken Langley and Robert Klaus Prepared for ME 340: Heat Transfer Winter Semester 2010

  2. Introduction • What makes the perfect cookie? • Soft, warm, chewy center • Outside that is firm enough to pick up • How can you know when to eat the cookie after it comes out of the oven? ?

  3. Objectives • Determine how a cookie’s internal temperature changes over time to identify how long it will take to perfectly cool a cookie. • Create a MatLab code that will visually show how the internal temperature of the cookie is changing. • EAT COOKIES!!!!

  4. Heat Transfer Principles • To model 1D Transient Conduction we used the Explicit Finite-Difference Method. • The cookie is modeled as a flat plate with convection on both sides.

  5. Solution Cookie Dough Properties ρ = 1252.3 kg/m3 k = .405 W/(m*K) cp = 2940 J/(kg*k) Ti = 175 ºC Tf = 60 ºC T∞ = 27 ºC Cookie Thickness = 0.015 m Number of Divisions = 20 Case I Properties h = 10 W/(m2*K) Time Step = 1 s Case I Properties h = 100 W/(m2*K) Time Step = 0.1 s

  6. Conclusions & Recommendations • From our simulation we realized that the convective heat coefficient (h) is the most important parameter in cooling a cookie. • We recommend that if you want to eat a perfect cookie with a soft, warm center and a firm exterior you must use forced convection with a convective heat coefficient of at least 100 W/(m2*K).

  7. Appendix if(Fo>0.5) disp('Problem is unstable, delta x is too small'); disp('The new value of delta x is '); disp(delta_x); delta_x= sqrt(alpha*delta_t/0.4); Fo= 0.4; M= floor(L/delta_x); end %Initialize Temperature and Length Matrcies x=0:delta_x:L; T=zeros(15000,M+1); T(1,:)=Ti; %Calculate temperatures until middle node reaches Tf m=floor(M/2); j=2; while T(j-1,m)>Tf, %Calculate the temperature at the boundary nodes T(j,1)=2*Fo*(T(j-1,2)+Bi*Tinf)+(1-2*Fo-2*Bi*Fo)*T(j-1,1); T(j,M+1)=2*Fo*(T(j-1,M)+Bi*Tinf)+(1-2*Fo-2*Bi*Fo)*T(j-1,M+1); %Calculate the temperature at the interior nodes for i=2:M, T(j,i)=Fo*(T(j-1,i+1)+T(j-1,i-1))+(1-2*Fo)*T(j-1,i); end j=j+1; end d=size(T,1); %Plot results stepping through time figure(1) fig = figure(1); set(fig,'DoubleBuffer','on'); set(gca,'xlim',[0 L],'ylim',[Tinf Ti],'nextplot','replace','Visible','on'); hold on fps = 10; aviobj = avifile('Temp_dist_ANIMATION.avi','fps',fps,'quality',100); for i=1:100:j; plot(x,T(i,:)); hold on set(gca,'DrawMode','fast') frame = getframe(fig); aviobj = addframe(aviobj,frame); end aviobj = close(aviobj); disp('Movie Finished'); %File: ME340_FiniteDifference.m %By: Robert Klaus and Kenneth Langley %This program uses the 1-D Transient Finite Difference Method to compute %the transient heat conduction in a flat plate. clc clear all clf %Thermophysical properties of cookie dough %k=0.405 W/m*K %rho=1252.3 kg/m^3 %cp=2940 J/kg*K cookie = input('Do you want to model a cookie (1=yes)? '); if(cookie == 1) k = 0.405; rho = 1252.3; cp = 2940; else %obtain user input k= input('Enter thermal conductivity of plate [k(W/m*K)]:'); rho= input('Enter density of plate (kg/m^3):'); cp= input('Enter specific heat of plate (J/kg*K):'); end h= input('Enter convection coefficient of surrounding fluid [h(W/m^2*K)]:'); delta_t= input('Enter time step (s):'); L= input('Enter length of plate (m)]:'); M= input('Enter number of length divisions:'); Ti= input('Enter intial temperature of plate (degrees C):'); Tinf= input('Enter temperature of surrounding fluid (degrees C):'); Tf= input('Enter final temperature (degrees C):'); %Calculate delta_x, Biot and Fourier Numbers, and alpha alpha=k/(rho*cp); delta_x=L/M; Fo= alpha*delta_t/(delta_x)^2; Bi= h*delta_x/k;

  8. References Kulacki, FA, Kennedy, SC. “Measurement of the Thermo-Physical Properties of Common Cookie Dough.” Journal of Food Sciences. Vol. 43(2), pp. 380-384. 1978.

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