A two dimensional rectangular plate is subjected to prescribed boundary conditions. Using theresults of the analytical solution for the heat equation presented in class, calculate the temperatureat the midpoint (1,0.5) by considering the first five nonzero terms of the infinite series that mustbe evaluated.T₁ = 50°Cy (m)1T₂=150°CT₁ = 50°C►x (m)2-T₁ = 50°C

Answered: A two dimensional rectangular plate is…

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter8: Natural Convection

Section: Chapter Questions

Problem 8.53P

See similar textbooks

Similar questions

2.3 The shield of a nuclear reactor is idealized by a large 25-cm-thick flat plate having a thermal conductivity of . Radiation from the interior of the reactor penetrates the shield and there produces heat generation that decreases exponentially from a value of at the inner surface to a value of at a distance of 12.5 cm from the interior surface. If the exterior surface is kept at 38°C by forced convection, determine the temperature at the inner surface of the field. Hint: First set up the differential equation for a system in which the heat generation rate varies according to .
If the surface of a plane wall with heat conduction coefficient k is under constant heat flux (q0 ") condition at x = 0 and its surface at x = L is at temperature Ts, which of the following is the temperature distribution of this plane wall?
The heat conducts through the shape below. The temperature of the right face is 93 °C, while the left face is at 23 °C. If the top and bottom faces are completely insulated, and the thermal conductivity of the material decreases with decreasing temperature. * Assume that the thermal conductivity is 100 at 23, decreased to 10 at 93. A) Sketch the temperature profile inside the plate. B) If both sides of the plate in the above problem is exposed to air: Left side (h = 20 W/m2K, TL = 20 °C) and right side (h = 90 W/m2K). Calculate the temperature of the air on the right side.
4) In a tempering process, glass plate, which is initially at a uniform temperatureTi, is cooled by suddenly reducing the temperature of both surfaces to Ts Theplate is 20 mm thick, and the glass has a thermal diffusivity of 6x 10-7 m2/s.(a) How long will it take for the midplane temperature to achieve 50% of itsmaximum possible temperature reduction? Ans t= 63 s(b) If (Ti -T5) = 300°C, what is the maximum temperature gradient in the glass atthe above time? Ans. -2.36 104 °C/m.
Thermodynamics problem. A membrane type electrical heater of 20,000 w/m? capacity is sandwiched between an Insulation of 25 mm thickness with thermal conductivity of 0.029 W/m-K and a metal plate with k = 12.6 W/m-K of thickness 15 mm. The convection coefficient is 150 W/m2-K. The surroundings are at 5°C. Determine the surface temperature of the heater and the flow on either side.
A coil-shaped cooling pipe is made of SS-304 material. This pipe is 1 ft long, 0.4 inch outside diameter, and inch inside diameter. This coil cooling pipe is used to cool the water in the bath. The temperature of the inner coil pipe is 40oF while the outer coil in contact with water is 80oF. The thermal conductivity of SS-304 is a function of temperature where k(T) = 7.75 + (7.78 x 10-3).T where k is in Btu/h.ft.oF and T is in oF. Calculate the rate of heat dissipation in watts! (1287.7)
A 10 cm diameter cylindrical bar, heated in furnace to a uniform temperature of 2000 C, is allowed to cool in an environment with convective coefficient of 150 W/m2 K and temperature 400 Determine i) the temperature required to cool the centre of the bar to 600 C ii) temperature of the surface at this instant. For the material of the bar thermal conductivity = 50 W/m K and thermal diffusivity = 2.0 X 10-5 m2/sec.
A steel rod, which is free to move, has a length of 200 mm and diameter of 20 mm at a temperature of 15°C. If the rod is heated uniformly to 115°C, determine the length and the diameter of this rod to the nearest micron at the new temperature if the linear coefficient of thermal expansion of steel is 12.5 x 10 m/m/°C. Wrong solution will be reported instantly
Write the appropriate Nusselt value for the each set of conditions provided below.1. Forced convection over a flat plate at constant qs. Calculated Re at mean temperature is 3500 and Pr= 0.7154. 2. Natural convection in a small holding tank with a heating element at the bottom. The calculated Ra number is 2.37 x10^93. Forced convection through an elliptical duct at constant Ts, where a/b=8. The temperature of the fluid at the inlet is higher than at the exit. Flow is fully developed with Re = 33370 and Pr= 0.693. 4. Natural convection over a sphere with Ra = 5 x 10^9 and Pr = 0.7362 PS. Do not round off intermediate values
37. A long and slender shaft of diameter 2R and length L1 + L2 is insulated overlength L1 and produces heat only in this section while over length L2, it is exposedto a convection boundary (h, Tf). Write the governing differential equations andthe associated boundary conditions from which temperatures in sections L1 and L2can be obtained. Both ends may be treated as adiabatic surfaces.
Two sides AB and AD of a reetangular plate ABCD lie along the xand y axes respectively. The remaining two sides are the lines x = 5and y = 2. The sides BC, CD and DA are maintained at zerotemperature. The temperature distribution along AB is defined byf (x) = x (x - 5). Determine an expression for the steady statetemperature at any point in the plate.
Three (3) bricks, specifically A, B, and C were arranged horizontally in such a way that it can be illustrated as a sandwich panel. Consider the system to be in series and in the order of Brick A, Brick B and Brick C. The outside surface temperature of Brick A is 1,500℃ and 150 ℃ for the outside surface of Brick C. The thermal conductivities for Brick A, Brick B and Brick C, are 2 ?/? °? , 0.50 ?/? °? , 60 ?/? °?. The thickness of Brick A and Brick C are 50 cm and 22 cm. The rate of heat transfer per unit area is 1,000 ?/?2 . Determine the following: The thickness of Brick B in the unit of mm. Assume that all the conditions were retain except that the thickness of Brick B was increased to 800 mm, what is the new value for the rate of heat transfer per unit area in ???/ℎ? . ??2 please explain the principles to solve this

SEE MORE QUESTIONS

Recommended textbooks for you

Principles of Heat Transfer (Activate Learning wi…

Mechanical Engineering

ISBN:

9781305387102

Author:

Kreith, Frank; Manglik, Raj M.

Publisher:

Cengage Learning