When the surface of an object suddenly experiences a temperature change, an exchange of heat with the object takes place. This heat flow is typically a function of time ( t ) and the amount of temperature change ( DT ). Depending on the size of the object, the heat transfer rate can be calculated from one of the following expressions:

Small Object (such as a small concrete block): q=(mc_p)(DT)e^-(1/T)t

Very Large Object(such as a large and thick concrete wall):

q=(k(DT))/(sqrt(pi*)t)

Where:

m=Mass of the object (kg) for 1kg of concrete

c_p= Specific heat of the object ( j/(kg-K)) for 750 j/kg-K

T = Thermal time constant of the object (sec) for 750 sec

k = Thermal conductivity of the object (w/(m-K)) 1w/m-K

= Thermal diffusivity (m²/sec) 5.5e-7 sec

DT = Temperature change at the surface ( K )

q= Heat transfer rate (w)

t= Time(sec)

(1) Write a primary function called heat_transfer with t and DT as the input arguments; this function has no output argument. This function should call two separate subfunctions called Small and large, each calculating the heat transfer rate for an object based on the above expressions. Each of the subfunctions has t and DT as its input arguments and each return the corresponding heat transfer rate in its output argument.

(2) The primary function should also plot the heat transfer rates as a function of time in one figure containing two curves.This plot should be semilog on yaxis. Make sure to place labels, title, and legend.

(3) Write a script that calls the primary function for t between 0.01 to 1000 seconds, with an increment of 0.01, and DT= 50 K. When one runs this script, a plot should be generated.

(4) Define two global variables representing the heat transfer rate at 200 sec for a small and a large object. Have the values of these variables calculated in the primary function but have them displayed in your script file.