matrix inversion; temperature node distribution

Please show all the work. The matrix inversion method has to be shown in details, the formula used in the class for temperature node distribution was Tm+1,n + Tm-1, n + Tm, n+1 + Tm, n-1 ? 4Tm,n =0 (where ?m? is the X?axis and ?n? is the Y-axis) Please see attachment for problem. Thanks

Heat Losses; Estimation of length; Thermal Conductivity etc.

Please help with the attached problems including: Heat Losses; Estimation of length; Thermal Conductivity etc. Thanks!

Conduction

2 questions - Included: A 5-m-long section of hot and cold water pipers run parallel to each other in a thick concrete layer. The diameters of both pipers are 5cm, and the distance between the centrelines of the pipes is ... (see attachment) a) Determine the the rate of heat transfer between the pipes ... (see attachment for complete list of questions please!)

Radiation

2 questions, including: Consider the 5m x 5m x 5m cubical furnace ... (see attachment) a) the rate of radiation heat transfer between the base and the side surfaces (see attachment for complete list of questions - thanks!)

First Law of Thermodynamics

Two 800-kg cars moving at a velocity of 90 km/h have a head-on collision on a road. Both cars come to a complete rest after the crash. Assuming all the kinetic energy of cars is converted to thermal energy, determine the average temperature rise of the remains of the cars immediately after the crash. Take the average specific heat of the cars to be 0.45 kJ/kg degrees C.