2. Find T(x,t) for transient one dimensional heat transfer for a rod with T=0 at both ends for all time and an initial temperature distribution given by f(x) = ¾ sin(лx/L) + ¼ sin(3лx/L). The rod has a length L = 10 cm and a cross sectional area of 1 cm².

You are asked to estimate the maximum human body temperature if the metabolic heat produced in your body could escape only by tissue conduction and later on the surface by convection. Simplify the human body as a cylinder of L=1.8 m in height and ro= 0.15 m in radius. Further, simplify the heat transfer process inside the human body as a 1-D situation when the temperature only depends on the radial coordinater from the centerline. The governing dT +q""=0 dr equation is written as 1 d k- r dr r = 0, dT dr =0 dT r=ro -k -=h(T-T) dr (k-0.5 W/m°C), ro is the radius of the cylinder (0.15 m), h is the convection coefficient at the skin surface (15 W/m² °C), Tair is the air temperature (30°C). q" is the average volumetric heat generation rate in the body (W/m³) and is defined as heat generated per unit volume per second. The 1-D (radial) temperature distribution can be derived as: T(r) = q"¹'r² qr qr. + 4k 2h + 4k +T , where k is thermal conductivity of tissue air (A) q" can be calculated…

A large 100-mm thick steel plate is initially at uniform temperature T = 180°C at time t = 0. Both sides of the plate are exposed to 30°C oil with convection coefficient h = 1500 W/m².K. The thermal conductivity, heat capacity, and density of the steel are k = 38 W/m-K, cp = 485 J/kg-K, and p = 7800 kg/m³. a) Find the temperature at the center of the slab when t = 125 s. b) Find the temperature at the surface of the slab when t=125 s.

Q4/The outside wall of a building 6 m high receives an average radiant heat flux from the sun of 1100 W/m². Assuming that 95 W/m² is conducted through the wall, estimate the outside wall temperature. Assume the atmospheric air on the outside of the building is at 20°C. Ans. 170°C