Fourier's Law of Heat Conduction Calculator

✖Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%
✖A Temperature Gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location.ⓘ Temperature Gradient [ΔT]			+10% -10%

✖Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q".ⓘ Fourier's Law of Heat Conduction [q']

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Formula

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Fourier's Law of Heat Conduction

Formula

`"q'" = "k"*"ΔT"`

Example

`"407.2W/m²"="10.18W/(m*K)"*"40K/m"`

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Fourier's Law of Heat Conduction Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Flux = Thermal Conductivity*Temperature Gradient
q' = k*ΔT
This formula uses 3 Variables

Variables Used

Heat Flux - (Measured in Watt per Square Meter) - Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q".
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Temperature Gradient - (Measured in Kelvin Per Meter) - A Temperature Gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location.

STEP 1: Convert Input(s) to Base Unit

Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Temperature Gradient: 40 Kelvin Per Meter --> 40 Kelvin Per Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q' = k*ΔT --> 10.18*40

Evaluating ... ...

q' = 407.2

STEP 3: Convert Result to Output's Unit

407.2 Watt per Square Meter --> No Conversion Required

FINAL ANSWER

407.2 Watt per Square Meter <-- Heat Flux

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 6 Conduction Calculators

Thermal Resistance for Radial Heat Conduction in Cylinders

Go Thermal Resistance = ln(Outer Radius/Inner Radius)/(2*pi*Thermal Conductivity*Length of Cylinder)

Conduction Thermal Resistance in Slab

Go Thermal Resistance = Slab Thickness/(Thermal Conductivity*Area of Slab)

Conduction Shape Factor of Wall

Go Conduction Shape Factor of Wall = Wall Area/Wall Thickness

Fourier's Law of Heat Conduction

Go Heat Flux = Thermal Conductivity*Temperature Gradient

Conduction Shape Factor of Corner

Go Conduction Shape Factor of Corner = 0.15*Wall Thickness

Conduction Shape Factor of Edge

Go Conduction Shape Factor of Edge = 0.54*Length of Edge

< 20 Hypersonic Flow Parameters Calculators

Coefficient of Pressure with Similarity Parameters

Go Pressure Coefficient = 2*Flow Deflection angle^2*((Specific Heat Ratio+1)/4+sqrt(((Specific Heat Ratio+1)/4)^2+1/Hypersonic Similarity Parameter^2))

Pressure Ratio having High Mach Number with Similarity Constant

Go Pressure Ratio = (1-((Specific Heat Ratio-1)/2)*Hypersonic Similarity Parameter)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Mach Number with Fluids

Go Mach Number = Fluid Velocity/(sqrt(Specific Heat Ratio*Universal Gas Constant*Final Temperature))

Pressure Ratio for High Mach Number

Go Pressure Ratio = (Mach Number ahead of shock/Mach Number behind shock)^(2*Specific Heat Ratio/(Specific Heat Ratio-1))

Moment Coefficient

Go Moment Coefficient = Moment/(Dynamic Pressure*Area for Flow*Chord Length)

Deflection Angle

Go Deflection Angle = 2/(Specific Heat Ratio-1)*(1/Mach Number ahead of shock-1/Mach Number behind shock)

Normal Force Coefficient

Go Coefficient of Force = Normal Force/(Dynamic Pressure*Area for Flow)

Supersonic Expression for Pressure Coefficient on Surface with Local Deflection Angle

Go Pressure Coefficient = (2*Deflection Angle)/(sqrt(Mach Number^2-1))

Dynamic Pressure given Coefficient of Lift

Go Dynamic Pressure = Lift Force/(Lift Coefficient*Area for Flow)

Coefficient of Drag

Go Drag Coefficient = Drag Force/(Dynamic Pressure*Area for Flow)

Dynamic Pressure

Go Dynamic Pressure = Drag Force/(Drag Coefficient*Area for Flow)

Lift Coefficient

Go Lift Coefficient = Lift Force/(Dynamic Pressure*Area for Flow)

Axial Force Coefficient

Go Coefficient of Force = Force/(Dynamic Pressure*Area for Flow)

Drag Force

Go Drag Force = Drag Coefficient*Dynamic Pressure*Area for Flow

Lift Force

Go Lift Force = Lift Coefficient*Dynamic Pressure*Area for Flow

Mach Ratio at High Mach Number

Go Mach Ratio = 1-Hypersonic Similarity Parameter*((Specific Heat Ratio-1)/2)

Hypersonic Similarity Parameter

Go Hypersonic Similarity Parameter = Mach Number*Flow Deflection angle

Shear-Stress Distribution

Go Shear Stress = Viscosity Coefficient*Velocity Gradient

Fourier's Law of Heat Conduction

Go Heat Flux = Thermal Conductivity*Temperature Gradient

Newtonian Sine Squared Law for Pressure Coefficient

Go Pressure Coefficient = 2*sin(Deflection Angle)^2

Fourier's Law of Heat Conduction Formula

Heat Flux = Thermal Conductivity*Temperature Gradient
q' = k*ΔT

What is Fourier's law of thermal conductivity?

The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows

How to Calculate Fourier's Law of Heat Conduction?

Fourier's Law of Heat Conduction calculator uses Heat Flux = Thermal Conductivity*Temperature Gradient to calculate the Heat Flux, The Fourier's Law of Heat Conduction formula is defined as the product of thermal conductivity of the gas at the wall to the temperature gradient of gas at the wall. Heat Flux is denoted by q' symbol.

How to calculate Fourier's Law of Heat Conduction using this online calculator? To use this online calculator for Fourier's Law of Heat Conduction, enter Thermal Conductivity (k) & Temperature Gradient (ΔT) and hit the calculate button. Here is how the Fourier's Law of Heat Conduction calculation can be explained with given input values -> 407.2 = 10.18*40.

FAQ

What is Fourier's Law of Heat Conduction?

The Fourier's Law of Heat Conduction formula is defined as the product of thermal conductivity of the gas at the wall to the temperature gradient of gas at the wall and is represented as q' = k*ΔT or Heat Flux = Thermal Conductivity*Temperature Gradient. Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance & A Temperature Gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location.

How to calculate Fourier's Law of Heat Conduction?

The Fourier's Law of Heat Conduction formula is defined as the product of thermal conductivity of the gas at the wall to the temperature gradient of gas at the wall is calculated using Heat Flux = Thermal Conductivity*Temperature Gradient. To calculate Fourier's Law of Heat Conduction, you need Thermal Conductivity (k) & Temperature Gradient (ΔT). With our tool, you need to enter the respective value for Thermal Conductivity & Temperature Gradient and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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