Derive an expression for the temperature distribution in a plane wall in which distributed heat sources vary according to the linear relation

Derive the one-dimensional heat conduction equation for a sphere.

Diagram of the problem, necessary formulas, clearance and numerical solution Two heat reservoirs with respective temperatures of 325 K and 275 K are brought into contact by an iron rod 200 cm long and 24 cm2 in cross section. Calculate the heat flux between the reservoirs when the system reaches its steady state. The thermal conductivity of iron at 25 ◦C is 79.5 W/m K.

The temperature distribution in a certain plane wall is: T-Ty =C₁+Cx²+C₁x² Where TI and T2 are the temperatures on each side of the wall. If the thermal conductivity of the wall is constant and the wall thickness is L, derive an expression for the heat generation per unit volume as a function of x, the distance from the plane where T-T1. Let the heat- generation rate be 'q0 at x = 0

PLEASE ANSWER WITH UNIT!!!!! A copper sphere having a diameter of 2 cm is initially at a uniform temperature of 312 F. It is then suddenly exposed to an air-forced- convection environment at 20 C of which the convective heat transfer coefficient is 200 W/m2K. Embedded in the sphere is a thermocouple to measure the temperature as a function of time. How long will it take for the thermocouple to indicate 30 C. What is the time constant for this system? (Density of copper is 8890 kg/m3) , (Specific heat for copper is 398 J/kg.K).

2. The slab shown is embedded in insulating materials on five sides, while the front face experiences convection off its face. Heat is generated inside the material by an exothermic reaction equal to 1.0 kW/m'. The thermal conductivity of the slab is 0.2 W/mk. a. Simplify the heat conduction equation and integrate the resulting ID steady form of to find the temperature distribution of the slab, T(x). b. Present the temperature of the front and back faces of the slab. n-20- 10 cm IT- 25°C) 100 cm 100 cm