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Temperature inside plane wall at given thickness x with symmetrical boundary conditions Solution

STEP 0: Pre-Calculation Summary
Formula Used
temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature
T = -(((qG*(t)^2)/(2*k))*((x/t)-(x/t)^2))+Tw
This formula uses 5 Variables
Variables Used
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)
Thickness - Thickness is the distance from one end to the desired end of the body or object. (Measured in Meter)
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)
STEP 1: Convert Input(s) to Base Unit
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
Thickness: 2 Meter --> 2 Meter No Conversion Required
Surface temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = -(((qG*(t)^2)/(2*k))*((x/t)-(x/t)^2))+Tw --> -(((100*(5)^2)/(2*10))*((2/5)-(2/5)^2))+300
Evaluating ... ...
T = 270
STEP 3: Convert Result to Output's Unit
270 Kelvin --> No Conversion Required
FINAL ANSWER
270 Kelvin <-- Temperature
(Calculation completed in 00.017 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

Temperature inside plane wall at given thickness x with symmetrical boundary conditions Formula

temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature
T = -(((qG*(t)^2)/(2*k))*((x/t)-(x/t)^2))+Tw

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 Temperature inside plane wall at given thickness x with symmetrical boundary conditions?

Temperature inside plane wall at given thickness x with symmetrical boundary conditions calculator uses temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature to calculate the Temperature, The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source. Temperature is denoted by T symbol.

How to calculate Temperature inside plane wall at given thickness x with symmetrical boundary conditions using this online calculator? To use this online calculator for Temperature inside plane wall at given thickness x with symmetrical boundary conditions, enter Internal heat generation (qG), Wall thickness (t), Thermal Conductivity (k), Thickness (x) & Surface temperature (Tw) and hit the calculate button. Here is how the Temperature inside plane wall at given thickness x with symmetrical boundary conditions calculation can be explained with given input values -> 270 = -(((100*(5)^2)/(2*10))*((2/5)-(2/5)^2))+300.

FAQ

What is Temperature inside plane wall at given thickness x with symmetrical boundary conditions?
The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source and is represented as T = -(((qG*(t)^2)/(2*k))*((x/t)-(x/t)^2))+Tw or temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature. 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, Thickness is the distance from one end to the desired end of the body or object & 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. .
How to calculate Temperature inside plane wall at given thickness x with symmetrical boundary conditions?
The Temperature inside plane wall at given thickness x with symmetrical boundary conditions formula gives the value of temperature at desired thickness inside the plane wall provided with an internal heat generation source is calculated using temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature. To calculate Temperature inside plane wall at given thickness x with symmetrical boundary conditions, you need Internal heat generation (qG), Wall thickness (t), Thermal Conductivity (k), Thickness (x) & Surface temperature (Tw). With our tool, you need to enter the respective value for Internal heat generation, Wall thickness, Thermal Conductivity, Thickness & Surface temperature 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 Temperature?
In this formula, Temperature uses Internal heat generation, Wall thickness, Thermal Conductivity, Thickness & Surface temperature. 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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