W A 30-cm-radius metallic sphere is having thermal conductivity of k = 100; , overall density of mk kg = 1500- and heat capacity of C₂ = 3000; . The sphere is initially at a uniform temperature of kgk T¡ = 20°C and is dropped into boiling water at T = 90°C. The convective heat transfer coefficient is assumed to be only h = 50- W m²K Jsing lump model, compute the temperature of the sphere after t = 1200 seconds. n solving this problem, please use and show the following steps (do not use EES) 1. Compute the volume and surface area of the sphere Vol = Vol 2. Compute the characteristic length Lc = As k 3. Compute the diffusivity a pCp h Lc k 5. Calculate the Fourier number Fo= (at)/Lc² 6. Calculate the excess temperature using 8 = exp(-Bi * Fo) T-Too 7. Compute the target temperature T using 8 = Ti-Too 4. Compute the Biot number Bi = ³ and A² = 4²

A long 3-mm diameter rod of steel (ρ = 7840 kg/m3, c = 460 J/kgK, k = 43 W/mK)has a uniform initial temperature of 650C. The rod is then suddenly immersed in alarge container of 25C water. The hot rod causes the water immediately surroundingthe rod to boil, giving rise to a heat transfer coefficient of 5600 W/m2K. The boilingstops when the rod reaches a temperature of 100C, at which time the heat transfercoefficient becomes 750 W/m2K. Find the time period during which boiling occursand the total time required for the rod to reach a temperature of 40C. Use acharacteristic length for this problem.

Problem 6. ART TAT Consider the cylindrical pipe shown in the figure. Heat is being generated in the pipe wall at a rate of R in units of W/m³, and the thermal conductivity of the wall is k, the heat transfer coefficients at the inside and outside of the pipe are h; and ho, respectively. At a given location along the pipe axis, the temperature of the fluid flowing inside of the pipe is Ti and that at the outside is To i. ii. Find the expression for the temperature distribution in the pipe wall. Find the total heat transfer rate from the pipe to both fluids.

A certain liquid flow inside a 4 cm diameter pipe, 6 meter long with an entering temperature of 350 C. the wal temperature is maintained at 575 C, and the mass flow rate of the metal is 60 kg/min. p=6000 kg/m, Npr = 0.003, m = 0.003 N-s/m, k = 6.2 w/m-k, Cp = 0.41 kj/kg-k. what is the convection coefficient of the liquid (w/m-k)

The 0.5 m x 1.2 m wall of an industrial furnace is constructed from L = 0.15-m-thick fireclay brick having a thermal conductivity of 1.7 W/m-K. The temperature distribution, at an instant in time, is T(x) = a + bxwhere a = 1400 K and b = -950 K/m. Determine the heat fluxes, q, and heat rates, q,, atx = 0 and.x = L, in W/m2 and W respectively. Do steady-state conditions exist? i W/m? i W/m? Ix=0 = i W i W Ix=L = Steady-state conditions exist. ||

2-D: A fin may be manufactured as an integral part of a surface by using a casting or extrusion process, or it may be separately brazed or adhered to the surface. From thermal considerations, which option is preferred? 2-E: What is the difference between steady-state and transient heat transfer processes? Give an example for each of them. 2-F: What is the physical interpretation of the Biot number? 2-G: For flow over a flat plate, sketch variation of local convective heat transfer coefficient, h(x), versus the distance along the plate x for laminar, transition, and turbulent flow regimes.

(3) Spheres 4rk (T; – To) q= 1/r; - 1/ro The heat flow rate Prove this equation!!