Hot water (cph = 4188 J/kg*K) with mass flow rate of 2.5 kg/s at 100 deg C enters a thin- walled concentric tube counterflow heat exchanger with a surface area of 23 m^2 and an overall heat transfer coefficient of 1000 W/m2*K. Cold water (cpc = 4178 J/kg*K) with mass flow rate of 5 kg/s enters the heat exchanger at 20 deg C, determine (a) the heat transfer rate for the heat exchanger and (b) the outlet temperatures of the cold and hot fluids.

A shaft of 0.06-m diameter is heat treated in a gas-fired furnace whose gases is at 1200 K and provide a convection coefficient of 125 W/m² K. If the shaft enters the furnace at 300 K and stays in the furnace. (1) What is the centerline temperature (in K) of the shaft after 900 seconds? (2) What is the value of the dimensionless Fourier number? The shaft material has a density of 7000 kg/m², thermal conductivity of 50 W/m.K, and specific heat capacity 500 J/kg.K. Please show your work and assumptions.

plz write neatly, do not copy and paste solution

À wall of area 30 m² having a density of 1500 kg/m', thermal conductivity 30 W/m.K, and specific heat capacity 4 kJ/kg.K. The temperature distribution across a wall 0.5 m thick at a certain instant of time is given as T(x) = 30-5 x-7x The wall is generating a uniform heat (q.) of 1000 W. (1) Find the rate of heat transfer entering and leaving the wall (in W). (2) Find rate of energy stored in Watt. (3) Find (dFT/dx²) (4) Derive the change in temperature with respect to time equation (time rate of temperature change)- remember to substitute the value of (d T/dx²) from (part 3) and values of all other properties into final equation. %3D