1. Question 1- Laplace Equation: Leibmann's Method The four sides of a square plate of side 12cm, made of homogenous material, are kept at a constant temperature 0°C and 100°C as shown in Figure 1. Using a grid of mesh 4cm and applying Leibmann's method, perform up to four (4) iteration to find the temperature at the various mesh points.

PARTS A and B ( Label Them ) SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer for both Question : Chilled pharmaceutical is transported through a steel pipe ( k= 15.0 W/m.k) with an inner diameter of 36 mm and a wall thickness of 2 mm. The liquid and ambient air are at temperatures of 5 C and 25 C, while the inner and outer convection coefficients are 500 W/m2.K and 10 W/m2.K respectively. If a 10 mm thick layer of calcium silicate ( k= 0.05 W/m.K) is applied to the tube, answer the following questions: Part A : What is the heat gain per 1m of the tube? Part B : What is the outside temperature of the calcium silicate?

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I have a problem similar to this in my case the problem is from the outside in. the heat is entering the interior and I don't know what temperature it will have inside since part of the heat will be lost in the thickness of the cylinder, I want to know how to fix the formula so that I can obtain the temperature inside the cylinder.