Model the cooling of a keg of beer at 25 0C which is placed in a coolroom held a

Question

Model the cooling of a keg of beer at 25 0C which is placed in a coolroom

held at 00c.


The rate of cooling of the keg is given by the equation:


d?beer = UA (?room-?beer)
dt             mCp


where: d?beer = temperature of the beer and keg (0C); room = tem-

perature of the coolroom ( 0C); t = time ( s); m = cobined mass of

beer and the keg ( kg); Cp = combined heat capacity of beer and keg

( KJ Kg-1 K-1); U = overall heat transfer coefficient (KWm-2 k-1); A

= surface area of keg (m2).

The keg contains 50 L of beer. The beer has a density of 1008 kgm-3.

The empty keg weighs 10 kg. The combined heat capacity of beer

and keg is 3:56 KJ Kg-1 K-. The overall heat transfer coefficient is

0:1 KWm-2 k-1. The keg is a cylinder 460mm high and 390mm in

diameter.
b) Write a function that calculates the rate of cooling of the keg.

Explanation / Answer

function y=rateofcooling(D,L,Den,V,Cp,U,Mkeg,Troom,Tbeer)

Mbeer=Den*V;

M=Mbeer+Mkeg;

A=pi*D*L;

y=(U*A*(Troom-Tbeer))/(M*Cp);

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