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Starting wih an energy balance on a rectangular volume element, derive the one- dimensional transient heat conduction equation for a plane wall with constant thermal conductivity and no heat generation.

Consider two concentric spheres forming an enclosure with diameters of 12 cm and 18 cm the spheres are maintained at uniform temperatures ti-50°c and t2 = 250°c and have emissivities .45 and .8, respectively. determine the net rate of radiation heat transfer between the two spheres per unit surface area.

Asimply supported beam abc of length l has ab of length hl and second moment of area / and bc of length hl and second moment of area i2. determine the strain energy stored in the beam when it is subject to a vertical load f at its midpoint and the consequential central deflection.