Passage of an electric current through a long conducting rod of radius r; and thermal conductivity kr, esults in uniform volumetric heating at a rate of q.. The conduction rod is wrapped in an electrically non-conducting cladding material of radius ro and thermal conductivity ke and convection cooling is provided by an adjoining fluid. For steady-state conditions, a) Determine an expression for the heat transfer per unit length q', passing through the cladding in terms of 9, and ri. b) Determine an expression for T, the temperature of the cladding at 7; and also for To at ro. c) Calculate these cladding temperatures in °C when r and ro are 3 mm and 5 mm, ġ. = 200 kW/m³, ke = 0.15 W/m/K, T = 20°C and h = 20 W/m²/K. Conducting rod, å, k, Cladding, k d) Calculate the critical radius. To decrease the internal cladding temperature would it be necessary to increase or decrease ro; or should it remain unchanged? Explain. Th 201

The steady-state temperature distribution in a one-dimensional wall of thermal conductivity k=83 (W/m) °C) and thickness 300 mm is observed to be T(°C) = ax2+bx+c, where a = -2500 °C/m2 , b = 500 °C/m, c = 250 °C and x is in meters. a) What is the heat generation rate ?̇ (W/m3 ) in the wall ? b) Find the maximum and minimum temperatures in the wall. c) Find the amount of heat transferred to the right side of the wall (for 1 m2 surface area.)

Please show solution clearly

1.1 Consider the fireclay brick wall of Example 1.1 that is operating under different thermal conditions. The tem- perature distribution, at an instant in time, is T(x) = a+ bx where a 1400 K and b = -1000 K/m. Determine the heat fluxes, q", and heat rates, q, at x = 0 and x = L. Do steady-state conditions exist?

Pls handwrite

Heat transfer

Please show all work for this mechnical measure problem. Not Ai generated the answers have been wrong I need to understand.

Give True or False for the following: 1.In liquids and gases, heat transmission is caused by conduction and convection 2.The surface geometry is the important factor in convection heat transfer 3. The heat transfer by conduction from heated surface to the adjacent layer of fluid, 4. The heat transfer is increased in the fin when &> 1 5.The unit of the thermal diffusivity is m²/s 6. Temperature change between the materials interfaces is attributed to the thermal contact resistance 7. A material that has a low heat capacity will have a large thermal diffusivity. 8. Heat conduction flowing from one side to other depends directly on thickness 9.Fin efficiency is the ratio of the fin heat dissipation with that of no fin 10.The critical radius is represented the ratio of the convicted heat transfer to the thermal conductivity

Derive a formula for the thermal resistance, R₁, for a spherical shell assuming one- dimensional heat flux in the radial direction. The inside and outside radii of the spherical shell are r; and r., respectively, and the shell is made of a material having thermal conductivity k. Assume the temperatures at the inside and outside surfaces of the shell are T and T., respectively. The thermal resistance formula assumes the rate of heat transfer through the spherical shell, Q, is constant. The heat flux is in the radial direction for this one-dimensional case, and the dT heat flux is given by Fourier's law: q, = -k The rate of heat transfer through a dr spherical surface is Q =q₁A where A = 4лr². Derive the formula for the thermal 1 ++)) r = resistance for a spherical shell answer: R₁ 1 1 4лk ri

Please show all work for this mechnical measure problem. Not Ai generated the answers have been wrong I need to understand.