You received the following letter as a heat transfer expert. You need to answer the letter taking into consideration that your consulting fees depend on your answer. We have been testing long, cylindrical samples of stainless steel in our laboratory under constant heat flux conditions at the outer radius. We are attempting to determine the length of time it takes the surface to reach its melting temperature of 1480C. Two tests on 10 cm diameter cylinders have given the following results Test 1 2 q" W/m = 94,638 157,730 Time (sec) 1580 882 The initial temperature in each test was 27C. The laboratory assistant feels that the data should be fitted with the following hyperbola: q't 1.5x108 where q" is in W/m, and t in seconds. I'm hesitant to rely on the hyperbola even though it closely fits the data and has the right qualitative behavior. I would appreciate learning the answers to the following questions: a. Is the hyperbola correct in predicting no influence in diameter b. Is the hyperbola correct in predicting that the thermal properties of the material have no effect C. Does heat theory support the hyperbola conclusion d. If the hyperbola is not valid, please provide a better relation