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Maximum temperature in plane wall with symmetrical boundary conditions Solution

STEP 0: Pre-Calculation Summary
Formula Used
maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity))
Tmax = Tw+((qG*(t)^2)/(8*k))
This formula uses 4 Variables
Variables Used
Surface temperature - Surface temperature is the temperature at or near a surface. Specifically, it may refer to: Surface air temperature, the temperature of the air near the surface of the earth. .. (Measured in Kelvin)
Internal heat generation - Internal heat generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium. (Measured in Watt Per Cubic Metre)
Wall thickness - Wall thickness is simply the width of the wall that we are taking under consideration. (Measured in Meter)
Thermal Conductivity - Thermal Conductivity is the rate at which heat passes through a specified material, expressed as the amount of heat that flows per unit time through a unit area with a temperature gradient of one degree per unit distance. (Measured in Watt per Meter per K)
STEP 1: Convert Input(s) to Base Unit
Surface temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Internal heat generation: 100 Watt Per Cubic Metre --> 100 Watt Per Cubic Metre No Conversion Required
Wall thickness: 5 Meter --> 5 Meter No Conversion Required
Thermal Conductivity: 10 Watt per Meter per K --> 10 Watt per Meter per K No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tmax = Tw+((qG*(t)^2)/(8*k)) --> 300+((100*(5)^2)/(8*10))
Evaluating ... ...
Tmax = 331.25
STEP 3: Convert Result to Output's Unit
331.25 Kelvin --> No Conversion Required
FINAL ANSWER
331.25 Kelvin <-- Maximum temperature
(Calculation completed in 00.015 seconds)

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Temperature at given thickness x inside plane wall surrounded by fluid
temperature = (Internal heat generation/(8*Thermal Conductivity))*((Wall thickness)^2-(4*(Thickness)^2))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature Go
Temperature inside solid cylinder at given radius immersed in fluid
temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Radius)^2)+Fluid temperature+(Internal heat generation*Cylinder Radius/(2*Convection heat transfer coefficient)) Go
Maximum temperature inside solid cylinder immersed in fluid
maximum_temperature = Fluid temperature+(((Internal heat generation*Cylinder Radius)/(4*Convection heat transfer coefficient))*(2+(Convection heat transfer coefficient*Cylinder Radius/Thermal Conductivity))) Go
Temperature inside plane wall at given thickness x with symmetrical boundary conditions
temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature Go
Maximum temperature in plane wall surrounded by fluid with symmetrical boundary conditions
maximum_temperature = (Internal heat generation*(Wall thickness)^2/(8*Thermal Conductivity))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature Go
Temperature inside solid cylinder at given radius
temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Given radius)^2)+Surface temperature Go
Maximum temperature in solid sphere
maximum_temperature = Surface temperature+((Internal heat generation*(Radius of Sphere)^2)/(6*Thermal Conductivity)) Go
Maximum temperature in solid cylinder
maximum_temperature = Surface temperature+((Internal heat generation*(Cylinder Radius)^2)/(4*Thermal Conductivity)) Go
Maximum temperature in plane wall with symmetrical boundary conditions
maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity)) Go
Location of maximum temperature in plane wall with symmetrical boundary conditions
location_of_maximum_temperature = Wall thickness/2 Go

Maximum temperature in plane wall with symmetrical boundary conditions Formula

maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity))
Tmax = Tw+((qG*(t)^2)/(8*k))

What is steady state conduction?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant.

What is internal heat generation?

Internal heat generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.

How to Calculate Maximum temperature in plane wall with symmetrical boundary conditions?

Maximum temperature in plane wall with symmetrical boundary conditions calculator uses maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity)) to calculate the Maximum temperature, The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal. Maximum temperature is denoted by Tmax symbol.

How to calculate Maximum temperature in plane wall with symmetrical boundary conditions using this online calculator? To use this online calculator for Maximum temperature in plane wall with symmetrical boundary conditions, enter Surface temperature (Tw), Internal heat generation (qG), Wall thickness (t) & Thermal Conductivity (k) and hit the calculate button. Here is how the Maximum temperature in plane wall with symmetrical boundary conditions calculation can be explained with given input values -> 331.25 = 300+((100*(5)^2)/(8*10)).

FAQ

What is Maximum temperature in plane wall with symmetrical boundary conditions?
The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal and is represented as Tmax = Tw+((qG*(t)^2)/(8*k)) or maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity)). Surface temperature is the temperature at or near a surface. Specifically, it may refer to: Surface air temperature, the temperature of the air near the surface of the earth. , Internal heat generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium, Wall thickness is simply the width of the wall that we are taking under consideration & Thermal Conductivity is the rate at which heat passes through a specified material, expressed as the amount of heat that flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
How to calculate Maximum temperature in plane wall with symmetrical boundary conditions?
The Maximum temperature in plane wall with symmetrical boundary conditions is the temperature when the temperature at both surfaces of the plane wall is equal is calculated using maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity)). To calculate Maximum temperature in plane wall with symmetrical boundary conditions, you need Surface temperature (Tw), Internal heat generation (qG), Wall thickness (t) & Thermal Conductivity (k). With our tool, you need to enter the respective value for Surface temperature, Internal heat generation, Wall thickness & Thermal Conductivity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Maximum temperature?
In this formula, Maximum temperature uses Surface temperature, Internal heat generation, Wall thickness & Thermal Conductivity. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity))
  • location_of_maximum_temperature = Wall thickness/2
  • maximum_temperature = Surface temperature+((Internal heat generation*(Cylinder Radius)^2)/(4*Thermal Conductivity))
  • maximum_temperature = Surface temperature+((Internal heat generation*(Radius of Sphere)^2)/(6*Thermal Conductivity))
  • temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Given radius)^2)+Surface temperature
  • temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Radius)^2)+Fluid temperature+(Internal heat generation*Cylinder Radius/(2*Convection heat transfer coefficient))
  • temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature
  • temperature = (Internal heat generation/(8*Thermal Conductivity))*((Wall thickness)^2-(4*(Thickness)^2))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature
  • maximum_temperature = (Internal heat generation*(Wall thickness)^2/(8*Thermal Conductivity))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature
  • maximum_temperature = Fluid temperature+(((Internal heat generation*Cylinder Radius)/(4*Convection heat transfer coefficient))*(2+(Convection heat transfer coefficient*Cylinder Radius/Thermal Conductivity)))
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