Reference no: EM132409300
Assignment - Mathematical Modeling Of Differential Equation
We are going to cook a big pot of soup late at night and we know that refrigeration is essential to preserve the soup overnight. However, the soup is going to be too hot to be put directly into the fridge once it is going to be ready (the soup is going to be 100oC, and our fridge is not powerful enough to accommodate a big pot of soup if it is any warmer than 25oC). We're planning to cool the soup by first pouring it into an hermetic recipient and then immerse the hermetic recipient in a sink full of cold water, (kept running, so that its temperature is going to be roughly constant at 5 degrees). The recipient is a square prism whose width, depth and height are respectively 25cm, 25cm and 45 cm, and we know that the density of the soup is ρ = 1.05 kg/l, the specific heat of soup is c = 3000 J kg-1oC-1 and the heat transfer coefficient is h = 24 W m-2oC-1.
(a) Write the word equation and the differential equation that describes the problem. Explain the steps used to come to your answer.
(b) After keeping the recipient immersed in the sink of cold water for 30 minutes which will be the temperature of the soup?
(c) How long should we keep the recipient immersed in the sink of cold water for the soup to reach a temperature of 24oC?
(d) If we use a cylindrical hermetic container of the same height and capacity would it be quicker or slower to cool the soup? Justify your answer.
Check Matlab code to graph the temperature against time page 232. Must follow the standard of book Explain step and justify answer.
Textbook - MATHEMATICAL MODELLING WITH CASE STUDIES - Using Maple and MATLAB, Third Edition by B. Barnes and G. R. Fulford.